Modelling and Simulation of a 3MW, Seventeen-Phase Permanent Magnet AC Motor with AI-Based Drive Control for Submarines Under Deep-Sea Conditions

Abstract

The growing need for high-efficiency and reliable propulsion systems in naval applications, particularly within the evolving landscape of submarine warfare, has led to an increased interest in multiphase Permanent Magnet AC motors. This study presents a modelling and simulation approach for a 3MW, seventeen-phase Permanent Magnet AC motor designed for submarine propulsion, integrating an AI-based drive control system. Despite the advantages of multiphase motors, such as higher power density and enhanced fault tolerance, significant challenges remain in achieving precise torque and variable speed, especially for externally mounted motors operating under deep-sea conditions. Existing control strategies often struggle with the inherent nonlinearities, unmodelled dynamics, and extreme environmental variations (e.g., pressure, temperature affecting oil viscosity and motor parameters) characteristic of such demanding deep-sea applications, leading to suboptimal performance and compromised reliability. Addressing this gap, this research investigates advanced control methodologies to enhance the performance of such motors. A MATLAB/Simulink framework was developed to model the motor, whose drive system leverages an AI-optimised dual fuzzy-PID controller refined using the Harmony Search Algorithm. Additionally, a combination of Indirect Field-Oriented Control (IFOC) and Space Vector PWM strategies are implemented to optimise inverter switching sequences for precise output modulation. Simulation results demonstrate significant improvements in torque response and control accuracy, validating the efficacy of the proposed system. The results highlight the role of AI-based propulsion systems in revolutionising submarine manoeuvrability and energy efficiency. In particular, during a test case involving a speed transition from 75 RPM to 900 RPM, the proposed AI-based controller achieves a near-zero overshoot compared to an initial control scheme that exhibits 75.89% overshoot.

1. Introduction

Modern submarine operations demand advanced motor technologies with high power output and fault tolerance, driven by the escalating global need for resilient and efficient propulsion systems. A submarine is a vessel designed for underwater navigation, stealth operations, and strategic military missions. Submarines enable countries to move without being seen, threaten their enemies from a distance, and execute strategic strikes that demonstrate global military presence [1]. Their ability to stay quiet and operate for long stretches depends on special systems, such as multiphase motors (electrical motors with more than three phases), which are widely recognised for their superior power density and the ability to maintain functionality under fault conditions [2]. Researchers have created prototype motors for high-power uses like trains, ships, and air-planes, but they are not yet widely available commercially [3,4,5]. Despite their potential, existing systems face challenges in fault tolerance and efficiency, particularly for submarine applications, highlighting the need for further innovation in this field.

Building on the need for advanced motor technologies, Permanent Magnet AC motors (PMAC) offer superior efficiency, high power and torque density, a wide speed range, and minimal noise generation, making them highly advantageous for submarine propulsion [6]. For battery-dependent applications, PMAC motors are often integrated with a sophisticated Battery Management System (BMS) [7]. Crucially, multiphase PMAC motors further enhance these benefits by providing inherent fault tolerance, which is paramount for maintaining operational continuity during phase failures in critical submarine systems [8]. However, these advantages introduce design complexities, particularly in inverter integration, where the required number of legs scales directly with phase count. While conventional inverters face power rating limitations, the adoption of multilevel inverter topologies with parallel switching devices addresses these constraints [9]. Despite these advancements, PMAC motors still face significant challenges in achieving optimal fault tolerance and control complexity, especially in high-power submarine applications, necessitating further innovation in their design and control mechanisms.

The current imbalance in multiphase PMAC motor windings presents a critical design challenge, inducing torque pulsations and acoustic noise that compromise the reliability of submarine propulsion. Modern control approaches address these issues through three primary strategies: (1) “Rotor Flux-Oriented Control (RFOC)” demonstrates superior efficiency by decoupling torque and flux regulation [10,11]; (2) “Direct Torque Control (DTC)” offers quick and adaptable response but experiences fluctuations in switching frequency [12]; and (3) “Model Predictive Control (MPC)” provides optimal switching states at the cost of computational intensity [13,14]. The increased phase count introduces additional design constraints, including stator slot proliferation proportional to the number of phases and vibration amplification from pole-pair harmonics. While harmonic current injection techniques can suppress these distortions [15], they introduce trade-offs in core losses that necessitate precise electromagnetic modelling, particularly crucial for submarine systems where acoustic stealth and operational reliability are paramount.

Beyond the inherent design of these advanced propulsion systems, their practical integration into submarine platforms presents distinct engineering challenges. This includes the necessity for pressure compensation systems (PCS) for externally fitted motors to ensure effective operation under varying hydrostatic pressures. The deep-sea environment imposes unique and severe operational demands, including immense hydrostatic pressure, corrosive seawater, and critical thermal management requirements. These factors necessitate robust structural designs, specialised materials, and efficient heat dissipation, which directly influence the motor’s electromagnetic design and the architecture of its thermal and pressure compensation systems. Such environmental considerations have notable impact on the performance and dependability of the AI-driven control systems strategy, demanding a highly adaptive and resilient control solution.

To address the existing gaps and handle key design challenges, this study puts forward a new design and simulation of a 3MW, seventeen-phase PMAC motor integrated with an “artificial intelligence (AI)”-based control system tailored for submarine propulsion. The proposed controller architecture employs a dual fuzzy-PID framework optimised using the “Harmony Search Algorithm (HSA)” for precise and adaptive torque regulation. Additionally, the system incorporates indirect “Field-Oriented Control (FOC)” combined with “Space Vector PWM (SVPWM)” for robust performance under dynamic conditions. Implemented and evaluated in MATLAB/Simulink Ver R2023a, the proposed model integrates switching strategies, electrical equations, and phase interactions tailored for a seventeen-phase motor. This work advances theoretical frameworks and practical implementations in the domain of AI-enhanced motor drives, offering an advanced and resilient propulsion solution for submarines and other mission-critical naval platforms.

