Motion Synchronization Control for a Large Civil Aircraft’s Hybrid Actuation System Using Fuzzy Logic-Based Control Techniques

Abstract

The motion synchronization of the hybrid actuation system (composed of a servo-hydraulic actuator and an electro-mechanical actuator) is very important for all applications, especially for civil aircraft. The current research presents a nested-loop control design technique to synchronize motion between two different actuators, such as a servo-hydraulic actuator (SHA) and an electro-mechanical actuator (EMA). The proposed strategy consists of a trajectory, an intelligent position controller (fuzzy logic-based controller), a feed-forward controller, and an intelligent force controller (fuzzy logic-based controller). Position, speed, and acceleration signals are produced by trajectory at a frequency that both SHA and EMA can follow. The SHA/EMA system’s position tracking performance is enhanced by the feed-forward controller and intelligent position controller working together, while the intelligent force tracking controller lowers the issue of force fighting by focusing on the rigid coupling effect. To verify the effectiveness of the proposed strategy, simulations are performed in the Matlab/Simulink environment. The result shows that the proposed intelligent control strategy not only reduces initial force fighting, but also improves load-rejection performance and output-trajectory tracking performance.

1. Introduction

One of the main issues in the study on flight vehicle control nowadays is actuator failure [1,2]. A thorough research has recently been conducted to describe every possible issue that could arise with a flight vehicle system [3]. The primary flight control systems have adopted hybrid actuation systems to increase reliability and safety. One such example is the Airbus A320, which uses a hybrid actuation system to power the aileron, rudder, and elevator [4]. The actuators are an important component of the flight control system due to their responsibility for controlling the motion of the aircraft’s control surface [5]. For a long time, hydraulic power was the only source of power for actuators to drive the aircraft’s control surface. Later, safety and reliability became the most important topics in the flight control system. With the advancement of the aircraft industry, a similar redundant actuation configuration was introduced to meet the requirements of safety and reliability. Later, it was found that safety risk is still a problem when common-mode/common-cause errors occur in similar redundant actuation systems. It put limitations on further advancement in the safety and reliability of similar redundant actuation systems [6,7]. Further progress in research on redundant actuation systems gave us the idea to introduce an electro-mechanical actuator into redundant actuation systems along with a hydraulic actuator so that the aircraft industry can overcome the problem of common-mode and common-cause error and enhance the reliability and safety of redundant actuation systems [8,9].

Finally, the progress in research helped us to develop a heterogeneous drive actuation system (hybrid actuation system) composed of electro-hydraulic servo actuators (SHA) and electro-mechanical actuators (EMA), which improves the safety and reliability of the actuation part of aircraft [10]. The research on more electric aircraft (MEA) has enabled the ability to increase reliability by introducing electric motors, electrical distribution systems, generator drives, actuators, and power electronics [11,12]. A combination of SHA and EMA helped to develop an SHA/EMA hybrid actuation system that fulfils the demand for high safety and reliability. Furthermore, it reduces common-mode and common-cause errors, ultimately resulting in an increase in the robustness and efficiency of the aircraft’s actuation system [13].

