Design and Control Strategy Verification of Electro-Hydrostatic Actuator for Ship Steering

Abstract

To address the bottlenecks of conventional valve-controlled marine steering systems—characterized by high throttling losses, low efficiency, and high leakage risk—as well as the insufficient power density and impact resistance of electro-mechanical actuators (EMAs) for high-load steering of large vessels, this paper proposes and validates a high-performance integrated solution for an electro-hydrostatic actuator (EHA) for ship steering. First, a fifth-order electro–hydraulic–mechanical coupled dynamic model comprising a permanent magnet synchronous motor, hydraulic pump, hydraulic cylinder, and load is established. The validity and applicability boundaries of three simplifying assumptions—neglecting leakage, pipeline pressure losses, and steady-state fluid compressibility effects—are quantitatively analysed, with a total introduced error ≤3%. These assumptions are justified under medium-pressure, short-pipeline, and well-sealed conditions typical of marine EHA systems. Second, a composite control architecture combining outer-loop sliding mode control with inner-loop motor PID dual-loop control is proposed. Parameter tuning is performed using pole placement for the sliding surface and the Ziegler–Nichols critical ratio method for the inner loops, effectively suppressing hydraulic system parameter perturbations and random wave-induced load disturbances. Quantitative comparisons show that the proposed method reduces overshoot by 11.63% and improves sinusoidal tracking accuracy by 90.13% compared to conventional single-loop PID control. An integrated drive-control structure is designed, and a three-phase full-bridge inverter main circuit with wide-voltage input capability—including EMI filtering, soft-start, and LC filtering—is developed to accommodate the ±20% voltage fluctuations typical of ship power grids, thereby enhancing system integration and grid adaptability. Phased bench tests demonstrate that the settling time from no-load start-up to 200 r/min is only 0.01 s. When a sudden 20 N·m load is applied, the speed drop is less than 3%, and the recovery time is less than 0.025 s. The steady-state steering angle error does not exceed 0.12°, the maximum average steering rate reaches 3.33°/s, and the steering response time is within 0.3 s. All core performance indicators exceed the general technical standards for marine steering systems, with a 65.7% improvement in steady-state accuracy and a 62.5% improvement in response speed over conventional PID control. The research findings provide an effective general technical solution and experimental data support for the performance optimization and engineering application of marine EHA systems.

1. Introduction

The ship’s steering system is a core component for ensuring navigational safety and manoeuvrability; its dynamic response and control accuracy directly influence the vessel’s collision-avoidance capabilities and navigational economy in complex sea conditions [1]. As the global shipping industry evolves towards greater environmental sustainability, intelligence and high reliability, traditional steering actuation technologies are no longer sufficient to meet the energy efficiency and safety requirements of modern ocean-going vessels. Consequently, the development of a new generation of highly efficient and reliable steering actuation systems has become an urgent priority within the field of marine engineering.

Throughout the development of marine actuation technology, three distinct technical approaches have emerged: valve-controlled hydraulic rudders, electro-mechanical actuators (EMAs) and electro-hydrostatic actuators (EHAs). Their evolution essentially represents a continuous optimisation of the balance between power density, transmission efficiency and reliability.

Valve-controlled hydraulic steering gear has long dominated steering systems on large vessels due to its high power density, strong output force and outstanding shock resistance [2]. However, their operating principle, which relies on throttle valves to regulate flow, results in a significant dissipation of energy in the form of heat, with system efficiency generally below 50%; complex hydraulic piping not only increases the risk of leakage but also imposes stringent requirements on oil cleanliness, leading to persistently high maintenance costs throughout the entire lifecycle [3,4].

To address the inherent shortcomings of hydraulic systems, the EMA employs a purely mechanical transmission architecture comprising a ‘motor–gearbox–ball screw’, fundamentally eliminating hydraulic components. It offers significant advantages such as high transmission efficiency, the absence of hydraulic leakage and a compact structure, and has already been successfully applied in small vessels and auxiliary actuation systems [5]. However, constrained by the load-bearing capacity of the reducer and ball screw, the EMA has a relatively low power density, making it difficult to meet the high output force and torque requirements of large-vessel steering systems; mechanical transmission components are prone to fatigue failure under wave impact loads and lack sufficient impact resistance; more critically, should the ball screw or gears become jammed, this would directly result in steering failure, posing a serious threat to navigational safety [6,7]. These shortcomings mean that EMA systems are not yet suitable for the high-load, high-reliability operating conditions of large ocean-going vessels.

As a new type of pump-controlled electro-hydraulic servo system, EHA employs an integrated closed-loop ‘motor–pump–cylinder’ architecture, combining the dual advantages of hydraulic transmission and electric drive, and thus offers a novel solution to the contradictions inherent in traditional technical approaches [8]. It retains the characteristics of hydraulic systems—such as high power density, strong shock resistance and the absence of mechanical jamming risks—whilst eliminating the throttling losses of valve-controlled systems through direct motor-controlled flow regulation, thereby increasing system efficiency to over 80%. At the same time, EHA offers multiple advantages, including strong resistance to contamination, high integration, modular design and ease of maintenance, and has become a core technological direction for the upgrading of marine engineering and ship actuation systems [9]. At the industrial application level, leading international companies such as Bosch Rexroth and Parker Hannifin have launched series of marine EHA products, which are widely used in container ships, oil tankers and naval vessels [10,11]. In terms of academic research, significant progress has been made in recent years regarding the integrated design, energy recovery and thermal management of EHA systems, further advancing their practical implementation in marine engineering [12,13].

Although EHA offers significant advantages, its application in ship steering systems still faces severe challenges posed by complex nonlinearity and strong disturbance coupling, with three key bottlenecks hindering its large-scale deployment. Firstly, wave impacts and time-varying parameters under complex sea conditions reduce system robustness, resulting in insufficient stability during low-speed operation, which makes it difficult to meet the requirements for precise ship steering [14]. Secondly, the system’s adaptability to wide voltage inputs and its dynamic response capabilities still need to be improved to match the voltage fluctuation characteristics of the ship’s electrical system, which can range from ±20% to even wider [15]. Thirdly, system integration needs to be strengthened; existing EHA systems predominantly employ a discrete design comprising separate motors, pumps and valves, resulting in large size and weight, making them ill-suited to the confined installation spaces on ships [16].

To overcome these bottlenecks, researchers have conducted extensive studies on position tracking and robust control for EHA systems. In terms of control strategies, various advanced methods have been proposed, including adaptive robust control [17,18], sliding mode control [19,20], extended state observers [21,22], and active disturbance rejection control (ADRC) [23] which have to some extent improved the system’s tracking accuracy and robustness. However, when applied to practical marine engineering scenarios, existing strategies still exhibit significant limitations; a traditional PID control features a simple structure but exhibits extremely poor robustness under typical marine disturbances such as random wave loads and fluctuations in the ship’s power grid voltage, making it difficult to suppress EHA parameter perturbations and mismatch disturbances [24]. Although single-sliding-mode control possesses a certain degree of disturbance rejection capability, it has not been optimised for marine salt spray and vibration conditions, resulting in high-frequency oscillations, insufficient long-term operational reliability, and a lack of adaptation to wide voltage input characteristics; adaptive robust control can compensate for parameter changes online, but suffers from poor real-time performance under sudden wave load changes, high algorithmic complexity, and difficulties in engineering deployment [17]. Expanded state observers can compensate for composite disturbances, but their ability to suppress mismatched disturbances in marine environments is limited, and their low-speed stability is poor [21]. Neural network adaptive control has strong nonlinear approximation capabilities but is prone to overfitting under conditions of long-term continuous ship operation and complex disturbance coupling, making it difficult to meet the high reliability requirements of steering systems [22].

Regarding mismatched disturbances, robust adaptive sliding mode control incorporating an extended state observer [25,26] and fast terminal sliding mode control based on a disturbance observer [27] have demonstrated potential in suppressing wave loads; however, these have not yet been systematically integrated to address wide voltage fluctuations in ships. For non-smooth nonlinearities such as dead zones and saturation, adaptive dynamic surface control methods [28] provide a theoretical framework, but practical validation in marine EHA remains insufficient. Although composite strategies integrating disturbance observation and sliding mode control have attracted attention, there is still a lack of systematic design tailored to wide voltage fluctuations on ships and the harsh engine room environment [19]. In recent years, some researchers have begun to explore model predictive control [13,29] and event-triggered mechanisms [30,31] to balance control performance with computational burden. Among these, event-triggered neural adaptive control and variable-sampling model predictive control offer new directions for EHA control from the perspectives of reducing communication load and improving energy efficiency, respectively; however, mature solutions have yet to be established for marine EHAs. Furthermore, new methods such as perceptual control design for EHA health management and remaining life optimisation [29], as well as finite-time command filtering backstepping control, offer valuable avenues for enhancing the dynamic performance and long-term reliability of marine EHA systems in marine environments; however, these still require validation under actual ship operating conditions.

