Loads Simulator System for Testing and Qualification of Flight Actuators

Abstract

The flight actuation system plays important role in the accurate guidance of the flight vehicles. The actuators driving the control surfaces are aerodynamically loaded during flight. The design, testing and selection process of the flight actuators play important role to ensure the stable and safe flight. Since a reliable flight actuation system can ensure appropriate guidance, the importance of qualification process cannot be neglected. Qualification of the actuators through field trials is a very costly and time-consuming process. The testing process using real flights takes more time and is costly. For ground testing, aerodynamic loading systems are used. The aerodynamic loading system is ground-based hardware in the loop (HWIL) simulator that can be used for exerting aerodynamic loads on actuation system of flight vehicles in real-time experiment. The actuation system under test is directly connected to the loading motor through a stiff shaft and the aerodynamics loading is applied in real time according to the flight trajectory generated by a flight computer.

1. Introduction

In a flight control system, aerodynamic loads are introduced during flight at the control surfaces or fins of flight vehicle as a function of air density, fin angle, etc. The fin control system must respond to these loads to maintain the accuracy of flight control system [1–3]. Since load simulators are used for the qualification of flight actuation system, the control performance of load simulators is vital [4, 5]. Before the invention of the motorized load simulators, the mechanical springs or torsion bars were utilized for the testing process. Conventional testing has several disadvantages, for example, the loading devices are not adaptable to varying loads. In modern ages, the testing and qualification of flight actuators are done through a hardware in the loop simulator system. In order to reduce cost and time, hardware in the loop simulators are utilized in which a loading motor is used as the aerodynamic loading device [6–9]. There are three types of load simulators depending on the type of applications and loading requirements [2–6]. Electro-hydraulic load simulators (EHLS) are widely used as hardware-in-the-loop-simulation (HILS) system in flight control applications that can simulate the air load executed on flight actuation systems. The EHLS can simulate rapid and large torque/force loads with big volume. Some advantages and disadvantages are listed. The hydraulic load simulators move fast and have rapid steering. The natural frequency of the electro-hydraulic servo valve is generally above 100 HZ, so the hydraulic load simulator’s frequency response is very fast and smooth. The low-speed performance of electro-hydraulic actuator is good. The load simulators can be operated in wide speed range. On other hand, due to big size and volume, maintenance cost is high. Temperature effects can cause degradation of performance. At low temperature the friction loss is high, and at high temperatures the leakage phenomenon is significant. Leakage of hydraulic fluid or oil is a major drawback. It causes the environmental pollution. This can easily cause a fire. The oil contamination causes system blockage and system failures. Another type is the pneumatic load simulator that is a typical hardware in loop (HIL) system used to apply medium-range torque/force loads on the actuator under test. The pneumatic load simulator can track the fast deployed load with compressibility. Pneumatic systems are often used instead because pneumatic pressure is usually cheaper to obtain, especially since most industrial facilities already have compressed air available. The pneumatic load simulators use air or any other compressed gas to transmit power. It is hard to obtain smooth performance due to large compressibility factor, especially at low speeds. Similarly, temperature changes can degrade the performance of pneumatic load simulators. The pneumatic load simulators are smaller in size and volume as compared to hydraulic load simulators, so the maintenance cost is lower. The electrical load simulator is an important ground-based hardware tester simulator used for qualification of flight actuation system, such as the aircraft control surfaces, ship steering system, robotics arm, undercarriage of the plane and high-speed elevator system. The electrical load simulators are used to apply medium and small loads on actuators under test. Some advantages of electrical load simulator are its small size and volume, low installation and maintenance cost, less sensitive to temperature changes as compared to hydraulic and pneumatic load simulators and high performance. There are no environmental hazards associated with electrical load simulators.