The past research helped us to develop an SHA/EMA hybrid actuation system (HAS), but there are still some problems associated with the SHA/EMA hybrid actuation system, and these problems must be addressed. The SHA and EMA both have different dynamics. They produce different displacement output under the same pilot command input signal, and their output force is also different under the same input signal. This is happening due to the different working principles of SHA and EMA [14]. There will be an intercoupling effect (between EMA and SHA) when both actuators are connected to the aircraft control surface via rigid coupling. Force fighting occurs when the control surface of an aircraft is pushed together by both actuators. The difference in output force of two dissimilar redundant actuators is referred to as “force fighting”. Force fighting affects the tracking efficiency of the aircraft control surface, and can result in damage to the control surface [7]. So, the aviation industry needs to design a controller that can solve the problem of force fighting and easily synchronize the motion of two actuators. Salman did some efforts to solve this problem of force by using different types of control techniques [15,16,17,18,19]. It was found that synchronization is an important task in motion control to reduce force fighting [20,21]. Later, the aviation industry started to focus on the design of synchronization controllers. An average actuator force difference and real actuator force were imported into the integrator to eliminate force fighting by producing a position demand offset in order to achieve synchronous output force from two unlike actuators [22]. The studies have also demonstrated the design of controllers that encounter the static force fighting for an HAS (hybrid actuation system) composed of an EMA and SHA [14,23]. Moreover, for further improvement in tracking control precision and accuracy, uncertainties, external disturbances, and nonlinear dynamics, along with the coupling effect between EMA and EHSA, must be considered while designing the controller. The motion-state synchronization method is an efficient way to deal with the problem of forces fighting between the two different actuators. Motion-state synchronization can be used to keep such actuators’ motion states, such as displacement, velocity, acceleration, jerk, etc., stable [7]. Rehman has focused the motion synchronization for electro-hydrostatic and servo-hydraulic hybrid actuation systems using different types of control techniques [24,25,26,27,28]. Wang made some efforts to propose sensor-less control for motion synchronization of the hybrid actuation system [29,30,31]. Progress in the research of hybrid actuation systems helped Cochoy et al. to develop a force equalization controller by employing state signals of displacement, velocity, and force [8], according to the ideal hypothesis which states that all contributed signals are important to develop a controller. Getting these state variables allows the created hybrid actuation system to predict the system movement. However, it is tough to acquire the entire state signals of a physical actuation system in an airplane. In order to deal with this matter, an HAS (hybrid actuation system) test bench was developed to achieve all-state signals by introducing several sensors [10]. However, this method would significantly raise the weight and cost of the actuators which would limit their application. In the current research, a nested-loop intelligent control technique is presented that is comprised of trajectory, force controller, and position controller for each actuator.

2. Problem Description

The SHA, EMA, and control surface are the key components of a hybrid actuation system (HAS), and are depicted in Figure 1. An electrically-driven actuator that controls the flow of hydraulic fluid to an actuator is known as a servo-hydraulic actuator (SHA). Powerful hydraulic cylinders are frequently controlled by servo valves using a very small electrical signal. Servo valves have good post-movement damping qualities and can offer fine control of position, velocity, pressure, and force. An electro-mechanical actuator (EMA) is a tool that uses an electric motor to transform electricity into mechanical force. Electric motors turn a spindle in a rotating motion by using an electric current. Through the employment of gears, this rotating motion is transformed into linear motion. $u_{sv}$ and $u_m$ are used as an input control signal for SHA and EMA, respectively. The EMA and SHA are rigidly coupled to the aircraft control surface. SHA has a servo valve as an actuating element, while EMA has an electric motor. When two actuators push the control surface of an aircraft together, they produce force fighting. Force fighting is the difference between the output forces of two actuators. Force fighting can be eliminated when two actuators contribute equally to driving the control surface. The SHA is faster than the EMA; that is the reason for force fighting. EMA is slower because the response time of the motor is large as compared to the servo valve. Force fighting can be removed by synchronizing the motion of two actuators so they contribute equally to drive the control surface of the aircraft. Mathematically it is given by:

$$\mathrm{Force}\mathrm{Fighting}=F_{fight}=F_s-F_m$$

(1)

$$F_{fight}=F_s-F_m=k_s\left(x_s-x_c\right)-k_m\left(x_m-x_c\right)$$

(2)

$$F_{fight}=F_s-F_m=k\left(x_s-x_m\right)\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\therefore k_m=k_s=k$$

(3)

where $F_s$ is force delivered by SHA, $F_m$ is force delivered by EMA, $x_s$ is displacement given by SHA, $x_m$ is displacement given by EMA, and $x_c$ is linear motion of aircraft’s control surface. The analysis of Equation (3) shows that a hybrid actuation system will have no force fighting when both actuators have the same displacement, provided the transmission stiffness is the same for both actuators.

3. Mathematical Model of Hybrid Actuation System (HAS)

The hybrid actuation system is composed of the control surface, electro-mechanical actuator, and servo-hydraulic actuator, which will be modeled one by one.