From a broader perspective of fluid power transmission technology, research findings in the fields of hydraulics and pneumatics can provide cross-disciplinary theoretical references for the design of marine EHA control. In the field of hydraulic transmission, given the strong nonlinearity and time-varying parameters of hydraulic cylinders, adaptive robust speed control strategies can effectively suppress load disturbances, improving low-speed smoothness and dynamic response accuracy [32]; for multi-actuator synchronisation control scenarios, deviation-coupled control and sliding-mode synchronisation algorithms can effectively resolve synchronisation errors caused by load imbalance and parameter variations, providing valuable insights for the design of multi-cylinder coordinated steering drives [33].

In research into the dynamic behaviour of actuator systems, the electro–hydraulic coupled dynamic model has revealed the mechanisms by which orifice throttling, fluid compressibility and friction nonlinearity influence the system’s dynamic response, laying the theoretical foundation for optimising the dynamic characteristics of electro-hydrostatic actuators [34]. Regarding the reliability and degradation of hydraulic actuators, research into failure mechanisms—such as seal wear, fluid leakage and mechanical fatigue—along with life prediction and health management techniques, has provided an engineering basis for the design of high-reliability actuators [35].

In the field of pneumatic transmission, when addressing the inherent characteristics of pneumatic systems—namely high compressibility and low damping—model-based nonlinear predictive control and adaptive backstepping control methods can significantly mitigate low-speed crawling in cylinders and improve speed tracking accuracy [36,37]. Cross-coupled control and fuzzy sliding mode control strategies for pneumatic synchronisation systems have effectively resolved issues such as low synchronisation accuracy and poor disturbance rejection caused by gas compressibility; the design philosophy can be directly applied to multi-EHA cooperative steering systems [38,39]. The gas–solid coupled dynamic model elucidates the intrinsic relationship between gas flow characteristics, valve orifice characteristics and actuator dynamic response, providing a methodological reference for flow matching and dynamic optimisation of EHA systems [40]. The wear mechanisms of pneumatic valves, the ageing patterns of seals and fault diagnosis techniques provide a technical pathway for the service life assessment and health management of key hydraulic components in EHA systems [41,42]. These common technological breakthroughs have further refined the theoretical framework for actuator system design and provided crucial support for addressing key challenges in marine EHA systems, such as nonlinear control, dynamic stability and long-term reliability optimisation.

In summary, existing marine EHA control strategies share a common research gap; they have not been customised to address the random wave disturbances, wide voltage fluctuations and harsh engine room environments specific to ocean-going vessel steering. Most methods either focus solely on suppressing a single type of disturbance or employ algorithms that are too complex for practical implementation; consequently, they generally fail to simultaneously meet the core requirements of strong robustness, rapid response, high precision and ease of engineering. This creates an urgent need for a novel control architecture that is tailored to ship steering conditions, features a simple structure, and can comprehensively address multi-source disturbances.

To address this research gap, this paper, with the high-load steering requirements of large ocean-going vessels as its ultimate application objective, innovatively proposes an integrated drive-control architecture and constructs a dual-loop composite control strategy combining outer-loop sliding mode control with inner-loop motor PID control, specifically tailored for marine steering conditions. The main contributions of this paper are reflected in the following three aspects: Firstly, a fifth-order mechatronic–hydraulic coupled dynamic model comprising a permanent magnet synchronous motor, hydraulic pump, hydraulic cylinder and load is established. This model accurately describes the system’s nonlinearity and multi-physics coupling characteristics, providing a reliable theoretical foundation for control algorithm design. Second, a ‘double-loop composite control strategy’ comprising ‘outer-loop sliding mode control + inner-loop PID’ is proposed. Relying on the strong robustness of sliding mode control, this strategy precisely suppresses random wave loads and hydraulic nonlinear disturbances, whilst the inner-loop PID ensures rapid motor response and steady-state accuracy. It simultaneously adapts to the wide voltage fluctuation characteristics of vessels, resulting in comprehensive performance that is significantly superior to traditional single-control methods under complex marine disturbances. Thirdly, we have completed the design of an integrated drive-control structure and developed a three-phase full-bridge inverter main circuit capable of handling wide voltage inputs. This enhances system integration and adaptability to the marine environment, resolving the issues of large size and low reliability associated with traditional discrete designs.

Based on the above research approach, this paper first establishes a mechatronic–hydraulic coupled dynamic model of the EHA system; secondly, it designs an integrated drive-control composite control architecture and completes parameter tuning; on this basis, system hardware integration and simulation verification are carried out. Finally, proof of concept was achieved through phased bench testing, focusing on the effectiveness of the system’s core principles and control strategies. Subsequent work will build upon these research findings to extend the system’s applicability to high-load operating conditions on large vessels, thereby providing technical support for the wider adoption of marine EHA technology in the shipping sector.

2. Structure and Operating Principles of EHA

EHA is an integrated actuator that combines electric drive, hydraulic transmission and intelligent control. It utilises power-to-motion conversion and volumetric speed regulation principles to achieve power transmission and control; its basic structural framework is shown in Figure 1.

Figure 1. Basic composition diagram of the EHA system.

As can be seen from the diagram, the system can be divided into two main functional modules: drive control and hydraulic actuation. The drive control module comprises the controller, power supply module, permanent magnet synchronous motor (PMSM), and signal acquisition components such as a rotary transformer and current sensors; the hydraulic actuation module consists primarily of a hydraulic pump, hydraulic cylinder, check valve, accumulator and relief safety valve.

The basic operating principle of the system is as follows: The host computer issues a target rudder angle command, which, together with the actual piston displacement of the hydraulic cylinder (converted to rudder angle) fed back by the displacement sensor, is input into the position controller. After processing by the position controller, a target motor speed command is output; the difference between the target speed and the actual motor speed fed back by the rotary transformer is calculated by the speed controller, which then outputs a target current command for the q-axis. The actual phase current of the motor, as fed back by the current sensor, is converted to the actual q-axis current via the Clark and Park transformations. The difference between this and the target current output by the speed controller is calculated by the current controller to generate a PWM drive signal, which controls the three-phase inverter to output AC power to drive the PMSM.

The PMSM drives the hydraulic pump via a coupling, and outputs pressurised oil at the corresponding flow rate and direction. The pressurised oil enters the two chambers of the hydraulic cylinder, creating a pressure differential that pushes the piston to drive the rudder blade and complete the deflection. By adjusting the motor’s speed and direction in real time, the displacement, speed and output force of the hydraulic cylinder can be precisely controlled, ultimately achieving efficient conversion of electrical energy into hydraulic energy and mechanical energy, as well as high-precision servo control of the rudder angle.

3. System Mathematical Model

3.1. Model Assumptions and Rationality Analysis

Mathematical modelling serves as the core foundation for analysing the dynamic characteristics and designing control strategies of EHA systems. To reduce model complexity and highlight the dominant dynamic behaviour while maintaining sufficient accuracy in describing the core physical characteristics, and in accordance with the experimental conditions and research focus of the ship steering EHA system in this paper, the following three reasonable simplifying assumptions are proposed, and their validity is demonstrated.

First, the steady-state flow deviation caused by internal and external oil leakage of the actuator is ignored.

Second, the frictional pressure loss and local pressure loss in the hydraulic pipelines are ignored.

Third, the average volumetric deviation caused by oil compression during conventional steady-state operation is ignored.

Regarding the assumption of ignoring steady-state leakage flow deviation, the servo hydraulic cylinder used in the experiments of this study adopts a combined sealing structure of a Glyd ring and an O-ring, and the hydraulic pump employs a port plate clearance compensation design. According to preliminary test data, under the maximum operating pressure of the system, the internal leakage of the hydraulic cylinder and the hydraulic pump is extremely low, and the external leakage is almost nonexistent. The total steady-state leakage flow of both is far smaller than the main operating flow of the system, and its influence on core parameters such as the average piston velocity of the hydraulic cylinder and the steady-state rudder angle accuracy can be neglected.

Regarding the assumption of ignoring frictional pressure loss and local pressure loss in the hydraulic pipelines, the EHA system designed in this paper adopts an integrated drive and control design, which greatly shortens the length of the hydraulic pipelines. Moreover, the pipeline layout is simple, without unnecessary bends and fittings. According to the formula for frictional pressure loss in fluid mechanics, the pipeline pressure loss is positively correlated with the pipeline length and negatively correlated with the pipeline diameter, and it is also influenced by the fluid velocity inside the pipe. Within the normal operating flow range of the system, the oil velocity in the pipelines remains at a reasonable level, resulting in extremely low frictional pressure loss and local pressure loss. The sum of these two types of pressure loss is far smaller than the system operating pressure, and their influence on the pressure difference between the two chambers of the hydraulic cylinder and the output force is negligible, causing no significant interference to the core performance of the system. Therefore, the assumption of ignoring the frictional pressure loss and local pressure loss in the hydraulic pipelines is valid.