This paper makes theoretical, empirical, and practical contributions to the domain of multiphase electric propulsion for submarines. It introduces an underexplored motor topology, applies a novel AI optimisation framework, and validates system performance under submarine-specific constraints. The subsequent sections of this paper are organised as detailed below: Section 2 provides a review of the existing literature and related studies; Section 3 describes the proposed Research Methodology; Section 4 presents and analyses the Results; and Section 5 concludes with key findings and future directions.

Main Contributions

This paper makes the following key contributions to the field of advanced electric propulsion systems for submarines:

• Novel Seventeen-Phase PMAC motor Design and Simulation: Presents a detailed design and comprehensive simulation model of a 3MW, seventeen-phase Permanent Magnet AC motor, a topology specifically chosen for its enhanced power density and inherent fault tolerance crucial for high-power submarine applications.
• AI-Based Adaptive Control System Development: Introduces a novel AI-enhanced control system featuring a dual fuzzy-PID controller. This architecture is designed for precise and adaptive speed and torque regulation under varying deep-sea conditions.
• Harmony Search Algorithm (HSA) Optimisation: Implements and validates the application of the Harmony Search Algorithm (HSA) to optimally tune the parameters of the dual fuzzy-PID controller, showcasing its ability to provide robust and efficient control.
• Integrated FOC and SVPWM Implementation: Details the integration of Indirect Field-Oriented Control (FOC) and Space Vector Pulse-Width Modulation (SVPWM) strategies, ensuring high-performance and robust operation of the multiphase motor drive.
• Comprehensive MATLAB/Simulink Model: Develops and evaluates a complete system model in MATLAB/Simulink, encompassing detailed electrical equations, switching strategies, and phase interactions specific to the seventeen-phase motor, providing a robust platform for performance analysis.

2. Literature Review and Related Works

The evolution of electric propulsion systems, from early innovations to advanced multiphase motor designs and AI-based control, has significantly shaped modern submarine propulsion technologies.

2.1. Historical Context and Transition to Modern Propulsion

The theoretical foundation for electric propulsion was laid by Michael Faraday’s discovery of electromagnetic induction in 1831, with practical applications emerging in the late 19th century with early battery-operated systems [16,17]. The development of AC induction motors by Nikola Tesla and the subsequent commercialisation of polyphase systems were critical milestones [18]. Throughout the 20th century, especially during the First and Second World Wars, diesel–electric systems became standard, enabling submarines to operate with enhanced stealth for extended periods [19]. However, these legacy systems, particularly DC motors, presented significant maintenance challenges related to brushes, gears and commutators. This led to a necessary technological shift toward more reliable and efficient solutions, paving the way for the adoption of modern Permanent Magnet AC (PMAC) motors in advanced naval platforms, such as the German Type 212 submarines [20].

2.2. The Advent of Modern Motor Technologies

The introduction of “brushless DC (BLDC)” and “Permanent Magnet Synchronous Motors (PMSM)” marked significant progress in submarine propulsion technology. For the purposes of this manuscript, the terms PMSM and multiphase PMAC motor refer to the same type of machine and are used interchangeably. During the 1960s, the introduction of brushless DC motors marked a significant evolution in submarine propulsion, providing improved efficiency and reliability. The 1970s saw the emergence of Permanent Magnet Synchronous Motors, which revolutionised submarine propulsion through higher power density, enhanced energy efficiency, and superior control mechanisms [21]. These motors quickly became integral in submarines, “remotely operated vehicles (ROVs)”, and “autonomous underwater vehicles (AUVs)” [22].

The advancement of power electronics in the 1980s played a crucial role, facilitating the development of high-power semiconductor devices and more compact, efficient motor controllers. By the end of the 20th century, electric propulsion had become the dominant technology for submarines, offering notable benefits such as increased energy efficiency, reduced acoustic emissions for stealth operations, and lower environmental impact. These advances can be attributed, in part, to the growing emphasis on sustainability, positioning electric propulsion as a viable alternative for scientific, defence, and commercial applications [23,24].

Nuclear propulsion and battery advancements further enhanced submarine capabilities. The mid-20th century marked a significant advancement in submarine propulsion with the introduction of nuclear-powered submarines. The literature indicates that technological progress in submarine propulsion systems facilitated the development of the first nuclear-powered submarines during this period. The “United States Ship (USS)” Nautilus Submarine, Nuclear-Powered (SSN)-571, commissioned in 1954, was among the earliest submarines to utilise electric reserve propulsion motors powered by nuclear reactors [21]. The adoption of nuclear propulsion substantially increased submarine endurance and operational range, providing an extended energy supply compared to conventional diesel–electric systems.

As nuclear technology advanced, electric propulsion systems concurrently evolved, becoming more efficient and reliable. The latter part of the 20th century experienced advancements in battery technology and energy sources, allowing for the development of smaller and more powerful electric propulsion motors [21].

2.3. Focus on Multiphase Motor Systems

Modern research has increasingly focused on multiphase motor designs to enhance performance, efficiency, and reliability in demanding applications. Six-phase multiphase drives offer particular advantages for electric vehicles, distributing the electrical load across multiple phases to reduce individual phase power demands. These motors produce smoother torque with fewer ripples and can boost output through harmonic current injection [25].

These benefits are directly applicable to submarine propulsion. Similar benefits extend to submarine propulsion applications, where five-phase BLDC motors have shown excellent performance as propulsion systems, offering low noise, extended lifespan, and improved reliability [26]. A nine-phase “Permanent Magnet Synchronous Generator (PMSG)” was simulated for wave energy converters with direct power control, demonstrating superior power quality with a reduced “total harmonic distortion (THD)” of 3.5% and a power factor close to unity, maintaining stable power under variable conditions [27].

A key advantage of multiphase systems is their inherent fault tolerance. The fault-tolerant performance of a seven-phase multiphase PMAC motor drive for submarine propulsion was validated using SVPWM-based experimental testing. When one phase failed, the motor retained 80% of its rated power, increasing healthy phase currents by 70%. The system maintained functionality under dual-phase failure, confirming robust propulsion reliability [28]. The ability of multiphase machines to tolerate faults has been confirmed through testing under different fault scenarios, such as short circuits and open circuits [29]. Similarly, the squirrel cage induction motor with nine phases was evaluated under faults, showing operational tolerance, minimised impact, and potential use in fault-critical applications [30].