3.1. Modelling of Aircraft’s Control Surface

According to the law of motion, the dynamics involved in the motion of the control surface of the aircraft are given by:

$$\left(F_s+F_m\right)r_c=j_c{\ddot{\theta }}_c+F_{air}{r}_c$$

(4)

$$F_s=k_s\left(x_s-x_c\right)$$

(5)

$$F_m=k_m\left(x_m-x_c\right)$$

(6)

where $j_c$ is inertial moment and $r_c$ is the radial displacement which appears during angular motion ${\theta }_c$. The $k_s$ is the stiffness coefficient for SHA and $k_m$ is the stiffness coefficient for EMA. It is found that the magnitude of angular displacement is very small. In such scenarios, ${\theta }_c$ and $x_c$ (linear movement of aircraft control surface) can be taken to be linear [32], and given by the relationship:

$$x_c={\theta }_c{r}_c$$

(7)

3.2. Mathematical Model of SHA

The servo-valve actuator consists of the servo valve, hydraulic cylinder, and additional accessories. The servo valve is a very effective element for fluid transmission control and widely used in many applications for controlling the transmission of fluid where the end result is motion control through fluid power [33,34]. According to previous studies, the dynamics of a servo valve and a hydraulic cylinder is given by [14]:

$$x_{sv}=k_{sv}{u}_{sv}$$

(8)

$$Q_{sv}=k_{sq}{x}_{sv}-k_{sc}{p}_f$$

(9)

where $x_{sv}$ is displacement of the spool of the servo valve, $u_{sv}$ is an input signal to the coil of the servo valve and $k_{sq}$ is flow/opening gain, and $k_{sc}$ is flow/pressure gain.

The force dynamics and the flow dynamics of a servo-hydraulic actuator is given by [14,35]:

$$\begin{array}{l}{Q}_{sv}=A_j{\dot{x}}_s+\frac{v_j}{4E_j}{\dot{p}}_f+k_{ac}{p}_f\\ F_j=m_j{\ddot{x}}_s+B_j{\dot{x}}_s+F_s\end{array}$$

(10)

where $A_j$ is piston effective area, $p_f$ is load pressure, $v_j$ is piston effective volume, $k_{ac}$ is the leakage coefficient, $E_j$ is the oil bulk modulus, $F_j=A_j{p}_f$ is the force provided by the jack, $m_j$ is the piston mass, and $B_j$ is damping coefficient.

Define $x_1={\left[x_{11},x_{12},x_{13}\right]}^T={\left[x_s,{\dot{x}}_s,{\ddot{x}}_s\right]}^T$ as the state vector of SHA system and let suppose $u_1=u_{sv}$. The state space form of SHA can be given as:

$${\mathsf{\Omega }}_{SHA}=\left\{\begin{array}{l}{\dot{x}}_{11}=x_{12}\\ {\dot{x}}_{12}=x_{13}\\ {\dot{x}}_{13}=f_1\left(x_1\right)+g_1+{\sigma }_1{u}_1\end{array}\right.$$

(11)

where:

$$f_1\left(x_1\right)=-\frac{4E_j{k}_{hs}\left(k_s+k_{ac}\right)}{m_j{v}_j}{x}_{11}-\frac{4E_j{A}_j^2+4E_j{B}_j\left(k_s+k_{ac}\right)+v_j}{m_j{v}_j}{x}_{12}-\frac{4E_j{m}_j\left(k_s+k_{ac}\right)+B_j{v}_j}{m_j{v}_j}{x}_{13}$$

$$g_1=\frac{4E_j{k}_{hs}\left(k_{sq}+k_{ac}\right)}{m_j{v}_j}{x}_c-\frac{k_{hs}}{m_j}{\dot{x}}_c$$

$${\sigma }_1=\frac{4A_j{E}_j{k}_{sq}{k}_{sv}}{m_j{v}_j}$$

3.3. Mathematical Model of EMA

The electrical dynamics of an electric motor which is present in an electro-mechanical actuator, is given by [10,36]:

$$u_m=k_m{\omega }_m+L_m\frac{d{i}_m}{dt}+R_m{i}_m$$

(12)

$$T_m=k_{bm}{i}_m$$

(13)

$R_m$, $i_m$, and $L_m$ are resistance, current, and inductance of armature, respectively. $k_{bm}$ is back-emf constant, ${\omega }_m$ is the angular velocity, and $T_m$ is electro-magnetic torque. The torque provided by the motor is converted into load torque and inertial dynamics and overcomes the damping dynamics.

$$T_m-T_L=j_m\frac{d{\omega }_m}{dt}+B_m{\omega }_m$$

(14)

where $j_m$ is total inertia, $B_m$ is damping constant, and $T_L$ is load torque. The transition relationship between rotational and translational parts is given by:

$$\left\{\begin{array}{l}{\dot{x}}_m=\frac{1}{{\eta }_m{k}_{gm}}{\omega }_m\\ T_L=\frac{1}{{\eta }_m{k}_{gm}}{F}_m\end{array}\right.$$

(15)

where ${\eta }_m$ is transmission efficiency and $k_{gm}$ is transmission coefficient.