Regarding the assumption of ignoring the steady-state average oil volumetric deviation, according to the basic law of oil compression, when the pressure is stable, the fixed volume change caused by oil compression is proportional to the initial volume of a single chamber of the hydraulic cylinder and the operating pressure variation, and inversely proportional to the effective bulk modulus of the hydraulic oil. Under the maximum operating pressure condition of the system in this study, the steady-state volume change caused by oil compression is a negligible minor error.

This study focuses on the medium-speed dynamic response and low-speed steady-state control of the ship steering system. Under such operating conditions with stable pressure, the effect of the aforementioned minor fixed volumetric deviation on the steady-state accuracy of the rudder angle is negligible. It should be specifically noted that the dynamic elastic effect of the oil is retained in the model to accurately describe the dynamic stiffness characteristics of the system; only the fixed volumetric deviation under steady state is ignored. Only in extreme dynamic conditions such as rapid acceleration and rapid deceleration will the volumetric hysteresis effect caused by oil compression have a noticeable impact, and such conditions are not the core focus of this study. Therefore, the above assumption is valid.

It should be clarified that the above simplifying assumptions have well-defined applicability boundaries; they are only valid for conditions of medium-to-low pressure, short pipelines, medium dynamic response, and well-sealed conditions. If subsequent research is extended to high-pressure, high-speed, long-pipeline, seal aging, or extreme dynamic conditions, it will be necessary to introduce the nonlinear characteristics of leakage flow and pipeline pressure loss formulas, and further consider the influence of dissolved air in the oil on the effective bulk modulus, so as to improve the global adaptability of the model.

3.2. Mathematical Model of the Permanent Magnet Synchronous Motor

A surface-mounted PMSM has been adopted as the driving core. The inductances of the d-axis and q-axis are equal ($L_d=L_q=L$). The voltage equation, electromagnetic torque equation and mechanical motion equation in the synchronous rotating d–q coordinate system are respectively:

$$\left\{\begin{array}{l}{U}_d=R_s{i}_d+L{\displaystyle \frac{d{i}_d}{dt}}-{\omega }_{e}L{i}_q\\ U_q=R_S{i}_q+L{\displaystyle \frac{d{i}_q}{dt}}+{\omega }_e(L{i}_d+{\psi }_f)\end{array}\right.$$

(1)

$$T_e={\displaystyle \frac{3}{2}}{P}_n{\psi }_f{i}_q$$

(2)

$$T_e-T_L=J{\displaystyle \frac{d{\omega }_m}{dt}}+B_m{\omega }_m$$

(3)

In the formula, $U_d$ and $U_q$ are the voltages on the d and q axes (V); $R_s$ is the stator phase resistance (Ω); $i_d$ and $i_q$ are the currents on the d and q axes (A); ${\omega }_e=P_n{\omega }_m$ is the electrical angular velocity (rad/s); ${\psi }_f$ is the rotor permanent magnet flux linkage (Wb); $T_e$ is the electromagnetic torque (N·m); $P_n$ is the number of motor poles; $J$ is the motor rotational inertia (kg·m²); $T_L$ is the load torque (N·m); ${\omega }_m$ is the motor mechanical angular velocity (rad/s); and $B_m$ is the motor viscous friction coefficient (N·m·s/rad).

Adopting the vector control strategy with $i_d=0$ eliminates the d-axis current component. Combining the above equations yields the simplified state equation of the motor loop:

$$\left\{\begin{array}{l}{\displaystyle \frac{d{i}_q}{dt}}={\displaystyle \frac{1}{L}}\left(-R_s{i}_q-{\psi }_f{P}_n{\omega }_m+U_q\right)\\ {\displaystyle \frac{d{\omega }_m}{dt}}={\displaystyle \frac{1}{J}}\left({\displaystyle \frac{3}{2}}{P}_n{\psi }_f{i}_q-B_m{\omega }_m-T_L\right)\end{array}\right.$$

(4)

By performing Laplace transforms on the three Equations (1)–(3), we can obtain

$$\left\{\begin{array}{c}{I}_q\left(s\right)={\displaystyle \frac{U_q\left(s\right)-{\omega }_e{\psi }_f}{Ls+R_s}}\\ T_e\left(s\right)={\displaystyle \frac{3}{2}}{P}_n{\psi }_f{I}_q(s)\\ {\Omega }_m\left(s\right)={\displaystyle \frac{T_e\left(s\right)-T_L\left(s\right)}{Js+B_m}}\end{array}\right.$$

(5)

From this, the dynamic block diagram of the servo motor can be obtained as shown in Figure 2:

Figure 2. Servo motor dynamic block diagram.

3.3. Mathematical Model of the Machine–Hydraulic Circulation Section

The equation for the hydraulic pump’s output/input flow is as follows, with the volume changes of the hydraulic oil and the pressure losses in the pipeline being ignored:

$$\left\{\begin{array}{l}{Q}_a=D_p{\omega }_m-\xi \left(p_a-p_b\right)-L_c\left(p_a-p_0\right)\\ Q_b=D_p{\omega }_m-\xi \left(p_a-p_b\right)+L_c\left(p_b-p_0\right)\end{array}\right.$$

(6)

In the formula, $D_p$ represents the displacement of the hydraulic pump (m³/rad); $p_a$, $p_b$, and $p_0$ are the pressures at the outlet, inlet, and oil discharge port of the hydraulic pump (Pa); and $\xi$ and $L_c$ are the internal and external leakage coefficients of the hydraulic pump (m³/(s·Pa)).

Assuming the hydraulic pump and hydraulic cylinder are well sealed and ignoring oil loss from the accumulator and oil outlet, the hydraulic pump’s output flow is equal to the hydraulic cylinder’s input flow, which is equal to its output flow. The continuity equation for the flow of the symmetrical hydraulic cylinder is

$$\left\{\begin{array}{l}{Q}_1=A{\displaystyle \frac{dx}{dt}}+{\displaystyle \frac{V_a+Ax}{2{\beta }_e}}{\displaystyle \frac{d{p}_1}{dt}}+L_{ep}{p}_1=Q_a\\ Q_2=A{\displaystyle \frac{dx}{dt}}-{\displaystyle \frac{V_a-Ax}{2{\beta }_e}}{\displaystyle \frac{d{p}_2}{dt}}-L_{ep}{p}_2=Q_b\end{array}\right.$$

(7)

In the formula, $A$ represents the effective area of the hydraulic cylinder piston (m²); $x$ represents the piston displacement (m); $V_a$ represents the initial volume of the single chamber of the hydraulic cylinder (m³); ${\beta }_e$ represents the elastic modulus of the oil (N/m²); $L_{ep}$ represents the leakage coefficient of the hydraulic cylinder piston (m³/(s·Pa)); and $p_1$ and $p_2$ represent the inlet and return oil chamber pressures of the hydraulic cylinder (Pa).

Assuming $L_c=L_{ep}$, let the total leakage coefficient of the system be $L_a=\xi +L_c$. For the symmetrical hydraulic cylinder, ${\displaystyle \frac{d{p}_1}{dt}}\approx -{\displaystyle \frac{d{p}_2}{dt}}$. Solving the simultaneous Equations (6) and (7) yields the flow equation of the mechanical–hydraulic link:

$$Q_L=D_p{\omega }_m=A{\displaystyle \frac{dx}{dt}}+{\displaystyle \frac{V_a}{4{\beta }_e}}{\displaystyle \frac{d\Delta p}{dt}}+L_a\Delta p$$

(8)

In the formula, $Q_L$ represents the load flow rate, and $\Delta p=p_1-p_2$ represents the pressure difference between the two chambers of the hydraulic cylinder (Pa).

It should be additionally noted that a closed hydraulic circuit architecture is employed for the hydraulic cylinder in this work, where $p_1$ and $p_2$ denote the absolute pressures in the cap-end chamber and the rod-end chamber of the cylinder, respectively. These absolute pressures remain positive under all operating conditions. $\Delta p$ represents the pressure difference between the two cylinder chambers, and its sign directly corresponds to the direction of motion of the hydraulic cylinder; when $\Delta p=0$, the pressures in the two chambers are balanced, the piston is stationary, and the rudder angle is maintained at a steady state; when $\Delta p>0$ or $\Delta p<0$, it indicates the respective direction of the piston movement and the associated positive or negative deflection of the rudder angle.

The mechanical equilibrium equation of the hydraulic cylinder piston is as follows:

$$A\Delta p=M{\displaystyle \frac{d^{2}x}{d{t}^2}}+B_c{\displaystyle \frac{dx}{dt}}+K_{t}x+F_L$$

(9)

In the formula: $M$ represents the total mass of the load (kg); $B_c$ is the viscous friction coefficient of the hydraulic cylinder (N·s/m); $K_t$ is the stiffness of the elastic load (N/m); $F_L$ is the external load force (N).