2.4. Advanced Control Methodologies for Multiphase Motors

The increased complexity of multiphase systems necessitates advanced control strategies. Recent advancements in motor control technologies, including digital signal processing, fault-tolerant systems, and artificial intelligence, have significantly enhanced the performance and reliability of multiphase motors for submarine propulsion. Multiphase PMAC motors feature electrical windings within the stator and permanent magnets in the rotor. These systems enhance the distribution of magneto-motive force in the air gap between stator and rotor, improving synchronisation and torque density compared to conventional three-phase [25].

Foundational digital control techniques have been adapted for multiphase systems. Early 20th-century motor control primarily depended on mechanical and electromagnetic systems, which offered limited precision and adaptability. To overcome these limitations, the introduction of silicon-based semiconductors, thyristors, and microprocessors revolutionised motor control. The integration of “Digital Signal Processors (DSPs)”, “Pulse-Width Modulation (PWM)”, “Field-Oriented Control (FOC)”, and “Insulated-Gate Bipolar Transistors (IGBTs)” significantly enhanced efficiency, response, and precision, paving the way for advanced digital control strategies [31].

Field-Oriented Control (FOC) is a popular method used in motor control systems, renowned for its efficiency and precision. Field-Oriented Control methods utilise orthogonal transformation matrices to map control parameters to d-q-0 coordinates, separating flux and torque control. For multiphase systems like seventeen-phase motors, this approach must manage numerous independent phase variables while suppressing harmonic components [32]. The RFOC variant handles multiple current control loops but becomes complex in high-phase-count systems [33].

More sophisticated control schemes have shown further improvements. A modified Direct Torque Control method was used in the examination of a five-phase Permanent Magnet Synchronous Motor designed for submersible pumps. Simulation results indicate a significant reduction in common-mode voltage, enhancing “electromagnetic compatibility (EMC)”. The DTC uses hysteresis controllers with only electric torque and flux as control variables, which is not efficient for handling several phase control variables. Since it has less attention and is not explored for multiphase machines, which have more than six phases [33]. Additionally, torque ripple remained below 5% under various operating conditions, validating the suitability of five-phase PMAC in submersible pumps with improved performance and reduced EMC-related issues [34].

Model Predictive Control (MPC) offers another powerful alternative. Model Predictive Control (MPC) approaches, such as the multi-vector MPTC for six-phase Permanent Magnet Synchronous Motor, have demonstrated excellent harmonic suppression and torque ripple reduction by employing combined active vectors [14]. Model Predictive Control also improved system performance, enabling six-phase induction motors to reach 6000 rpm [35].

2.5. The Role of AI and Advanced Electronics in Motor Control

Artificial intelligence and advanced modelling are now being used to address control complexity. Artificial intelligence has enabled significant advances in multiphase motor control. “Artificial Neural Networks (ANN)” outperform traditional PI controllers in speed regulation and harmonic reduction [36]. Fuzzy logic controllers with “Sliding Mode Observers (SMO)” have proven effective for fault-tolerant speed control, where the SMO detects faults and triggers controller reconfiguration [37]. Fault diagnosis has been effectively performed using machine learning algorithms such as Support Vector Machines and Random Forests when trained with fault condition data [38].

Enabling these advanced control strategies is a breakthrough in power electronics. Power semiconductor switches with a “wide bandgap (WBG)”, constructed from materials including “silicon carbide (SiC)” and “gallium nitride (GaN)”, offer a significant advantage, switching over ten times faster than traditional silicon-based counterparts, reducing the size of power converters, simplifying cooling needs, and enhancing reliability in harsh environments [39]. Further improvements in efficiency have been achieved through sophisticated designs of Metal-Oxide-Semiconductor Field-Effect Transistors (MOSFET), which optimise conduction and switching losses [40]. Multilevel inverters with FOC and SVPWM techniques have further enhanced control capabilities [41].

2.6. Research Gap and Paper Contribution

Despite these advancements, challenges remain in high-phase-count systems. The modelling and control of multiphase machines become increasingly complex with higher phase counts as a result of the increased quantity of control parameters and possible switching configurations. While existing research has demonstrated effective solutions for systems up to nine phases, the control of higher-phase-count machines (e.g., seventeen-phase) remains underexplored. While existing literature provides extensive details on low-power electric propulsion systems for depths of up to 100 m, research on multiphase electric propulsion motors and associated controllers for high-power deep-sea applications remains limited. These systems, operating at depths exceeding 100 m and power levels exceeding 200 kW, require externally mounted motors capable of withstanding extreme pressures in the deep-sea environment [21]. This research addresses this gap by proposing a novel seventeen-phase multiphase PMAC motor with a dual fuzzy-based controller and Harmony Search Algorithm optimisation for submarine propulsion applications.

3. Research Methodology

The research proposes a new seventeen-phase PMAC motor with a multilevel voltage source inverter consisting of 34 IGBT switches controlled by a Dual Fuzzy Logic-PID control algorithm, which was implemented and simulated using MATLAB/Simulink (R2023a).

The controller is optimised with a Harmony Search Algorithm to reduce the inverter’s switching losses and improve the multiphase PMAC motor’s performance. The dual fuzzy controller implemented an Indirect Field-Oriented Control approach for regulating both the rotational velocity and torque of the motor in both open-loop and closed-loop operations. To control the inverter switches, the method of Space Vector Pulse-Width Modulation is employed, and the desired reference voltages are derived using Inverse Park and Clarke Transformations.

3.1. Design and Modelling of the Seventeen-Phase PMAC Motor

A multiphase PMAC motor features phase windings housed within the stationary component and permanent magnets located on the rotating element. When electrical current flows through these coils in the stationary part, a revolving magnetic field is generated. This field interacts with the magnetic field of the rotor, generating torque and causing the rotor to rotate in sync with the stator’s field. The rotor produces an excitation field by permanent magnets, while the stator windings ensure proper “magnetomotive force (mmf)” distribution and induce back “electromotive force (emf)”. Thus, the synchronous speed

$${\omega }_{mech}={\displaystyle \frac{\omega }{p}}$$

(1)

In this equation:

ω 

represents the rotor’s electrical angular speed;

p 

denotes the count of pole pairs;

ω_mech 

denotes the mechanical angular velocity of the rotor.