2. Working of load simulator system

Laboratory testing and qualification of flight actuators play vital role for ensuring the design of reliable flight control with cost-effective solutions. The hardware diagram given in Figure 1 is the minimal setup that is used in the laboratory testing of the flight actuators. The flight actuator is directly connected to the loading motor through a stiff shaft. The direct mechanical connection allows the application of the loading torque generated at the output shaft of loading motor in a close loop system. The Autopilot controller is used to set the reference position trajectory of the flight actuator. An important block of the system is the aerodynamic load calculator system, and the inputs to this block are the reference position command of the actuator system, air speed, Mach number and angle of attack. The output of the load calculator block serves as reference command to the loading motor. Thus, the torque load loop is closed using the feedback signal from torque sensor. The advantage of using the proposed setup provides the designer a freedom for applying real-time loads simulated in the laboratory with minimum cost.

Figure 1.

Block diagram of electrical load simulator.

3. Actuator testing: a case study

The flight actuator under test is a brushless DC motor. A permanent magnet synchronous motor (PMSM) is used as the loading motor. For simplicity, the load calculator is used in proportional mode. In proportional mode, the output of the load calculator is directly proportional to the reference command of the flight actuator. Let θ_a represents the reference command of flight actuator, then the output of the load calculator T_r is Cθ_a where “C” represents the proportionality constant. The parameter T_r is set as reference command of the torque loading motor. From Figure 2, the reference command signal of the flight actuator θ_ais constructed from a real test scenario of a flight vehicle.

Figure 2.

Reference signal command of flight actuator.

Before discussing the control problem, basic understandings of system dynamics is a pre requisite. A PMSM is used as a loading motor. The voltage and torque balance equations of PMSM loading motor are written as

$\begin{array}{l}{u}_d=i_d{R}_s+L_{sd}\frac{d{i}_d}{dt}-P{L}_s{i}_q{w}_m\\ u_q=i_q{R}_s+L_{sq}\frac{d{i}_q}{dt}+P{L}_{sq}{i}_d{w}_m+P{\psi }_m{w}_m\\ T_e=\frac{3P}{2}[{\psi }_m{i}_q+\left(L_{sd}-L_{sq}\right)i_d{i}_q=J\frac{d{w}_m}{dt}+B{w}_m+T_f+T_L\end{array}$E1

In Eq. (1) [i_d i_q] is the d-axis and q-axis current vector, [u_d u_q] represents d-axis and q-axis voltage vector, w_m is the angular velocity of torque motor, [L_sq L_sd R_s] represents inductances and resistances of ELS motor,[P , ψ_m] represents the number of pole pairs and magnetic flux of rotor, [J, B] represents inertia and damping coefficient, $k_t=\frac{3P}{2}{\psi }_m$is torque constant, k_b = Pψ_m is back emf constant, and [T_e , T_f, T_L] is the electromagnetic torque, friction torque and output load torque. Assuming that inertia and damping coefficient of torque sensor is very small, thus the dynamics can be written as

$T_L=K_s\left({\theta }_m-{\theta }_a\right)$E2

Here, [θ_m θ_a] represents the angular position of loading motor and actuator, K_s is the total stiffness of torque sensor and connecting shaft. To achieve largest torque operation and to eliminate coupling effect between speed and currents, we set d-axis reference current $i_d^{\prime }$ equal to zero. Considering the effect of PWM driver and the current feedback, Eq. (2) can be written as given in [4]. For simplicity, we set L_sq = L and R_s = R

$\frac{d{i}_q}{dt}=-\frac{R}{L}{i}_q-\frac{K_b}{L}{w}_m+\frac{K_v{K}_i}{L}$E3

Here, k_i is the current controller gain. Current feedback is assumed to be unity. Assuming that load and friction torque are zero and taking Laplace transform of Eq. (3) and eliminating I_(s), we get the transfer function from input voltage to output position as

$\frac{{\theta }_m}{u_q}=\frac{\frac{K_v{K}_i}{K_b}}{S\left(t_m{t}_e{S}^2+t_{m}S+1\right)}$E4

In Eq. (4), $t_m=\frac{RJ}{k_t{k}_b}$ is the electromechanical time constant, $t_e=\frac{L}{R}$ is the electromagnetic time constant. Replace Eq. (2) into Eq. (2), the simplified relation can be written as