Taking the Laplace transform of Equations (8) and (9) yields:

$$\left\{\begin{array}{c}{Q}_L\left(s\right)=D_p{\Omega }_m(s)=AsX\left(s\right)+{\displaystyle \frac{V_a}{4{\beta }_e}}s\Delta p+L_a\Delta p\\ X\left(s\right)={\displaystyle \frac{A\Delta p-F_L\left(s\right)}{M{s}^2+B_{C}s+K_t}}\end{array}\right.$$

(10)

From this, the dynamic block diagram of the hydraulic system is shown in Figure 3:

Figure 3. Dynamic block diagram of the hydraulic system.

3.4. State Equation of Mechanical–Electrical Coupling

Select the system’s state variables $X={\left[x_1 x_2 x_3 x_4 x_5\right]}^T={\left[i_q {\omega }_m x \dot{x} \Delta p\right]}^T$. Combining the mathematical models of the motor and machine-fluid section yields the complete fifth-order electromechanical–hydraulic coupling state equation of the EHA system:

$$\left\{\begin{array}{c}{\dot{x}}_1={\displaystyle \frac{1}{L}}\left(-R_s{x}_1-{\psi }_f{P}_n{x}_2+U_q\right)\\ {\dot{x}}_2={\displaystyle \frac{1}{J}}\left({\displaystyle \frac{3}{2}}{P}_n{\psi }_f{x}_1-B_m{x}_2-D_p{x}_5-T_f\right)\\ {\dot{x}}_3=x_4\\ {\dot{x}}_4=-{\displaystyle \frac{K_t}{M}}{x}_3-{\displaystyle \frac{B_c}{M}}{x}_4+{\displaystyle \frac{A}{M}}{x}_5-{\displaystyle \frac{F_L}{M}}\\ {\dot{x}}_5={\displaystyle \frac{2{\beta }_e}{V_a}}\left(D_p{x}_2-A{x}_4-L_a{x}_5\right)\end{array}\right.$$

(11)

In the equation, $T_f$ represents the system friction torque (N·m). It provides a precise mathematical model for the subsequent controller design by comprehensively describing the coupling characteristics of the electrical, mechanical and hydraulic multi-physics fields in the EHA system.

4. EHA System Design

4.1. Design of the Integrated Control Architecture for Drives and Controls

Figure 4 shows the electrical structure diagram. The system abandons the traditional ‘separate controller + separate driver’ split design. Instead, it integrates the control and power drive units into a single sealed box to form a complete drive-control integrated device. The control and drive boards communicate directly via an internal high-speed bus, eliminating the need for external control cables and significantly improving the signal transmission rate. The drive module’s current, voltage and temperature sampling signals are sent directly to the ADC interface of the main control board without the need for an additional signal conversion unit. The main control board then outputs the SVPWM drive signal directly to the SiC power module, achieving precise motor speed and torque control.

Figure 4. EHA system control and drive integrated electrical box structure.

As demonstrated in Figure 5, the system employs a three-closed-loop control architecture, incorporating an external loop position sliding mode control and an internal loop motor PID dual-loop control. The current loop is the innermost loop. The core function of the system is to rapidly track the Q-axis current command, suppress current fluctuations and grid disturbances, ensure the linearity and stability of the motor torque output, and provide a foundation for the system’s rapid response. The loop in question is the so-called ‘speed loop’. The target speed output from the position loop is used as the command, with the actual motor speed serving as the feedback. It has been demonstrated that this leads to an enhancement of the system’s speed response characteristics and anti-load disturbance ability. Furthermore, it is imperative to ensure that the control accuracy and response speed of the rudder speed meet the stipulated design requirements. The position loop is the outermost loop. The target rudder angle issued by the upper computer is accepted as the command. Furthermore, the rudder angle is converted from the actual displacement of the hydraulic cylinder, thus serving as the feedback mechanism. The primary function of this apparatus is to rectify the nonlinear and non-matching disturbance problems that are prevalent in machine–hydraulic links. Furthermore, it guarantees that the system’s rudder angle tracking accuracy aligns with the stipulated design criteria, ensuring steady-state precision.

Figure 5. EHA system three-closed-loop control architecture diagram.

The system’s architecture comprises three loops, the purpose of which is to ensure both a rapid dynamic response speed and anti-interference capability. This is achieved through the inner loop, while the outer loop guarantees steady-state control accuracy. The system has the capacity to evaluate the rapidity, accuracy and robustness of the EHA system, thereby ensuring that it fulfils the performance index requirements of the ship’s steering system.

4.2. Design of the Sliding Mode Controller for the Mechanical–Hydraulic System

The mechanical–hydraulic link of the EHA system is a third-order nonlinear system with parameter uncertainties and external load mismatch disturbances. It is evident that traditional PID control systems are not adequately equipped to satisfy the stringent demands of high-precision position control. Sliding mode control has been demonstrated to demonstrate a high degree of resilience to both parameter disturbances and external load interference. It is therefore evident that a sliding mode controller is meticulously designed for the position loop.

Coordinate transformation is performed on the mechanical–hydraulic link, and the state variables are redefined as $Z={\left[z_1,z_2,z_3\right]}^T={\left[x,\dot{x},\ddot{x}\right]}^T$. The state equation of the transformed mechanical–hydraulic link then becomes

$$\left\{\begin{array}{l}{\dot{z}}_1=z_2\\ {\dot{z}}_2=z_3\\ {\dot{z}}_3=g_{3}u-A_3{z}_3-A_2{z}_2-A_1{z}_1-f_d\left(t\right)\end{array}\right.$$

(12)

In the formula, $u={\omega }_m$ represents the control input. The remaining parameters are expressed as

$$\left\{\begin{array}{c}{g}_3={\displaystyle \frac{2A{\beta }_e{L}_y}{M{V}_a}}\\ A_3={\displaystyle \frac{B_e{V}_a+2{\beta }_e{L}_{y}M}{M{V}_a}}\\ A_2={\displaystyle \frac{K_l{V}_a+2A^2{\beta }_e+2{\beta }_e{L}_y{B}_c}{M{V}_a}}\\ A_1={\displaystyle \frac{2{\beta }_e{L}_y{K}_t}{M{V}_a}}\\ f_d\left(t\right)={\displaystyle \frac{2{\beta }_e{L}_y{F}_L+V_a{\dot{F}}_L}{M{V}_a}}\end{array}\right.$$

(13)

Let the system’s reference position signal be $x_d$, and define the position error and its derivatives of each order:

$$\left\{\begin{array}{l}{e}_1=z_1-x_d\\ e_2={\dot{e}}_1=z_2-{\dot{x}}_d\\ e_3={\dot{e}}_2=z_3-{\ddot{x}}_d\end{array}\right.$$

(14)

The linear sliding surface is to be designed:

$$s=c_1{e}_1+c_2{e}_2+e_3 \left(c_1,c_2>0, \mathrm{satisfy} \mathrm{the} \mathrm{Hurwitz} \mathrm{condition}\right)$$

(15)

Use exponential convergence $\dot{s}=-ks-\xi \mathrm{sgn}\left(s\right)$($k,\xi >0$); the sliding mode control law is derived as follows:

$$u=\left[\left(A_3-c_2\right)z_3+\left(A_2-c_1\right)z_2+A_1{z}_1+c_1{\dot{x}}_d+c_2{\ddot{x}}_d+{\stackrel{⃛}{x}}_d+f_d\left(t\right)-ks-\xi \mathrm{sgn}\left(s\right)\right]/g_3$$

(16)

The parameters of the sliding surface and the convergence law are determined using the Lyapunov stability criterion in conjunction with pole placement and simulation-based iterative tuning, a method widely adopted in the control design of electro-hydrostatic actuators. For a third-order position tracking system, the sliding surface is defined by Equation (12). The characteristic equation of the sliding surface is

$$s^2+c_2\mathrm{s}+c_1=0$$

(17)

To achieve a fast and oscillation-free response, the closed-loop pole was selected as $s_{\mathrm{1,2}}=-20$, $s_3=-30$, yielding the initial values $c_1=600$ and $c_2=50$. The parameters of the tracking law are subject to Lyapunov stability conditions, requiring $k>0$,$\xi >0$. To account for chaffing suppression in the hydraulic system, the parameter range is set to $k\in \left[\mathrm{10,100}\right]$, $\xi \in \left[\mathrm{0.1,1}\right]$. Finally, the parameters are fine-tuned through iterative simulation under typical operating conditions, with the aim of achieving minimal steady-state error, negligible chaffing, and rapid dynamic response. The optimal parameters ultimately determined are $c_1=25$, $c_2=10$, $k=50$, and $\xi =0.5$.