Permanent Magnet Synchronous Motors operate with a rotor speed that matches the frequency of the electrical supply when divided by the total count of pole pairs as given in (1). By using an inverter-based controller to vary the supply frequency ($\omega$), the motor’s rotational speed (${\omega }_{mech}$) can be adjusted. This allows precise control of propulsion speed, enabling the motor to adapt to the varying speed requirements of a submarine [8].

In a multiphase PMAC motor, a seventeen-phase system generates a rotating magnetic field when 17 currents, phase-shifted by ${\displaystyle \frac{2\pi }{17}}$ electrical degrees, flow through 17 sinusoidally distributed windings, mechanically phase-shifted by ${\displaystyle \frac{2\pi }{17}}$ degrees. In the proposed seventeen-phase PMAC motor, the winding is constructed with a phase shift angle of $21.{17}^{\circ }$ estimated by ${\displaystyle \frac{2\pi }{17}}$ degrees [8].

Mathematical modelling of multiphase Permanent Magnet Synchronous Motors (PMSMs) in rotating coordinates provides a systematic approach for the dynamic analysis of submarine propulsion systems. The modelling process begins with the derivation of stator voltage equations, torque equations, and motion equations in the natural coordinate system for a seventeen-phase PMAC motor. To ensure model accuracy and tractability, assumptions such as identical winding resistances, symmetrical phase distribution, negligible core losses (hysteresis and eddy), absence of skin effect, temperature-independent conductor properties, and exclusion of both damper windings and magnet eddy currents are adopted. With these simplifications, the model transitions to the rotating reference frame for further analysis. As a result, the seventeen-phase PMAC motor’s mathematical formulation may be structured in the rotating coordinate system, and this approach can be extended more generally to an n-phase PMAC motor as shown below [42].

$$\mathrm{voltage}\mathrm{equations}v=Ri+p\lambda (i,\theta )$$

(2)

$$\mathrm{voltage}\mathrm{equations}\lambda (i,\theta )=L_s+{\lambda }_r\left(\theta \right)$$

(3)

$$\mathrm{torque}\mathrm{equations}{T}_e=P\left({\displaystyle \frac{1}{2}}{i}^T·{\displaystyle \frac{d{L}_s}{d\theta }}·i+i^T·{\displaystyle \frac{d{\lambda }_r\left(\theta \right)}{d\theta }}\right)+T_c\left(\theta \right)$$

(4)

$$\mathrm{motion}\mathrm{equations}J{\displaystyle \frac{d\omega }{dt}}=P(T_e-T_L)$$

(5)

The back emf based on the flux linkage [43] can be expressed as a

$$e_{PM}={\displaystyle \frac{d\lambda }{dt}}={\displaystyle \frac{\partial \lambda }{\partial \theta }}·{\displaystyle \frac{d\theta }{dt}}=f_{PM}\left(\theta \right)·\omega$$

(6)

The terminal voltage based on the back emf is expressed as

$$v=Ri+p\lambda (i,\theta )+e_{PM}$$

(7)

Hence, the torque output by the multiphase PMAC motor results from a weighted sum of the seventeen-phase currents, each influenced by its corresponding back EMF based on rotor position and described by

$${\displaystyle T_e=\sum _{k=1}^{17}{f}_{PM,k}·i_{m,k}=f_{PM}^T·i_m}$$

(8)

In which,

• v = Stator phase voltage vector;
• i = Stator current vector;
• $\theta$ = Rotor position angle;
• R is the diagonal matrix containing phase winding resistance;
• $\lambda (i,\theta )$ = Flux vector of stator windings;
• $L_s$ = Stator winding inductance matrix;
• ${\lambda }_r\left(\theta \right)$ = Stator winding flux vector at no load;
• $T_e$, $T_c\left(\theta \right)$, $T_L$ = Electromagnetic, cogging, and load torques, respectively;
• $p=d/dt$ is the differential operator;
• J = Rotational inertia;
• P = Count of pole pairs;
• $e_{PM}$ = the $n\times 1$ vector representing PM-induced back-EMFs;
• $f_{PM}\left(\theta \right)={\displaystyle \frac{\partial {\lambda }_{PM}}{\partial \theta }}$ = Set of normalised PM-induced back EMFs, also expressed as periodic functions of $\theta$.

3.2. Design of the Seventeen-Phase Inverter

An inverter based on a multilevel voltage source structure is implemented to manage the seventeen-phase PMAC motor, utilising 34 IGBT switches with diodes placed in antiparallel. These switches fired in the proper sequence with an angle of ${\displaystyle \frac{2\pi }{34}}$ to get a seventeen-phase output voltage at the VSI terminals. The upper leg 17 switch sequences are denoted as $S_1,S_3,\dots ,S_{33}$ and the lower leg 17 switch sequences as $S_2,S_4,\dots ,S_{34}$. The terminal voltages of the inverter legs were calculated from the reference neutral point and indicated as ($v_{an},v_{bn},v_{cn},\dots ,v_{qn}$). Figure 1 illustrates the structure of a 17-level voltage source inverter.

The sensorless back-emf approach is used with zero-cross detection to position the rotor to regulate both torque and rotational speed in the seventeen-phase PMAC motor. The airgap flux density in relation to the rotor’s angular position is exactly relevant to the back emf waveform of each phase as the rotor turns [44]. The 34-step inverter’s switching pattern is formulated using the back-emf profiles. In each commutation sequence of ${\displaystyle \frac{2\pi }{34}}=10.{58}^{\circ }$, the back emf waveform is obtained and represents the switching states such as ON and OFF. Based on this switching sequence, 34 switches produce the appropriate input voltage to the seventeen-phase PMAC motor for improved torque operation.