Let suppose state vectors for an electro-mechanical actuator are $x_2={\left[x_{21},x_{22},x_{23}\right]}^T={\left[x_m,{\dot{x}}_m,{\ddot{x}}_m\right]}^T$ and control input is $u_2=u_m$. The state space for EMA is given by:

$${\mathsf{\Omega }}_{EMA}=\left\{\begin{array}{l}{\dot{x}}_{21}=x_{22}\\ {\dot{x}}_{22}=x_{23}\\ {\dot{x}}_{23}=f_2\left(x_2\right)+g_2+{\sigma }_2{u}_2\end{array}\right.$$

(16)

where:

$$f_2\left(x_2\right)=-\frac{R_m{k}_{ms}}{L_m{j}_m{k}_{gm}^2{\eta }_m^2}{x}_{21}-\frac{k_{bm}{k}_m{k}_{gm}^2{\eta }_m^2+L_m{k}_{ms}+R_m{B}_m{k}_{gm}^2{\eta }_m^2}{L_m{j}_m{k}_{gm}^2{\eta }_m^2}{x}_{22}-\frac{B_m{L}_m+j_m{R}_m}{j_m{L}_m}{x}_{23}$$

$$g_2=\frac{R_m{k}_{ms}}{L_m{j}_m{k}_{gm}^2{\eta }_m^2}{x}_c+\frac{k_{ms}}{j_m{k}_{gm}^2{\eta }_m^2}{\dot{x}}_c$$

$${\sigma }_2=\frac{k_{bm}}{L_m{j}_m{k}_{gm}{\eta }_m}$$

4. Nested-Loop Intelligent Control Strategy

It is very difficult to synchronize an SHA/EMA system with just one controller due to inconsistent dynamics between SHA and EMA. So, a nested-loop intelligent control strategy is proposed for SHA/EMA systems. This proposed technique is made up of a trajectory generator, force controller, and position controller as shown in Figure 2. Where X_tr is the reference position, ${\dot{X}}_{\mathrm{tr}}$ is the reference velocity, and ${\ddot{X}}_{\mathrm{tr}}$ is the reference acceleration signal. $u_1$ and $u_2$ are position controller’s output of the SHA and the EMA, respectively. $u_{11}$ and $u_{21}$ are the outputs of the force controller for the SHA and the EMA, respectively.

4.1. Trajectory Generator

The trajectory-based systems perform well in the desired motion tracking application; that is why a trajectory is designed. The desired motion is achieved by a trajectory generator which generates position ($x_{tr}$), velocity $\left({\dot{x}}_{tr}\right),$ and acceleration $\left({\ddot{x}}_{tr}\right)$ signals. The desired trajectory designed by [24,37,38] is used. It is the second order-transfer function which is given by:

$$x_{tr}=\frac{{\omega }_{tr}^2}{s^2+2{\xi }_{tr}{\omega }_{tr}s+{\omega }_{tr}^2}{x}_r$$

(17)

where

• ${\omega }_{tr}$ = Reference natural frequency
• ${\xi }_{tr}$ = Reference damping factor
• $x_r$ = Reference input signal

The ideal trajectory is depicted in the left portion of Figure 3, while the realistic and practical trajectory is depicted in the right portion. There are two saturation thresholds: one for acceleration and one for velocity. The maximum speed is ±0.12 m/s, while the maximum acceleration is ±2 m/s. According to the dynamics of EHA, two trajectory parameters are set.