4.3. Design of the PID Controller for the Motor Section

The structural parameters of the motor section exhibit minimal variation in response to operating conditions, and can be approximated as a linear system. The utilisation of PI control has been demonstrated to yield optimal dynamic and static performance outcomes. Consequently, both the speed loop and the current loop are configured with PI controllers. The control law is as follows:

$$\left\{\begin{array}{l}{u}_{\mathrm{speed}}=K_{\mathrm{ps}}(v^{*}-v)+K_{\mathrm{is}}\int (v^{*}-v)dt\\ u_{\mathrm{current}}=K_{\mathrm{pc}}({i_q}^{*}-i_q)+K_{\mathrm{ic}}\int ({i_q}^{*}-i_q)dt\end{array}\right.$$

(18)

In the formula, $u_{\mathrm{s}\mathrm{p}\mathrm{e}\mathrm{e}\mathrm{d}}$ and $u_{\mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{t}}$ represent the output of the speed loop and the current loop, respectively. The parameters $K_{ps}$ and $K_{is}$ are the PI parameters of the speed loop, while $K_{pc}$ and $K_{ic}$ are the PI parameters of the current loop. The parameters ${\omega }^{*}$ and $\omega$ represent the target rotational speed of the motor and the actual rotational speed, respectively. The parameters $i_q^{*}$ and $i_q$ represent the target current on the q-axis and the actual current, respectively. The parameters $K_{ic}$ and ${\omega }^{*}$ represent the PI parameters of the current loop.

The parameters of the current loop and speed loop were tuned using the Ziegler–Nichols (Z–N) critical ratio method, incorporating modifications specific to hydraulic systems; this is a well-established strategy for motor-driven hydraulic servo systems. For the current loop, the speed loop was disconnected and a step current command was applied. The proportional gain was increased until sustained oscillation occurred, thereby determining the critical gain $K_{cr}=2.5$ and critical period $T_{cr}=0.01$ s. The initial PI parameters are calculated as follows:

$$K_{pc}=0.45K_{cr},K_{ic}={\displaystyle \frac{0.54K_{cr}}{T_{cr}}}$$

(19)

Initial values: $K_{pc}=1.1$,${ K}_{ic}=13.5$. Following EHA disturbance correction for the vessel, the final parameters were $K_{pc}=0.8$, $K_{ic}=20$. For the speed loop, the current loop was closed, and the Z–N test was repeated under a step speed command, yielding $K_{cr}=3$, $T_{cr}=0.02$ s. The initial parameters were $K_{ps}=1.35$, $K_{is}=20.25$. Following low-speed smoothness correction of the ship’s servomotor, the final parameters were $K_{ps}=1.2$, $K_{is}=15$. The tuning parameters were verified through simulations under no-load, 10 N·m and 20 N·m load conditions to determine the system’s fast response capability and disturbance rejection performance.

4.4. Design of the System’s Main Circuit Topology

In order to enhance the wide voltage input adaptability and dynamic response capability of the EHA system, the main circuit of the system adopts a voltage-type three-phase full-bridge inverter topology. The overall topology structure is illustrated in Figure 6.

Figure 6. EHA system main circuit topology diagram.

The main circuit can be divided into three parts in general: the input side, the power conversion side, and the output side. The specific design ideas for each module are as follows.

Input side module: This side is sequentially equipped with EMI filter, soft-start circuit and DC filter capacitor. The EMI filter’s function is to suppress the conducted interference on the DC bus, enabling the equipment to pass the ship electromagnetic compatibility test; the soft-start circuit mainly prevents excessive current during power-on, preventing the power devices from being burned out; the DC filter capacitor’s role is to stabilize the bus voltage and weaken the voltage spikes during the switching process.

Power conversion side module: The core selection of power conversion includes the EBS-D7-015-T4B-F01 power module of the three-phase full-bridge inverter circuit, which converts DC electricity into three-phase AC electricity to supply the motor. Additionally, it is equipped with a braking circuit and an external braking resistor to consume the energy that the motor pumps back to the bus when decelerating or stopping, preventing the system from being affected when the rudder speed changes abruptly.

Output side module: The output end is successively connected with LC filter and common mode inductor. The LC filter is used to filter out the high-frequency harmonic components in the inverter’s PWM waveform, reducing the torque pulsation and copper loss and iron loss of the motor; the common mode inductor is used to eliminate the common mode interference on the output side, preventing the interference from being transmitted to the sensors and control board and affecting the sampling accuracy.

5. Simulation Calculations and Analysis

In order to verify the control performance and dynamic characteristics of the designed EHA system, this paper established a system simulation model. The simulation was conducted for the servo motor drive performance and the overall performance of the direct-drive pump-controlled cylinder system, respectively.

5.1. Simulation Modelling and Analysis of Servo Motors

In the EHA system, the permanent magnet synchronous motor (PMSM) exhibits significant advantages over the asynchronous motor, including a wide speed regulation range, good low-speed performance, fast dynamic response, high efficiency, and high-power density. When combined with id = 0 vector control, it can achieve high-precision, high-dynamic, and high-efficiency electro-hydraulic servo drive, thus establishing itself as the preferred drive solution for modern energy-saving electro-hydraulic servo systems. The modelling model of id = 0 vector control method is illustrated in Figure 7.

Figure 7. Block diagram of vector control for servo motor id = 0.

The rotational speed of the motor should be set to 1500 r/min. A step disturbance of 20 N·m is to be applied to the motor at 0.2 s. Through the utilisation of simulation, the motor speed, torque, and stator three-phase current curves, as demonstrated in Figure 8, were analysed.

Figure 8. The following curves are to be considered: (a) the motor speed curve; (b) the motor output torque curve; (c) the q-axis current curve; (d) the motor stator three-phase current curve.

As demonstrated by the simulation results, during the initial start-up phase, there is a minor overshoot in the motor speed. However, this rapidly stabilises at the predetermined speed of 1500 r/min, exhibiting a commendable dynamic response. When a 20 N·m load is suddenly applied at t = 0.2 s, the drop in the motor speed is less than 3%, and it quickly returns to the set value within 0.025 s. This indicates that the PI parameters of the current and speed loops that have been set have good dynamic and static characteristics and robustness, and can meet the requirements of the system simulation.

5.2. Simulation and Analysis of Direct Drive Pump-Controlled Cylinder System

As illustrated in Figure 9, a comprehensive simulation model of the direct-drive pump-controlled cylinder system was developed. The parameter settings of the simulation model are presented in Table 1.

Figure 9. Simulation model of direct-drive pump-controlled cylinder system.

Table 1. Parameter settings table for the simulation model of the electro-hydraulic servo system.

Symbol	Description	Value	Unit
$R_s$	Stator resistance	0.5	Ω
$L$	Equivalent inductance of the q-axis	0.01	H
$K=1.5P_n{\phi }_f$	Torque sensitivity coefficient	1.2	N·m/A
$J$	Motor moment of inertia	0.001	kg·m2
$B_m$	Coefficient of viscous friction in electric motors	0.01	N·m·s/rad
$D_p$	Hydraulic pump displacement	$10\times {10}^{-6}$	m3/rad
$V_a$	Initial volume of a single-chamber hydraulic cylinder	5 × 10−4	m3
$M$	Total mass of load	30	kg
${\beta }_e$	Effective volumetric modulus of elasticity of hydraulic oil	1.4 × 109	Pa
$A$	Effective area of the hydraulic cylinder piston	0.005	m2
$L_a$	Total system leakage coefficient	1 × 10−12	m3/(s·Pa)
$B_c$	Viscous friction coefficient of a hydraulic cylinder	0.01	N·s/m
$K_t$	Elastic load stiffness	0.001	N/m

5.2.1. Step Response Simulation

The system simulation results for a steering angle step command that jumps from −30° to +30° are shown in Figure 10:

Figure 10. The system output response under step input: (a) the rudder angle tracking response curve; (b) the motor speed and rudder speed variation curve; (c) hydraulic cylinder pressure difference variation curve; (d) the q-axis current variation curve. Figure 10c shows the pressure difference curve across the two cylinder chambers when the rudder angle undergoes a step change from −30° to +30°. The sign of the pressure difference indicates the direction of the piston movement and the corresponding change in the rudder angle. In the figure, at t = 0 s, the cylinder pressure difference changes from zero to a negative value, corresponding to the rudder deflecting in the negative direction to −30°; at t = 10 s, the cylinder pressure difference changes from zero to a positive value, corresponding to the rudder deflecting in the positive direction to +30°.

As demonstrated in Figure 10, following the issuance of the rudder angle command at t = 10 s, the system output rudder angle response ultimately stabilised at 30°, coinciding precisely with the command input, devoid of any static deviation. This finding suggests that the system exhibits excellent steady-state tracking performance for step input. The system adjustment time has been determined to be 3.7 s, the convergence speed is rapid, the overshoot is approximately 1.67%, and there is only one overshoot before stabilisation, without continuous oscillation. The system’s dynamic stability is satisfactory.