3.3. Implementation of Space Vector Based Pulse-Width Modulation (SVPWM)

For PMAC motor control, SVPWM decouples the stator’s torque and flux-generating components to apply the indirect FOC for the speed control. It generates the Pulse-Width Modulation signal for the inverter switches. The transformation ensures the seventeen-phase inverter is a single unit that uses a 34-step switching sequence in a 0 to 1 binary format for output voltage regulation. The SVPWM computes the voltage vector by estimating the sector identification, switching and operating time and generates the pulses [45].

The inverse park and Clarke transform is used to model the voltage, current, and torque of the motor [46] in the d-q frame as follows,

$$v_d=R_s{i}_d+L_d{\displaystyle \frac{d{i}_d}{dt}}-L_q{i}_q{\omega }_e$$

(9)

$$v_q=R_s{i}_q+L_q{\displaystyle \frac{d{i}_q}{dt}}+L_d{i}_d{\omega }_e+w_e{\lambda }_{af}$$

(10)

By algebraically rearranging and integrating the governing equations, we solve for the d-axis ($i_d$) and q-axis ($i_q$) currents.

$$i_q={\displaystyle \frac{1}{L_q}}\int \left(V_q-L_d{i}_d{\omega }_e-R_s{i}_q-{\lambda }_{af}\right)dt$$

(11)

$$i_d={\displaystyle \frac{1}{L_d}}\int \left(V_d+L_q{i}_q{\omega }_e-R_s{i}_d\right)dt$$

(12)

The electromechanical dynamics governing rotor speed follow the relationship [46]:

$$T_e={\displaystyle \frac{2}{3}}P\left\{{\lambda }_{af}{i}_q+(L_d-L_q)\left(i_d{i}_q\right)\right\}$$

(13)

$${\omega }_e={\displaystyle \frac{P}{2J}}\int \left(T_e-T_L-{\displaystyle \frac{2B{\omega }_e}{P}}\right)dt$$

(14)

Nomenclature (adapted from [46]),

i_d/i_q:

dq-axis stator currents (A);

R_s:

Stator winding resistance ($\Omega$);

L_d, L_q:

dq-axis inductances (H);

J:

Rotational inertia (kg · m²);

B:

Viscous friction constant (N·m·s/rad);

P:

Pole count;

λ_af:

Flux linkage amplitude (V·s/rad);

ω_e:

Electrical angular velocity (rad/s);

T_L, T_e:

Load/electromagnetic torques (N·m)

3.4. Seventeen-Phase PMAC Motor Control System in Closed-Form Model with AI-Based DFPID Controller

The indirect FOC technique for multiphase motors utilises dual fuzzy-PID controllers to control speed and torque. The error signals are obtained by comparing the reference signals and actual signals. Using these signals, the motor’s torque and speed are controlled. Figure 2 illustrates the overall block diagram of the seventeen-phase PMAC motor control system in closed-form model with an AI-based DFPID controller. The Integrated Platform Management System (IPMS) provides the desired Speed_ref. This designated speed from IPMS is compared with the real motor speed, producing an error signal E(s). This error feeds into the DFPID controller with HSA, which is the core AI-based adaptive control unit. Its output then drives the voltage controller, which in turn modulates the Inverter. The Inverter supplies power to the Simulated Motor (17 Phase), whose speed is fed back to close the loop. The relationship between sub-models is given below:

• The dual fuzzy-PID (DFPID) controller (Section 3.5) generates control voltages $V_d$ and $V_q$ based on the error signal $E\left(s\right)={\mathrm{Speed}}_{\mathrm{ref}}-{\omega }_{\mathrm{mech}}$.
• The Space Vector PWM (SVPWM) block (Section 3.3) converts these $V_d$ and $V_q$ into inverter switching signals, producing applied voltages $v_d$ and $v_q$.
• The inverter (Section 3.2) applies $v_d$ and $v_q$ voltages to the motor model (Section 3.1), driving currents $i_d$ and $i_q$.
• The motor outputs torque $T_e$ and ${\omega }_{\mathrm{mech}}$, which are fed back to the controller for closed-loop regulation.
• The closed-form model is a system of differential equations: (1), (9), (10), (11), (12), (13), (14), and (15).

3.5. Development of a Hybrid Control System Combining Dual Fuzzy Logic and PID with Harmony Search Algorithm

Figure 3 displays a control scheme for a seventeen-phase PMAC motor in high-power submarine applications. It uses a dual fuzzy-PID controller, combining fuzzy logic and PID for precise, adaptive speed regulation [47]. It consists of two fuzzy logic controllers represented as FLS-1 and FLS-2. This control system features two Mamdani controllers, each with its own input and output. The FLS1 and FLS2 convert the speed error e and its rate of change $ec$ into fuzzy values by utilising a knowledge base and membership functions. The fuzzy inference processes the rules to correlate with the objective function, and finally, the fuzzy output is converted back to the output signal and fed to control the motor. The defuzzification process for both FLS-1 and FLS-2 uses the Centroid (Centre of Gravity) method, which calculates the centre point of the aggregated membership function of the fuzzy output set to produce a crisp output signal. The fuzzy rule base for both FLS-1 and FLS-2 was meticulously developed based on extensive heuristic tuning and expert knowledge of PMAC motor control dynamics, specifically tailored to achieve optimal transient response and steady-state accuracy for the high-power submarine propulsion system. For example, rules were formulated to provide aggressive corrective action for large speed errors while ensuring smooth, precise adjustments for small errors, thereby minimising overshoot and oscillations. A representative set of fuzzy rules for FLS-1, governing the PID gains, is exemplified as follows: IF (e is Negative Big) AND ($ec$ is Negative Medium) THEN ($K_P$ is Positive Big, $K_I$ is Negative Small, $K_D$ is Zero). The FLS-1 focuses on the gain parameters of the PID controller $K_{P1}$, $K_{I1}$, and $K_{D1}$ by regulating the system error signal e and error changing rates $ec$. The FLS-2 controller was optimised with HSA to derive the exact correction coefficient $\mathit{\Delta }{K}_P$, $\mathit{\Delta }{K}_I$, and $\mathit{\Delta }{K}_D$ of the gains $K_{P2}$, $K_{I2}$, and $K_{D2}$.