4.2. Position Controller

The position controller is made up of two parts: an intelligent position controller and feed-forward control. Both work together to improve the position tracking performance of the SHA/EMA system. The feed-forward control responds to disturbances in a predefined manner. It is designed to predict the behavior of the system. It responds before an error occurs. In this way, it helps to control sluggish dynamics and delay in the SHA/EMA system. The feed-forward control is designed for both SHA and EMA to follow a desired trajectory so that the system can be synchronized. Feed-forward controllers for SHA and EMA are given by:

$$u_{SHA}=\frac{1}{k_{sv}{k}_{sq}}\left[A_j{\dot{x}}_{tr}+\frac{1}{A_j}\left(\frac{v_j}{4E_j}+k_{ce}\right)\left(m_j{\ddot{x}}_{tr}+B_j{\dot{x}}_{tr}+F_s\right)\right]$$

(18)

$$u_{EMA}=k_m{k}_{gm}{\eta }_m{\dot{x}}_{tr}+\frac{\left(L_{m}s+R_m\right)}{k_{bm}}\left[\left(j_{m}s+B_m\right)k_{gm}{\eta }_m{\dot{x}}_{tr}+\frac{1}{k_{gm}{\eta }_m}{F}_m\right]$$

(19)

The use of fuzzy logic to control position is gaining popularity in recent days [39,40,41]. That is why a fuzzy logic-based PID controller is used for the position. The performance is enhanced due to the variable gain of tuning parameters that vary with the help of membership functions. The advantage is overcoming time delays and dealing with models that are not precise and accurate. The intelligent position tracking controller consists of two parts, such as a PID controller and a fuzzy logic controller. The PID controller is given by (20) while a proper range of each tuning parameter is found by using a mechanism which is given in (21).

$$u_n=\left(K_p^{\prime }{G}_1+G_2\right)e(t)+\left(K_i^{\prime }{C}_1+C_2\right){\displaystyle \underset{0}{\overset{t}{\int }}e(t})+\left(K_d^{\prime }{D}_1+D_2\right)\dot{e}(t)\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\therefore n\in \left\{SHA,EMA\right\}$$

(20)

$$K_z=(K_{z\max }-K_{z\min })K_z^{\prime }+K_{z\min }\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\therefore z\in \left\{P,I,D\right\}$$

(21)

where $C_1=K_{imax}-K_{imin}$, $C_2=K_{imin}$, $G_1=K_{pmax}-K_{pmin}$, $G_2=K_{pmin}$, $D_1=K_{dmax}-K_{dmin}$, $D_2=K_{dmin}$, $K_{\mathrm{p}}^{\prime }$, $K_{\mathrm{i}}^{\prime }$, and $K_d^{\prime }$ are the tuning parameters which are tuned by a fuzzy logic controller. Subscript z represents a type of tuning parameter; it may be derivative, integral, or proportional.

The fuzzy logic produces the desired value of tuning parameters according to input of error $e_p$ and change in error (${\dot{e}}_p$). The position error ($e_p$) and change in position (${\dot{e}}_p$) is fed into the fuzzy position controller, and the control inputs to the actuator can be determined from fuzzy rules presented in

Table 1. Fuzzy rules for the fuzzy position controller.

Note: NB: Negative big; NS: Negative small; PB: Positive big; PS: Positive small; ZE: Zero; S: Small; MS: Medium small; M: Medium; MB: Medium big; B: Big.

. Fuzzy input sets are mapped to a set of linguistic labels: negative big (NB), negative small (NS), zero (ZE), positive small (PS), and positive big (PB), over the ranges of the input variables. The output fuzzy sets correspond to the labels: small (S), medium small (MS), big (B), and medium big (MB) over the two output variable ranges. Table 1’s fuzzy rules are separated into four sections. Rising times are dominated by region 1 (the red region). Region 2 (the yellow region) predominates at its greatest overshoot time. The dominant region in the convergence stage is region 3 (light black). Region 4 (the white region) rules at steady state. There are four basic building blocks in the fuzzy logic controller. ① Rule base ② Inference mechanisms ③ Fuzzification ④ Defuzzification. ① Rule base: keeps information in the form of rules and a set of rules for the proposed system is given in Table 1. Each rule shows the states of membership functions. The membership functions are given in

Table 2. The fuzzy position controller’s membership functions.