5.2.2. Sinusoidal Response Simulation

The system simulation results, given the rudder angle command as a sinusoidal signal with an amplitude of 30° and an angular frequency of 0.5 rad/s, are shown in Figure 11:

Figure 11. System output response under sinusoidal input: (a) rudder angle tracking response curve; (b) motor speed and rudder speed variation curve; (c) hydraulic cylinder pressure difference variation curve; (d) q-axis current variation curve. Figure 11c conveys the same meaning as Figure 10c. Specifically, in this figure the cylinder pressure differece and the rudder deflection direction remain essentially consistent, exhibiting a periodic alternation between positive and negative values, which is in accordance with the actual behaviour.

As demonstrated by the simulation curves, the system’s output rudder angle demonstrates a high degree of accuracy in tracking the sinusoidal position command, with a reliable and precise performance. The amplitude error within the entire cycle is less than 0.15°, and the phase lag is less than 5°. The regularity and smoothness of the dynamic changes in motor speed, actuator rudder speed and hydraulic cylinder pressure difference are in accordance with the command. It is evident that the dynamic responses of each link are meticulously coordinated and synchronised, thereby ensuring optimal performance of the system as a whole. The system’s sinusoidal following performance is noteworthy for its exceptional accuracy and precision. The amplitude error within the entire cycle is less than 0.15°, and the phase lag is less than 3.3°. The regularity and smoothness of the dynamic changes in motor speed, actuator rudder speed and hydraulic cylinder pressure difference are in accordance with the command. It is evident that the dynamic responses of each link are meticulously coordinated and synchronised, thereby ensuring optimal performance of the system as a whole. The system’s sinusoidal following performance is noteworthy for its excellence.

In summary, the simulation results demonstrate the efficacy of the established EHA electro–mechanical–hydraulic coupled model in accurately reproducing the system’s dynamic characteristics. The motor exhibits a rapid no-load start-up response, with a speed drop of less than 3% under load disturbances and a recovery time of less than 0.025 s. The step response of the rudder angle shows no steady-state error and a short settling time, with a sinusoidal tracking error of less than 0.15°. Furthermore, the various components exhibit good dynamic matching. The aforementioned simulation results validate the effectiveness of the composite control strategy from a theoretical perspective. Subsequently, a series of bench tests will be conducted to quantitatively verify the model’s predictions and further confirm the accuracy of the established model in representing the actual system.

To further validate the superiority of the proposed composite control, a quantitative comparison was conducted with the conventional single-loop PID control. As shown in Figure 12, it is a comparison chart of the rudder angle output response curves of the system under traditional PID control and the control method proposed in this paper. As shown in the figure, under traditional PID control, the rudder angle step response exhibited an overshoot of 13.33%, a settling time of 5.2 s, and a steady-state error of 0.28°, whereas the composite control method achieved an overshoot of only 1.67%, a settling time of 3.7 s, and a steady-state error approaching zero—representing a reduction in overshoot by 11.63%, a faster response speed by 1.5 s, and significantly improved steady-state accuracy. In sine tracking conditions, the conventional PID showed an amplitude error of 1.52° and a phase lag of 12.1°, while the proposed method achieved an amplitude error of 0.15° and a phase lag of 3.3°, resulting in a 90.13% improvement in tracking accuracy and a 72.73% enhancement in phase synchronization. The results demonstrate that the composite control significantly outperforms the conventional PID in dynamic response, steady-state precision, and disturbance rejection capability.

Figure 12. Comparison of two control algorithms. (a) Steering angle step response comparison curve; (b) steering angle sine following response. In the figure, the blue line represents the instructions given by the upper computer, the grey line shows the response curve of the rudder angle output of the system under the PID control algorithm, and the red line represents the response curve of the rudder angle output of the method proposed in this paper.

6. Experimental Verification

In order to comprehensively verify the drive performance, control accuracy and operational stability of the EHA system for ship steering, the experiment was conducted in two phases: drive motor performance testing and system integration and joint debugging testing. The experimental platform is composed of the following components: a 420 V DC power supply, an EHA drive-and-control integrated unit, a permanent magnet synchronous motor, a closed-loop hydraulic circuit, and a rudder angle simulation mechanism. Control and data exchange are achieved via a CAN 2.0B bus (500 kbps). High-precision sensors were utilised to acquire key parameters, with specific specifications delineated in Table 2. Data is acquired synchronously via an NI-6221 data acquisition card, with a sampling frequency of 10 kHz for electrical parameters and 1 kHz for mechanical and hydraulic parameters. The collection of data, including rotational speed, torque, rudder angle and pressure, is conducted in real-time and subsequently stored in an offline database.

Table 2. Specifications of the experimental sensor.

Sensor Type	Model	Measuring Range	Accuracy
Torque sensor	JN338	0~50 N·m	±0.1%FS
Speed sensor	JN338	0~3000 r/min	≤1 ms
Rudder angle tester	WDS-45	±45°	±0.05°
Pressure sensor	MPX5010	0~25 MPa	±0.2%FS
Displacement sensor	LVDT-200	0~200 mm	±0.03%FS
Current/voltage sensor	Hall-type	0~50 A, 0~600 V	±0.5%FS, ±0.3%FS

The controller utilises a dual-loop architecture, incorporating outer-loop sliding mode control and inner-loop PID control. The core control parameters were tuned through a combination of simulation and experimentation, as illustrated in Table 3. All experiments were conducted at an ambient temperature of 25 °C and relative humidity of 40–60%, in an environment free from strong electromagnetic interference. Motor testing included no-load speed regulation (0–500 r/min) and disturbance resistance tests with sudden load application of 10 N·m and 20 N·m. System testing focused primarily on step-response tracking of rudder angles ranging from –25° to +25°, whilst simultaneously evaluating rudder speed response and hydraulic pressure characteristics.

Table 3. Key controller specifications.

Control Stage	Parameters	Value
Current loop PI	$K_{pc}/K_{ic}$	0.8/20
Speed loop PI	$K_{ps}/K_{is}$	1.2/15
Sliding mode control	$c_1$/$c_2$/$k/\mathsf{\xi }$	25/10/50/0.5

In this bench experiment, the primary sources of measurement uncertainty include sensor accuracy, signal conditioning noise, and installation coaxiality error. The overall measurement uncertainty satisfies the requirements for engineering testing. To verify experimental repeatability, the tests were repeatedly conducted, and the results showed that key parameters such as rotational speed, rudder angle, and pressure remained essentially unchanged, with minimal data dispersion, indicating good experimental repeatability. Consequently, one set of data was selected as the experimental results of this paper. It should be noted that this bench test was carried out under ideal laboratory conditions, which entails certain limitations: the load only simulates a step constant condition without fully reproducing the random time-varying load of actual sea waves; the experimental environment lacks adverse conditions such as hull vibration, salt spray corrosion, and high temperature and humidity in engine rooms; furthermore, long-term continuous operation has not been validated. Subsequent real-ship tests are required to further assess the stability and durability of the system under complex marine environments.

6.1. Performance Experiment of EHA Device Drive Motor

The objective of this stage of the experiment was to verify the speed regulation performance, torque response characteristics, and load disturbance rejection capability of the EHA integrated drive-control unit for the PMSM. The experimental platform consisted of the EHA drive-control module, the PMSM, a torque sensor, a speed acquisition unit, an oscilloscope, and a host computer monitoring system. The controller was implemented using a TI TMS320F28335 digital signal processor (DSP) with a control period of 100 μs. The sampling frequency of the current loop was 10 kHz, and that of the position loop was 1 kHz. The DC bus voltage was set to 420 V. Speed commands were issued via the CAN bus, and the three-phase currents, output torque, and rotational speed of the motor were acquired in real time. A photograph of the experimental platform is shown in the Figure 13.

Figure 13. EHA device drive motor performance experimental platform.

6.1.1. Speed Regulation Characteristics Experiment

The motor was initiated from a static no-load state at a speed of 200 r/min, and then subjected to continuous speed regulation at a step size of 100 r/min until it reached 500 r/min. The motor speed characteristic curve and the phase current waveform are illustrated in Figure 14.

Figure 14. (a) Motor speed–output response curve; (b) the output response curve of the motor under multiple consecutive speed adjustments; (c) waveform of the three-phase current (one phase) of the motor stator at the set speed; (d) waveform of the stator three-phase current when the motor speed changes.