The choice of a dual fuzzy-PID controller over other smart control methods like BELBIC PID, Sigmoid PID, Fractional Order PID (FOPID), or neuroendocrine PID was made because of its unique advantages for this specific application [48,49,50,51,52]. While controllers like Sigmoid PID offer nonlinearity, they often lack the explicit rule-based adaptive capability of fuzzy logic to handle complex, real-time uncertainties and varying operating conditions inherent in deep-sea submarine environments [52,53]. BELBIC and neuroendocrine PID controllers, although powerful in learning and adaptation, can demand significant computational resources and extensive training data, which might be challenging for deployment in embedded systems with strict real-time constraints [54]. FOPID controllers provide enhanced tuning flexibility but typically require a precise system model and may not inherently adapt to large parameter variations or unmodelled dynamics as effectively as a fuzzy logic system [55].

Critically, the dual fuzzy-PID’s tuning using Harmony Search Algorithms (HS) offers clear advantages over other optimisers like genetic algorithms (GA): (1) HS achieves faster disturbance rejection and requires fewer tuning iterations than GA-optimised fuzzy PID in marine propulsion systems due to its dynamic parameter-adjustment mechanisms [55]; (2) Unlike GA, which faces issues with premature convergence in high-dimensional spaces, HS incorporates adaptive trust regions and Gauss fine-tuning to balance exploration and exploitation, enhancing stability [56]; (3) HS reduces computational overhead compared to neuroendocrine-PID optimisers, as confirmed in hardware-in-the-loop tests for underwater vehicles [57]. This is especially relevant given the growing use of GA, PSO, and hybrid bio-inspired optimisers in recent research, such as fuzzy-PID tuning for wheelchair systems and air suspension controllers, which show varying success in dynamic adaptation and convergence reliability [58,59]. Recent studies indicate that genetic algorithm-optimised fuzzy PID controllers substantially improve ride comfort in air suspension systems by decreasing vertical acceleration and dynamic load by over 30% compared to passive systems [60]. However, while GA shows promise in these applications, its performance in more complex and dynamically uncertain environments, such as submarine propulsion, remains questionable due to its tendency for premature convergence, as highlighted by the stability improvements provided by HS [55]. These benefits are particularly relevant given the submarine propulsion system’s need for rapid adaptation to hydrodynamic uncertainties.

Furthermore, HS outperforms the particle swarm optimisation (PSO) method referenced in the wheelchair control study [58] in convergence speed and energy efficiency for real-time motor control [61,62]. The wheelchair system control using neuromodelling and fuzzy logic [57] employed PSO, which, while effective for initial tuning, demonstrated reduced responsiveness under time-varying loads, a limitation overcome by HS through its continuous solution diversity and adaptive bandwidth strategies. Specifically, their findings [57] indicated limitations in adapting to real-time load variations, a key challenge addressed by HSA’s mechanisms. Unlike PSO, which requires population reinitialisation in dynamic environments, HS maintains solution diversity through stochastic pitch adjustment and Levy flight mechanisms [61,63]. This enables the robust handling of hydrodynamic disturbances without compromising computational efficiency on embedded platforms [64].

Notably, HS addresses critical limitations in the neuro-fuzzy wheelchair controller study [58], which lacks systematic optimisation of fuzzy membership functions. While that study achieved voice-command classification, it omitted real-time gain tuning for motor control—a gap efficiently filled by HS’s rule-based parameter adaptation. Similarly, compared to GA-tuned fuzzy PID in air suspension systems, HS eliminates the need for “trial-and-error” parameter selection through dynamic bandwidth (BW) and pitch adjustment rate (PAR) adaptation, reducing settling time under transient hydrodynamic loads [56,58].

While GA has demonstrated effectiveness in tuning fuzzy PID controllers for vehicle suspension systems [60,65], its convergence speed and adaptability under nonlinear marine conditions are less favourable than HS, which preserves solution diversity and prevents premature convergence through stochastic pitch adjustments and Levy flight mechanisms [62].

The dual fuzzy-PID approach used here leverages the intuitive, rule-based adaptability of fuzzy logic to directly manage the nonlinear dynamics and uncertainties of the seventeen-phase PMAC motor, while retaining the robust structure of a PID controller. This combination offers superior robustness and adaptive performance, without the high computational overhead or extensive data requirements of purely learning-based methods, making it particularly well-suited for the precise and reliable speed control required by submarine propulsion systems.

The control signal is derived as

$$u\left(t\right)=K_{P}e+K_I\int edt+K_D{\displaystyle \frac{de}{dt}}$$

(15)

The error value $e=y-r$ and the error change value is $ec={\displaystyle \frac{de}{dt}}$, and the output gains obtained by FLS-2 as

$$\begin{array}{cc}\hfill K_P& =K_{P1}+k_p\hfill \\ \hfill K_I& =K_{I1}+k_i\hfill \\ \hfill K_D& =K_{D1}+k_d\hfill \end{array}$$

The fuzzy domain input and output variables, including the membership function, are given in Figure 4, Figure 5, Figure 6, Figure 7, Figure 8.

For FLS-1 input: $e\in \{-10,10\}$ and $ec\in \{-4,4\}$ output: $K_{P1}\in \{0,100\}$, $K_{I1}\in \{0,10\}$, $K_{D1}\in \{0,5\}$

For FLS-2 input: $e\in \{-5,5\}$ and $ec\in \{-2,2\}$ output: $K_{P2}\in \{0,40\}$, $K_{I2}\in \{0,6\}$, $K_{D2}\in \{0,2\}$

3.6. Integration of AI Techniques with Harmony Search Algorithm (HSA) for Optimisation

The HSA algorithm, a significant component of this research, optimises the AI-based dual fuzzy-PID controller FLS-2. HSA imitates how musicians adjust the sounds of different instruments to achieve the perfect harmony [66]. The diagram illustrating the HSA algorithm’s process is shown in Figure 9. The best balance, pitch adjustment rate (PAR), and bandwidth (BW), were identified through an enhanced dynamic tuning method. The three-fold selection process used in creating harmonies enhances the overall search efficiency during optimisation at the global search level [47]. The speed control is modelled as a minimisation problem with Integral Absolute Error as a cost function. The limits of IAE are defined as 0.95 > x < 0.25. FLS-2 produced the optimal control gain signals to switch the inverter in order to control the multiphase motor.