Parameters in Membership Function	Membership Function
	${\mathit{e}}_{\mathbf{p}}$					${\dot{\mathit{e}}}_{\mathbf{p}}$					${\mathit{K}}_{\mathbf{p}}^{\prime }$$,{\mathit{K}}_{\mathbf{i}}^{\prime }$$,{\mathit{K}}_{\mathit{d}}^{\prime }$
	NB	NS	ZE	PS	PB	NB	NS	ZE	PS	PB	S	MS	M	MB	B
ar	−15	−10	−5	0	5	−75	−50	−25	0	25	0.1	0.15	0.30	0.5	0.7
br	−10	−5	0	5	10	−50	−25	0	25	50	0.15	0.3	0.5	0.7	1
cr	−5	0	5	10	15	−25	0	25	50	75	0.3	0.5	0.7	1	1.15

and graphically presented in Figure 4.

The fuzzy rules are kept the same to get different tuning parameters while member functions change. ② Fuzzy inference mechanisms: interfaces with the rule base and makes a decision to choose a proper value of the tuning parameter. ③ The fuzzification: Convert input into such forms that are interpretable and can be compared to the rules. ④ Defuzzification: it produces tuning parameter values based on the judgments of fuzzy interference processes.

The triangular member function is used and is defined as:

$${\mu }_r=\left\{\begin{array}{ll}0\hfill & x\le a_r\hfill \\ \left(x-a_r\right)/\left(b_r-a_r\right)\hfill & a_r<x<b_r\hfill \\ \left(c_r-x\right)/\left(c_r-b_r\right)\hfill & b_r<x<c_r\hfill \\ 0\hfill & c_r\le x\hfill \end{array}\right.$$

(22)

where $r$ belongs to the following set $\left[\mathrm{NB},\mathrm{NS},\mathrm{ZE},\mathrm{PS},\mathrm{PB},\mathrm{S},\mathrm{MS},\mathrm{M},\mathrm{MB},\mathrm{B}\right]$.

4.3. Force Controller

The position controller tries to achieve motion synchronization between SHA and EMA by improving position tracking performance, while the force controller (FC) tries to achieve motion synchronization for SHA/EMA by improving force tracking performance. Force controller is a fuzzy based PID controller. Its hybrid structure is shown in Figure 5.

The $D_{f1}$ and $D_{f2}$ are input gains that convert input error into such a form which can conveniently interface with a fuzzy logic controller. The $\left[K_{ph}^{\prime },K_{ih}^{\prime },K_{dh}^{\prime }\right]$ and $\left[K_{pm}^{\prime },K_{im}^{\prime },K_{dm}^{\prime }\right]$ are tuning gains by a fuzzy logic controller for SHA and EMA, respectively. The $\left[K_{ph},K_{ih},K_{dh}\right]$ and $\left[K_{pm},K_{im},K_{dm}\right]$ are tuning parameters of PID controllers for SHA and EMA, respectively. $u_{11}$ and $u_{21}$ are the output of force controller, which are determined on the basis of fuzzy rules and membership function. The fuzzy rules are given in

Table 3. Fuzzy rules for the Force controller.

and the membership functions are given in

Table 4. Membership functions for the force controller.

Parameters in Membership Function	Membership Function
	${\mathit{e}}_{\mathbf{f}}$					${\dot{\mathit{e}}}_{\mathbf{f}}$					${\mathit{K}}_{\mathbf{ph}}^{\prime },{\mathit{K}}_{\mathbf{ih}}^{\prime },{\mathit{K}}_{\mathbf{dh}}^{\prime },{\mathit{K}}_{\mathbf{im}}^{\prime },{\mathit{K}}_{\mathbf{dm}}^{\prime }$					${\mathit{K}}_{\mathbf{pm}}^{\prime }$
	NB	NS	ZE	PS	PB	NB	NS	ZE	PS	PB	S	MS	M	MB	B	S	MS	M	MB	B
ar	−100	−10	−5	0	5	−100	−8	−4	0	4	0.1	0.15	0.3	0.5	0.7	0.87	0.90	0.92	0.95	0.97
br	−10	−5	0	5	10	−8	−4	0	4	8	0.15	0.3	0.5	0.7	1	0.90	0.92	0.95	0.97	1
cr	−5	0	5	10	100	−4	0	4	8	100	0.3	0.5	0.7	1	1.15	0.92	0.95	0.97	1	1.15

. The error ($e_f$) and change in error (${\dot{e}}_f$) are fed into the fuzzy force controller, and the control inputs to the actuator can be determined from fuzzy rules presented in the Table 3. Table 3’s fuzzy rules are separated into four sections. Rising times are dominated by region 1 (the red region). Region 2 (the yellow region) predominates at its greatest overshoot time. The dominant region in the convergence stage is region 3 (light black). Region 4 (the white region) rules at steady state.