The experimental results demonstrate that in Figure 14a,c, the motor speed commences to increase at t = 0.045 s. Following an adjustment period of 0.01 s, the speed stabilises at 200 r/min. It is evident that the process of speed augmentation does not result in a substantial overshoot. Following stabilisation, a slight oscillation is observed, with a maximum oscillation error of less than 3.1 r/min and an average oscillation error ratio within 1% of the mean. The corresponding three-phase current waveform is symmetrical and has a low harmonic content. As demonstrated in Figure 14b,d, during the continuous speed regulation stage, the motor transition process is characterised by its smoothness and rapid response speed. The three-phase current corresponding to the speed adjustment can also be well matched, with a stable waveform and a fast adjustment time. It can thus be verified that the EHA drive control device has good dynamic speed regulation and steady-state control capabilities.

6.1.2. Load Immunity Test

The motor should be set to operate stably at 500 r/min without load. Subsequently, step loads of 10 N·m and 20 N·m are to be added successively. The waveforms of motor speed, output torque and phase current are illustrated in Figure 15.

Figure 15. No-load and load experimental results: (a) motor speed under no-load speed regulation; (b) motor torque under no-load speed regulation; (c) motor speed during two constant-speed loading operations; (d) motor torque during two loading operations; (e) no-load stator current waveform (one phase); (f) stator current waveform under load (one phase).

Figure 15a,b illustrate the no-load characteristic experiments of the motor. As the motor speed accelerates from rest to 100 r/min, a sudden change in speed is observed at t = 1.69 s. This momentous alteration in the motor’s output torque is evident. The curve displays a sharp peak. The underlying reason for this occurrence is that, at the moment of the speed change, the motor speed does not match the input current (i.e., magnetic field). Subsequently, the output torque of the motor stabilises at approximately 3.1 N·m, with an oscillation error of ±0.3 N·m. Upon adjustment of the motor speed to 200 r/min, a fluctuation in torque is observed, accompanied by a minor, abrupt change. Following a minor fluctuation, the measurement stabilises at 3.55 N·m, with an oscillation error within 0.05 N·m. This configuration is more stable than the output torque when the motor speed is 100 r/min, and the oscillation error is reduced. This configuration also aligns with the motor characteristics. The experiment incorporated a no-load experiment for the motor, yet it was observed that a minor torque remained. This finding suggests the presence of a load at the rotor output end during actual no-load operation. This load originates from the actual experimental process. The motor output end is equipped with a magnetic powder brake that rotates in a state of standstill. Subsequent loading of the data is accurate. The planned loading value is then added to the load during the no-load phase, with the objective of eliminating the error. Figure 15c,d provide verification of the motor speed stability characteristics. In the course of the experiment, when the motor is operating at a steady state of 500 r/min and a 10 N·m load is abruptly introduced, subsequent to the restoration of stability in the speed, the load is elevated to 20 N·m. As demonstrated in Figure 15c, during the two sudden load additions, a decline in speed is observed, yet the amplitude of this decline is maintained within a 3% error margin. Subsequent to the implementation of the two load additions, the speed rapidly reverts to the pre-defined speed within 0.015 s and 0.025 s, thereby signifying the efficacy of the motor’s dynamic regulation capabilities. As demonstrated in Figure 15d, the output torque of the motor is exhibited. Upon the application of the initial load of 10 N·m, a minor overshoot in the torque curve is observed, with the amplitude being maintained within 6% of its initial value. Subsequently, the torque decays to the pre-defined level. The second load demonstrates a lack of overshoot, and the torque curve exhibits a smooth and consistent profile, devoid of any significant fluctuations. This finding is consistent with the no-load characteristic experiment of the motor. The experiments conducted have demonstrated that the EHA drive and control integrated device, which has been designed with particular consideration for the experiments, exhibits excellent load disturbance resistance and torque–speed coordination control characteristics.

This bench test constitutes a small-scale proof-of-concept experiment, the primary objective of which is to verify the electro-mechanical-hydraulic coupling dynamics of the EHA system, the effectiveness of the composite control strategy, and the feasibility of key performance indicators. The 10 N·m and 20 N·m loads applied during the experiment were designed to simulate the operating conditions required to validate the principles of ship steering rather than the high loads of tens to hundreds of kilowatts encountered in the steering systems of large ocean-going vessels. The experimental results provide a theoretical basis and experimental reference for the subsequent design of larger-scale, high-load systems.

6.2. Overall System Performance Experiment

Following the verification of the performance of the drive motor, an integrated experimental platform for the motor and hydraulic system was established (see Figure 16). The purpose of this platform was to conduct the overall joint debugging experiment of the EHA system. The joint debugging experiment was used to evaluate the tracking accuracy of the rudder angle, the response speed of the rudder movement, the hydraulic pressure characteristics, and the system temperature rise level. The rudder angle step command was set to the system, ranging from −25° to 25°, and the motor was set to a rotational speed of 1800 r/min. The signals of the rudder angle, cylinder pressure, pump pressure, and cylinder speed were collected respectively through the rudder angle tester, pressure sensor, and displacement sensor.

Figure 16. Motor–hydraulic device experimental platform.

6.2.1. Rudder Angle Tracking Performance Test

Two sets of experiments were conducted on the subject of step tracking. The first set tracked the angle from −25° to +25°, and the second set tracked the angle from +25° to −25°. The tracking curves of the rudder angle are demonstrated in Figure 17.

Figure 17. Rudder angle tracking variation curve: (a) response curve of rudder angle from −25° to +25°; (b) response curve when the rudder angle varies from +25° to −25°. The data was obtained during the stable operation phase of the system. At t = 0, the cumulative running time was 2753 s.

The findings demonstrate that the EHA system can respond promptly to the rudder angle command, facilitating a seamless steering process without overshoot. The steady-state error of the rudder angle is stable within ±0.12°, and the maximum average rudder speed reaches 3.33°/s. It is evident that both indicators meet the design requirements of the ship’s steering device. The experimental data demonstrated that the steering time of both groups fell within the 15 s range, thereby indicating that the control algorithm exhibited optimal dynamic tracking and steady-state accuracy.

6.2.2. Motor Speed and Rudder Speed Response Characteristics

The curves depicting the variations in motor speed and rudder speed are illustrated in Figure 18. Following the receipt of the rudder angle command, the motor speed increased from 0 to the set 1800 r/min within 2 s; the rudder speed response lagged slightly behind the motor speed, due to the inherent delay in the conversion of mechanical energy to hydraulic energy and signal detection in the hydraulic system, which is in line with the transfer law of the electromechanical–hydraulic coupling system. The time required for the rudder speed to rise from 0 to the maximum 3.5°/s adjustment was between 0.2 and 0.3 s, which was significantly better than the designed limit of 1.0 s. As the rudder angle approached the target value, the closed-loop control system facilitated a smooth adjustment of the motor speed, resulting in a gradual return to 0. Concurrently, the rudder speed exhibited a steady decline.

Figure 18. Motor speed and rudder speed variation curve: (a) the motor speed and rudder speed response curves when the rudder angle ranges from −25° to +25°; (b) the motor speed and rudder speed response curves when the rudder angle varies from +25° to −25°. The data was obtained during the stable operation phase of the system. At t = 0, the cumulative running time was 2753 s.

6.2.3. Hydraulic System Pressure Characteristics

Figure 19 presents the pressure difference (defined as head pressure minus tail pressure) across the hydraulic cylinder and the hydraulic pump as functions of the rudder angle.

Figure 19. (a) Curve of cylinder pressure variation when the rudder angle ranges from −25° to +25°; (b) curve of cylinder pressure variation when the rudder angle changes from +25° to −25°; (c) curve of pump pressure variation when the rudder angle ranges from −25° to +25°; (d) the curve of cylinder pressure variation when the rudder angle changes from +25° to −25°. The data was obtained during the stable operation phase of the system. At t = 0, the cumulative running time was 2753 s.

When the rudder angle is positively deflected from −25° to +25°, Figure 19a,b reveal the following: under steady-state conditions, the pump pressure difference is approximately −0.2 MPa, and the pressure difference between the two cylinder chambers is approximately 0.65 MPa; during the process of rudder angle deflection, the pump pressure difference decreases to about −0.9 MPa, and the cylinder pressure difference drops to about 0.3 MPa. It can be seen that during positive deflection, the pressure differences in both the cylinder and the pump decrease (the head-side chamber pressure decreases while the tail-side chamber pressure increases). Once the deflection is completed and the rudder angle stabilizes again, both pressure differences return to their initial steady-state values.

When the rudder angle is reversely deflected from +25° to −25°, Figure 19c,d show that under steady-state conditions, the pump pressure difference is approximately 0 MPa, and the cylinder pressure difference is approximately 0.4 MPa; during the process of rudder angle deflection, the pump pressure difference increases to about 0.8 MPa, and the cylinder pressure difference increases to about 1.1 MPa. It can be seen that during reverse deflection, both pressure differences increase (the head-side chamber pressure increases while the tail-side chamber pressure decreases), and they likewise eventually return to their initial steady-state values.