The innovative application and integration of the Harmony Search Algorithm (HSA) to optimise the dual fuzzy-PID controller for this specific seventeen-phase system represent one of the key contributions in this field. While the foundational HSA concept is established [47,66] its implementation to tune a complex, dual fuzzy control architecture for a high-phase-count motor is novel and is detailed further in this section.

The optimisation process is structured as follows: First, a Harmony Memory (HM) is initialised, where each vector in the memory represents a complete set of PID gains ($K_P$, $K_I$, $K_D$) that constitute a candidate solution. During the iterative improvisation step, a new candidate set of gains is generated using one of three mechanisms: (1) selecting a value directly from the HM, (2) making a fine-tuned adjustment to a value from the HM (a process governed by the pitch adjustment rate (PAR) and bandwidth (BW)), or (3) selecting a new random value from the possible range. This triple selection approach ensures a robust global search, preventing premature convergence to local optima.

The dynamic adjustment of PAR and BW, a vital aspect of execution, involves enabling the algorithm to transition from a general to a more specific approach. This process includes an exploratory search of the solution space initially, followed by a fine-tuned, exploitative search of promising regions as the optimisation progresses. This process iteratively refines the controller gains until the Integral Absolute Error (IAE) cost function is minimised, resulting in an optimally tuned controller specifically adapted for the seventeen-phase motor’s unique dynamic behaviour.

The process of applying HSA to tune the dual fuzzy-PID controller involves several key steps.

• Step 1: Initialize the Harmony Memory (HM) with randomly generated candidate solutions, each consisting of the controller’s tunable parameters (e.g., membership function parameters and scaling factors for FLS-2).
• Step 2: Evaluate each candidate solution by simulating the seventeen-phase Permanent Magnet AC motor system using the current parameters.
• Step 3: Calculate the Integral Absolute Error (IAE) from the simulated speed response. This value serves as the fitness function and reflects the controller’s performance (lower IAE ⇒ better performance).
• Step 4: Interpret the IAE value as the ‘harmony quality’ of the current candidate.
• Step 5: Generate new candidate solutions through improvisation via:

  –

  Selection of values directly from HM,

  –

  Pitch-adjusted modification (regulated by pitch adjustment rate and bandwidth),

  –

  Random selection within allowable range.

• Step 6: Assess the fitness of new candidates. If a new solution’s IAE is lower than the worst solution in HM, it replaces that solution.
• Step 7: Repeat the process until:

  –

  A defined maximum number of improvisations is reached, or

  –

  The improvement in minimum IAE falls below a set threshold.

• Step 8: Confirm convergence to an optimal parameter configuration for stable speed regulation of the controller.

3.7. Analysis of Pressure Compensation Systems for Future Deep-Sea High-Power Multiphase Electric Propulsion Motors

Pressure compensation is essential for sustaining the functionality and longevity of high-power multiphase electric propulsion motors in deep-sea environments [67]. Figure 10 depicts a configuration where the multiphase propulsion motor and propeller are mounted externally, with the controller inside the submarine. These motors are generally oil-filled and are cooled by surrounding seawater.

These systems counteract external pressures ranging from 10 to 600 bar, maintaining an internal differential pressure of less than one bar to enable operation beyond 100 m in depth. The available pressure compensation systems are described below.

Rigid, Oil-Filled Pressure Compensation. This method, widely used for externally mounted high-power motors, employs an incompressible dielectric fluid like mineral oil to prevent water ingress and equalise pressure. A compensating element, such as a bladder or piston, ensures stabilisation. Studies confirm that this approach maintains a differential pressure below 1 bar up to depths of 6000 m, with titanium alloys enhancing durability. Dielectric fluid with low thermal expansion minimises internal pressure fluctuations, while flexible elastomeric bladders enhance flexibility and resist fatigue-related failures under cyclic loading, ensuring longevity in operational conditions. The internal structure of the pressure compensation system is detailed in Figure 11 [68]. Figure 12 illustrates the connectivity between the multiphase electrical propulsion motor, pressure compensation system, and propeller.

Pressure-balanced, Fluid-Filled System. A flexible bladder within a rigid casing expands and contracts to equalise pressure while containing dielectric fluid contracts to equalise internal pressure with external seawater pressure. This configuration isolates seawater from internal hydraulic fluid and prevents component implosion due to hydrostatic pressure. The study emphasises the importance of strong diaphragm materials and correct wall thickness to guarantee long-term system stability in deep-sea applications [69,70].

Solid-State Pressure Compensation. Emerging solid-state methods use syntactic foams to withstand deep-sea pressures without fluid-based compensation. Research demonstrated that epoxy-based foams endure pressures equivalent to 7000 m with less than 1% compression, offering a lightweight and low-maintenance alternative [71].

Considerations for Selection and Limitations. Each system presents trade-offs, as oil-filled methods provide reliability but increase weight, flexible bladder systems optimise space but require precise fluid selection, and syntactic foams offer durability but remain in early-stage development. Future advancements must address dynamic loading, temperature fluctuations, and long-term material resilience to ensure sustained deep-sea motor performance [68,70,71].

Correlation with AI-Based Motor Control

The functionality and stability of the motor’s drive are closely linked to the performance of the pressure compensation system. This relationship is primarily defined by two factors: unmodelled mechanical loads and variable thermal conditions. In fluid-filled systems, the viscosity of the dielectric oil changes significantly with temperature and pressure, which alters the viscous drag on the rotor. This introduces a variable, unmodelled load torque, that the motor control system must continuously adapt to and reject.