5. Result and Discussion

To evaluate the performance of the suggested intelligent control method, a mathematical model for the hybrid actuation system of the SHA/EMA is developed in Matlab/Simulink. The simulations are performed by using simulation parameters which are given in

Table 5. Parameters for SHA/EMA actuation systems.

SHA/EMA Parts	Parameters			Values	Units
Servo-hydraulic Actuator (SHA)	Gain Coefficient ${\mathrm{k}}_{\mathrm{sv}}$			$3.04\times {10}^{-4}$	$\mathrm{m}/\mathrm{A}$
	Flow /opening gain ${\mathrm{k}}_{\mathrm{sq}}$			$2.7$	${\mathrm{m}}^2/\mathrm{s}$
	Flow / pressure gain ${\mathrm{k}}_{\mathrm{sc}}$			$1.75\times {10}^{-11}$	$\left({\mathrm{m}}^3/\mathrm{s}\right)\mathrm{Pa}$
	Area of Piston ${\mathrm{A}}_{\mathrm{j}}$			$1.1\times {10}^{-3}$	${\mathrm{m}}^2$
	Cylinder chamber volume ${\mathrm{v}}_{\mathrm{j}}$			$1.1\times {10}^{-4}$	${\mathrm{m}}^3$
	Mass of piston including chamber ${\mathrm{m}}_{\mathrm{j}}$			$25$	$\mathrm{Kg}$
	Damping constant ${\mathrm{B}}_{\mathrm{j}}$			$1\times {10}^4$	$\mathrm{N}·\mathrm{s}/\mathrm{m}$
	Bulk modulus constant ${\mathrm{E}}_{\mathrm{j}}$			$8\times {10}^8$	$\mathrm{Pa}$
	Coefficient of Leakage ${\mathrm{k}}_{\mathrm{ac}}$			$1\times {10}^{-11}$	$\left({\mathrm{m}}^3/\mathrm{s}\right)\mathrm{Pa}$
Electro-mechanical Actuator (EMA)	Bake emf constant ${\mathrm{k}}_{\mathrm{m}}$			$0.161$	$\mathrm{V}/\left(\mathrm{rad}/\mathrm{s}\right)$
	Armature Inductance ${\mathrm{L}}_{\mathrm{m}}$			$4.13\times {10}^{-3}$	$\mathrm{H}$
	Armature resistance ${\mathrm{R}}_{\mathrm{m}}$			$0.54$	$\mathsf{\Omega }$
	Electro-magnetic coefficient ${\mathrm{k}}_{\mathrm{bm}}$			$0.64$	$\mathrm{Nm}/\mathrm{A}$
	Total inertia of rotating parts ${\mathrm{j}}_{\mathrm{m}}$			$1.136\times {10}^{-3}$	$\mathrm{Kg}·{\mathrm{m}}^2$
	Damping coefficient ${\mathrm{B}}_{\mathrm{m}}$			$4\times {10}^{-3}$	$\mathrm{Nm}·\mathrm{s}/\mathrm{rad}$
	Transmission coefficient ${\mathrm{k}}_{\mathrm{gm}}$			$1.256\times {10}^3$	$\mathrm{rad}/\mathrm{m}$
	Transmission efficiency ${\mathsf{\eta }}_{\mathrm{m}}$			$0.9$
Control Surface	Connection stiffness	SHA	${\mathrm{k}}_{\mathrm{s}}$	$1\times {10}^8$	$\mathrm{N}/\mathrm{m}$
		EMA	${\mathrm{k}}_{\mathrm{m}}$
	Radial distance for control surface ${\mathrm{r}}_{\mathrm{cs}}$			$0.1$	$\mathrm{m}$
	Moment of inertia for control surface ${\mathrm{j}}_{\mathrm{cs}}$			$6.0$	$\mathrm{Kg}·{\mathrm{m}}^2$

. In order to compare results between classical PID control (tuned via particle swarm optimization) and the proposed nested-loop intelligent control strategy, the following notation will be used: $C_{PID}$ and $C_{Intelligent}$ for PID and the proposed nested-loop intelligent control strategy, respectively.