$\begin{array}{l}{T}_L=\frac{k_v{k}_i{k}_{t}u-s\left[\left(Ls+R\right)\left(Js+B\right)+k_b{k}_t\right]K_s{\theta }_a}{D\left(s\right)}\\ D\left(s\right)=s\left[\left(Ls+R\right)\left(Js+B\right)+K_b{K}_t\right]+T\left(Ls+R\right)\end{array}$E5

From the numerator of Eq. (5), it is concluded that extra torque is caused by the effect ofθ_a, ${\dot{\theta }}_a$ and ${\ddot{\theta }}_a$. If the reference input command of loading torque motor is zero, i.e.u = 0, then Eq. (5) is reduced to the following simplified relation

$T_L=\frac{-s\left[\left(Ls+R\right)\left(Js+B\right)+k_b{k}_t\right]K_s{\theta }_a}{D\left(s\right)}$E6

From Eq. (6), it is concluded that extra torque is acting on the loading torque motor even if the reference input command u is zero. Extra torque is a function of the acceleration and velocity components of the actuators movement. After some simplifications, the state equation representation of electrical load simulator is written as

${\ddot{T}}_L=-a{\stackrel{.}{T}}_L+bu-cf\left(T_{\mathit{extra}},T_f,T_L\right)$E7

In Eq. (7) the parameters are defined as

$\begin{array}{l}a=\frac{k_t{k}_b}{JR}+\frac{B}{J}\\ b=\frac{K_s{k}_t}{JR}\\ c=\frac{K_s}{J}\\ f\left(T_{\mathit{extra}},T_f\right)=\frac{K_s}{J}\left(T_{sft}+T_f\right)\end{array}$E8

In Eq. (7) the nonlinear friction is represented using LuGre model, which is written as

$\begin{array}{l}{T}_f=a_{0}Z+a_1\stackrel{.}{Z}+a_2\\ \stackrel{.}{Z}=v-\frac{a_0\left|v\right|}{g\left(v\right)}\\ g\left(v\right)=f_c+\left(f_c-f_s\right)e^{{\left[\frac{v}{v_s}\right]}^2}v\end{array}$E8

In Eq. (8) the parameter g(v) is the Stribeck effect, v_s is the Stribeck velocity, f_c is coulomb friction, f_s is static friction, z is the average bristle defection,a₀ is the stiffness of the bristles, a₁ is the damping term and a₂ is the viscous friction coefficient. Now to realistically apply the loading torque on flight actuator, a feedback torque control system plays vital role. In this study, adaptive fuzzy sliding mode control system is used to formulate the torque control system.

3.1. Adaptive fuzzy sliding mode control for electrical load simulator system

Sliding mode is a robust control method which has been widely applied to many nonlinear systems [10–15]. This section provides an overview of derivations of torque control system for electrical load simulator’s system. Let T_Lbe the output load torque and T_rbe the desired torque signal, we define tracking error vector as

$\left[\begin{array}{c}\hfill \begin{array}{c}\hfill e=T_L-T_r\hfill \\ \hfill \stackrel{.}{e}={\stackrel{.}{T}}_L-{\stackrel{.}{T}}_r\hfill \end{array}\hfill \\ \hfill \ddot{e}={\ddot{T}}_L-{\ddot{T}}_r\hfill \end{array}\right]$E9

Error surface vector is defined as

$\left[\begin{array}{c}\hfill s=\stackrel{.}{e}+\lambda e\hfill \\ \hfill \stackrel{.}{s}=\ddot{e}+\lambda \stackrel{\text{.}}{e}\hfill \end{array}\right]$E10

Assuming that the nominal parameters of the system are known, then by combining Eqs. (7), (9) and (10) yields

$\stackrel{.}{s}=\left(-a{\stackrel{.}{T}}_L+bu-f\left(T_{\mathit{extra}},T_f\right)\right)-{\ddot{T}}_r+\lambda \stackrel{\text{.}}{e}$E11