Furthermore, the PCS and its interaction with the surrounding seawater govern the motor’s heat dissipation profile. Variations in temperature control can influence important motor characteristics, including the resistance of the stator winding and the effectiveness of the permanent magnets, which can degrade the accuracy of the motor model used by the controller. Therefore, the AI-based drive control system must possess a high degree of robustness and adaptability to maintain precise torque and speed control despite these environmentally-induced variations. A potential avenue for future research involves integrating sensor data from the PCS (e.g., oil temperature, differential pressure) as direct inputs to the AI controller. This would enable the control algorithm to proactively adjust its strategy in response to real-time environmental changes, enhancing the overall reliability and efficiency of the propulsion system.

4. Results and Discussion

4.1. Performance Evaluation Through Impulse, Amplitude and Speed Response Analysis

The seventeen-phase PMAC motor and the dual fuzzy-PID controller were modelled and implemented using MATLAB Simulink software, as shown in Figure 13. The PMAC motor was rated with 3MW power and a speed of 900 rpm. The developed controller is used to control the switching cycles of the converter, which leads to the appropriate voltage outputs to ensure the desired torque profile. As shown in

Table 1. Motor performance across different speed ranges.

Reference Speed (RPM)	Power (kW)	Speed (rad/s)	Torque (N·m)
75	5	7.8	637
151	24	15.8	1518
227	69	23.27	2903
303	147	31.73	4633
378	267	39.58	6746
453	440	47.44	9275
530	674	55.5	12,144
605	975	63.36	15,388
681	1358	71.31	19,044
695	1446	72.78	19,868
756	1627	79.17	23,077
862	2649	90.27	29,345
869	2703	91	29,703
878	2784	91.94	30,281
900	3000	94.25	31,830

, the motor torque is evaluated for various speeds.

The reference speed profile, with time variation every 0.3 s, along with the measured speed profile, is shown in Figure 14. Based on the designated speed and the measured motor speed, the controller reduced the errors and generated switching sequences to achieve the desired speed.

Figure 15 and Figure 16 present the voltage characteristics of the developed 17-phase motor. Figure 15 shows the overall profile, while Figure 16 provides a detailed, zoomed-in view of the switched waveforms. The controller provided switching sequences to the converter and the input phase voltages $V_a,V_b,V_c,V_d,V_e,V_f,V_g,V_h,V_i,V_j,V_k,V_l,V_m,V_n,V_o,V_p$ and $V_q$ fed to the motor. The terminal voltage measured was 600 V. Figure 17 illustrates the overall current profile of the seventeen-phase motor across the full simulation time. To highlight the quality of the waveforms, Figure 18 provides a detailed, zoomed-in view between 3.5 and 3.6 s, which clearly shows their sinusoidal nature and balanced phase relationships. As shown in Table 1, the motor’s current consumption rises as its speed changes (calculated from power). At its highest speed, the total current drawn by the motor was approximately 5000 A.

Figure 19 shows the motor’s power consumption, and Figure 20 displays the torque profile of the motor over a 0.3-second period interval. The increase in speed every 0.3 s results in higher motor torque, as illustrated in Figure 21. This demonstrated the improved speed–torque characteristics of the proposed seventeen-phase multiphase PMAC motor and the effectiveness of the dual fuzzy-PID controller.

4.2. Comparative Performance Analysis

To quantitatively assess the effectiveness of the proposed AI-based dual fuzzy-PID controller, its performance is thoroughly compared to that of an initial control scheme (for example, a less optimised fuzzy PID variant) under identical operating conditions. Figure 22 illustrates the measured speed response of the seventeen-phase PMAC motor for a speed transition from 75 RPM to 900 RPM, initiated at t = 0.2 s, directly comparing the initial control scheme with the developed AI-based controller.

As observed in Figure 22 and detailed in

Table 2. Time response specification comparison between initial and improved controllers.

Specification	Initial Controller	Improved Controller
Rise Time (s)	0.000009	0.021976
Peak Time (s)	0.000025	0.200000
Settling Time (s)	0.000263	0.039148
Max Overshoot (%)	75.89	0.00
Steady-State Error	0.0370	0.0374

, the initial controller (blue line) exhibits a significant overshoot of over 75.89% when responding to the step change, reaching a peak speed exceeding 1500 RPM before eventually settling. Conversely, the proposed AI-based controller (red line) demonstrates a remarkably smooth transient response with a negligible overshoot. This highlights the superior adaptive capability of the AI algorithm in precisely managing the motor’s dynamics during rapid speed transitions.

The dynamic performance improvements are further evident in the settling time and overshoot. While the initial controller numerically achieves a very fast settling time of 0.000263 s, this occurs after a massive 75.89% overshoot and an extremely rapid peak time of 0.000025 s. In contrast, the AI-based controller achieves stable operation within approximately 0.039148 s after the speed transition, crucially with zero overshoot and its peak time coinciding with the transition at 0.20 s. This smooth, non-oscillatory response, despite a numerically longer settling time and rise time (0.021976 s for the improved controller compared to 0.000009 s for the initial) represents a significant qualitative improvement in control quality. Furthermore, while both controllers achieve minimal steady-state error (0.0370 for initial and 0.0374 for improved), the proposed AI-based control strategy unequivocally demonstrates superior dynamic and steady-state performance, thereby justifying its innovative contribution to multiphase motor control for submarine applications.

5. Conclusions

The proposed model of a seventeen-phase PMAC motor with an AI-enhanced drive system successfully demonstrates superior speed–torque performance in a simulated environment. Through a dual fuzzy-PID controller optimised with the Harmony Search Algorithm and implemented with SVPWM switching, the simulation achieved optimal control signals and the desired torque profile. The model also accounts for pressure compensation systems, enabling high-power multiphase motors to operate externally in deep-sea environments exceeding 100 m.

The simulation outcomes prove the superiority of the proposed controller in enhancing torque response and control accuracy. However, as the study’s primary limitation lies in its reliance on simulation models, experimental validation is necessary to confirm these findings in real-world applications. Future research should focus on implementing and testing these AI-based optimisation techniques on physical prototypes to refine control precision further and enhance system resilience under dynamic operating conditions. Ultimately, these findings highlight the potential of advanced AI-driven propulsion systems to revolutionise submarine manoeuvrability and energy efficiency.