5.1. Results with Step Signal as Input Command

The step input command is given to a hybrid actuation system of SHA/EMA with an amplitude of 30 (mrad). It is found that displacement of the control surface of SHA/EMA is controlled by intelligent control strategy and follows the input signal better than the displacement of the control surface of SHA/EMA controlled by the PID controller, as shown in Figure 6. To check the disturbance rejection performance of the proposed intelligent control strategy against PID control for SHA/EMA, a jerk load is applied when time is 2.5 s. It is found that the maximum deviation for intelligent control strategy is 1 (mrad) using reference input signal while for PID control is 3 (mrad) using reference input signal in region 1.

In terms of disturbance rejection, the intelligent control technique performs better than PID control. Following the completion of the jerk load, region 2 illustrates how the intelligent control system swiftly locates an equilibrium position. Additionally, as demonstrated in Figure 7, the tracking error for the suggested intelligent control technique is lower than that of PID control.

The force fighting is basically the force difference between two different actuators such as SHA and EMA. It is due to different dynamic characters of SHA and EMA. In Figure 8, region 1 represents initial force fighting. An initial force fighting for PID control is found to be 16.3 KN, while for an intelligent control strategy, it is 3.7 KN. Similarly, when jerk load acts on control surface, then force fighting for PID control is 9.7 KN while for intelligent control it is 8KN, as shown in region 2 of Figure 8. A similar attitude is shown in region 3 of Figure 8. The result shows that the SHA/EMA hybrid actuation system has less force fighting under proposed intelligent control strategy as compared to PID control strategy.

5.2. Results with Dynamic Signal as Input Command

The dynamic signal is given as an input command to a hybrid actuation system of SHA/EMA. It is found that the displacement of the control surface of SHA/EMA controlled by the intelligent control strategy follows the input command signal better than the displacement of the control surface of SHA/EMA controlled by the PID controller, as shown in Figure 9.

To check the disturbance rejection performance of the proposed intelligent control strategy against PID control for SHA/EMA, a jerk load is applied when the time is 2.5 s. As shown in Figure 9, the SHA/EMA actuation system under intelligent control strategy always follows the reference command signal quickly, even after external force is applied. In order to carry out a better analysis of tracking errors, two regions are taken, such as region 1 and region 2, as shown in Figure 10. Region 1 depicts the tracking error prior to the application of external load force, whereas region 2 depicts the tracking error following the application of external load force. As illustrated in Figure 10, both regions show that the tracking error produced by the SHA/EMA actuation system controlled by intelligent control is always less than the tracking error produced by the SHA/EMA control system controlled by PID.

The force fighting is basically the force difference between two different actuators such as SHA and EMA. It is due to the different dynamic characters of SHA and EMA. In Figure 11, the black dotted line shows the force fighting by the SHA/EMA system which is controlled by intelligent control strategy while the continuous red solid line shows the force fighting of the SHA/EMA system which is controlled by PID. Figure 11 clearly shows that force fighting due to an intelligent control system is less as compared to a PID control system.

6. Conclusions

This paper focuses on intelligent control system design for hybrid actuation systems composed of servo-hydraulic actuators and electro-mechanical actuators. A trajectory, force controller, and position controller are also components of an intelligent control strategy of the nested loop kind. A feed-forward controller and a PID controller with fuzzy logic are also parts of the position controller. The outcomes have demonstrated that the feed-forward controller and position controller work in tandem to synchronize the SHA and EMA and enable the control surface to move along the appropriate trajectory with the least amount of force fighting. The outcome demonstrates that the force controller further enhances SHA and EMA’s synchronization so that both can equally drive the external aircraft control surface. The simulations have been done in Matlab/Simulink under different conditions of external air load and pilot command signal. The results show that the SHA/EMA system under the proposed nested-loop control strategy performs well as compared to the PID control strategy.