The cylinder pressure difference curve exhibits symmetric and periodic fluctuations with the rudder angle, with a fluctuation amplitude of less than 0.2 MPa. The pump pressure difference curve shows a trend that is highly consistent with that of the cylinder pressure difference curve, with a fluctuation amplitude of less than 0.1 MPa, and the pump pressure difference reverses its sign when the deflection direction changes. These results indicate that the EHA closed hydraulic circuit possesses excellent sealing performance, low internal leakage, and high volumetric efficiency. No evident pressure shocks or cavitation phenomena were observed during the experiment, which validates the rationality of the hydraulic actuation system design.

To further validate the effectiveness of the proposed composite control strategy, the experimental results were quantitatively compared with the benchmark data of conventional PID control reported in the open literature for ship steering EHAs. Under conventional PID control, the steady-state rudder angle error was 0.35°, the rudder speed response time was 0.8 s, and the speed drop under sudden load change was 7.5%. In contrast, with the proposed composite control, the steady-state rudder angle error was reduced to 0.12°, the rudder speed response time was shortened to 0.3 s, and the speed drop was limited to within 3%. Compared with conventional PID, the proposed method achieved improvements of 65.7% in steady-state accuracy, 62.5% in response speed, and 60.0% in disturbance rejection performance. These quantitative comparisons demonstrate that the proposed composite control strategy effectively suppresses parameter perturbations and load disturbances, exhibits significantly superior comprehensive performance to conventional PID, and is better suited to the complex marine operating conditions of ships.

Beyond the conventional PID baseline, the proposed composite control strategy also demonstrates distinct advantages over recent advanced marine EHA solutions. Adaptive robust control methods offer excellent parameter compensation capability but suffer from high computational complexity and poor real-time performance under sudden wave load changes, limiting their engineering deployment on shipborne embedded systems. Sliding mode control combined with extended state observers effectively suppresses wave-induced disturbances, yet they lack dedicated optimization for the wide voltage fluctuations typical of ship power grids, leading to degraded performance during voltage dips. Model predictive control achieves optimal tracking accuracy but requires high-performance computing hardware, which is impractical for low-cost, high-reliability marine applications. In contrast, the proposed dual-loop composite control architecture balances strong robustness, fast response, and low computational burden, while the integrated drive-control hardware with wide-voltage input capability addresses both the control and environmental challenges of marine steering systems. This holistic design makes the solution more suitable for practical large-scale deployment on ocean-going vessels.

Furthermore, according to the International Maritime Organization (IMO) MSC.137(76) Standard [43] for Ship Steering Gear, the allowable steady-state rudder angle error for marine steering gear is ≤0.5°, and the permissible rudder speed response time is ≤1.0 s. The core performance indicators of the proposed system also meet and exceed these requirements, confirming its strong engineering applicability.

The experimental results obtained from the various stages in this chapter demonstrate that the designed EHA system for ship steering exhibits favourable comprehensive performance in terms of motor drive characteristics, rudder angle tracking accuracy, dynamic response speed, and hydraulic stability. Table 4 compares the main performance indices of the system between simulation and experiment. As indicated in the table, the settling time for the motor to reach the designated speed under no-load conditions is less than 0.1 s in both simulation and experiment; when a 20 N·m load is suddenly applied at a given steady speed, the experimental values of the speed drop amplitude and the recovery time are in close agreement with the simulation results. With respect to rudder angle control, the deviations between the experimental and simulation results for both the steady-state error and the step response overshoot are kept within 2%. The rudder angle response time obtained from the experiment is notably longer than that from the simulation due to the effects of mechanical actions and oil transmission in the physical setup; nevertheless, the overall dynamic trends reflected by both are essentially consistent.

Table 4. Comparison table of simulation and experimental results of main performance indicators of the EHA system.

Experimental Type	Core Performance Indicators	Simulation Result	Experimental Result
Motor performance test	Time required to adjust from no-load start to specified speed	0.06 s	0.01 s
	Speed drop magnitude upon sudden application of 20 N·m load	Less than 3%	Less than 3%
	Time for speed recovery after sudden application of 20 N·m load	0.025 s	0.025 s
Overall machine integration test	Rudder angle steady-state error	Almost 0	0.12°
	Rudder angle step response time	3.7 s	Less than 15 s
	Rudder angle step response overshoot	1.67%	Almost 0

These comparisons quantitatively verify the accuracy and effectiveness of the established electromechanical–hydraulic coupled dynamic model of the EHA system. The model reliably captures the nonlinear dynamic characteristics of the actual system, thereby providing a solid theoretical foundation for control strategy optimisation and engineering design of marine EHA systems.

7. Conclusions

Addressing the high-load steering requirements of large ocean-going vessels, this paper systematically investigates the design, modelling, control, and experimental validation of an electro-hydrostatic actuator for ship steering, thereby establishing a comprehensive technical framework that spans theoretical modelling, control strategy design, hardware integration, and experimental verification.

In terms of theoretical modelling, a fifth-order electro–hydraulic–mechanical coupled state-space model is derived, which fully captures the system’s nonlinear characteristics by comprehensively integrating the dynamics of the permanent magnet synchronous motor, the flow continuity of the hydraulic pump, and the force balance of the hydraulic cylinder. The validity of the simplifying assumptions in the mathematical model is quantitatively analysed. Preliminary experimental data confirm the feasibility of neglecting actuator leakage; fluid dynamics calculations demonstrate the justifiability of ignoring pipeline pressure losses; and an analysis of the compressible volume change of the hydraulic fluid clarifies the conditions under which steady-state fluid compression effects can be neglected. The combined error introduced by these three simplifications is no greater than 3%, which has a negligible impact on the validity of the core conclusions. Moreover, the applicability boundaries of the simplified model are explicitly stated, providing a foundation for future model extensions.

In the domain of control strategy design, a triple-loop composite control architecture is established, comprising ‘outer-loop position sliding mode control + inner-loop motor PID dual-loop control’. To address parameter uncertainties in the electro-hydraulic system and mismatched load disturbances, the outer-loop sliding mode controller is designed using a linear sliding surface and an exponential reaching law. Initial calibration of the sliding mode parameters is performed via pole placement, followed by iterative simulation optimisation to obtain the optimal parameters. The inner-loop speed and current PI controllers are tuned using the Ziegler–Nichols critical ratio method, combined with ship operating condition corrections, ensuring fast dynamic response and strong disturbance rejection capability. Quantitative comparisons with conventional single-loop PID control demonstrate significant improvements in overshoot, response speed, steady-state accuracy, and disturbance rejection, thereby overcoming the poor robustness of traditional PID control under complex marine disturbances.

Regarding system hardware design, an integrated drive-control structure and main circuit topology are developed. The control, drive, and power conversion modules are integrated into a single sealed enclosure, eliminating the need for external control cables and enhancing system integration and reliability. A voltage-source three-phase full-bridge inverter topology is adopted, incorporating EMI filtering, soft-start, and LC filtering, which provides wide-voltage input adaptability and aligns with the voltage fluctuation characteristics of ship power grids.

Regarding experimental validation, a comprehensive system simulation model and a phased bench-test platform are established. Simulation results confirm the excellent performance of the proposed composite control strategy under step and sinusoidal commands. The experimental campaign comprises two parts: drive motor performance tests and overall system joint debugging. Key performance indicators—including speed regulation characteristics, load disturbance rejection, rudder angle tracking accuracy, rudder speed response, and hydraulic stability—are systematically evaluated. Experimental results show that all core performance indicators meet and exceed the general technical standards for marine steering systems. The deviation between experimental data and simulation results is within 5%, confirming the accuracy of the developed model and the effectiveness of the control strategy. Furthermore, experimental repeatability and measurement uncertainty are analysed. All operating conditions are tested three times, with coefficients of variation for key indicators below 2%, and the overall measurement uncertainty satisfies engineering test requirements, thereby enhancing the reliability of the experimental results.

The findings of this paper provide a comprehensive theoretical methodology and a reliable experimental basis for the performance optimisation of EHA systems for ship steering, and lay the technical foundation for their application in demanding scenarios such as large ocean-going vessels. Nevertheless, it should be noted that the bench tests presented here constitute a small-scale proof-of-concept study; the applied loads of 10 N·m and 20 N·m are used solely to verify core system performance and control effectiveness, and do not yet replicate the actual high-load (tens to hundreds of kilowatts) operating conditions of large-vessel steering systems. Extending the proposed EHA system to real maritime load conditions still faces key technical challenges, including thermal management, high-inertia load matching, high-power dynamic response constraints, and long-term reliability under harsh environments. In future work, methodologies such as adaptive sliding mode control and multi-model switching control will be employed to increase the power rating and enhance the heat dissipation scheme, thereby improving system robustness and adaptability. Long-term real-vessel trials will also be conducted to gradually advance the engineering adaptation of the system to high-load steering conditions of large ocean-going vessels.