The control law is given by

$u=\frac{1}{b}\left(a{\stackrel{.}{T}}_L+\widehat{f}\left(T_{\mathit{extra}},T_f|\theta \right)+{\ddot{T}}_r-\lambda \stackrel{.}{e}\right)-\frac{1}{b}\left(K_d.s-w.sgn\left(s\right)\right)$E12

From Eq. (12), it can be analyzed that the total control effort u is the sum of three terms

$u=u_T+u_f+u_{\mathit{extra}}$E13

Here, u_T is the control effort for torque tracking, u_f is the friction compensation control and u_extra is the extra torque compensation control. The unknown function $\tilde{f}\left(T_{\mathit{extra},}{T}_f|\theta \right)$is the estimated output of fuzzy logic for friction and extra torque.

3.1.1. Stability analysis

To prove stability of the closed loop, the Lyapunov function is chosen as

$\begin{array}{l}V=\frac{1}{2}\left(s^2+{\displaystyle \sum _{i=1}^n}{\eta }_i{{\tilde{\theta }}^2}_i\right)\\ \stackrel{.}{V}=s\stackrel{.}{s}+{\displaystyle \sum _{i=1}^n}{\eta }_i{\tilde{\theta }}_i\dot{{\tilde{\theta }}_i}\end{array}$E14

Here${\tilde{\theta }}_i={\widehat{\theta }}_i-{\theta }_i$ . Combine Eq. (11) and Eq. (14)

$\stackrel{.}{V}=s\left(\left(-a{\stackrel{.}{T}}_L+bu-f\left(T_{\mathit{extra}},T_f\right)\right)-{\ddot{T}}_n\right)+{\displaystyle \sum _{i=1}^n}{\eta }_i{\tilde{\theta }}_i\dot{{\tilde{\theta }}_i}$E15

Define ${\dot{T}}_n=-{\ddot{T}}_r+\lambda \dot{e}$ and combine Eq. (12) into Eq. (15)

$\begin{array}{l}\stackrel{.}{V}=s(-a{\stackrel{.}{T}}_L+a{\stackrel{.}{T}}_L+\widehat{f}\left(T_{\mathit{extra}},T_f\right)|\theta +{\ddot{T}}_n-K_{d}s-w.sgn\left(s\right)\\ -f\left(T_{\mathit{extra}},T_f\right)-{\ddot{T}}_n)+{\displaystyle \sum _{i=1}^n}{\eta }_i{\tilde{\theta }}_i\dot{{\tilde{\theta }}_i}\end{array}$E16

The fuzzy approximation error is defined as [3]

$\begin{array}{l}{e}_f=f\left(T_{\mathit{extra}},T_f\right)-\tilde{f}\left(T_{\mathit{extra}},T_f\right)|{\theta }^{*}\\ {\theta }_i{\xi }_i\left(\stackrel{.}{\theta }\right)=\widehat{f}\left(T_{\mathit{extra}},T_f\right)/\theta –\tilde{f}\left(T_{\mathit{extra}},T_f\right)|{\theta }^{*}\end{array}$E17

Combining Eq. (16) and Eq. (17) yields [16]

$\stackrel{.}{V}=s\left(\widehat{f}\left(T_{\mathit{extra}},T_f\right)/\theta -f\left(T_{\mathit{extra}},T_f\right)-K_{d}s-w.sgn\left(s\right)\right)+{\displaystyle \sum _{i=1}^n}{\eta }_i{\tilde{\theta }}_i\dot{{\tilde{\theta }}_i}$E18

$\begin{array}{l}\stackrel{.}{V}=s(\widehat{f}\left(T_{\mathit{extra}},T_f\right)/\theta –\tilde{f}\left(T_{\mathit{extra}},T_f\right)|{\theta }^{*}-\left(\left(f\left(T_{\mathit{extra}},T_f\right)-\tilde{f}\left(T_{\mathit{extra}},T_f\right)|{\theta }^{*}\right)\right)\\ -K_{d}s-w.sgn\left(s\right))+{\displaystyle \sum _{i=1}^n}{\eta }_i{\tilde{\theta }}_i\dot{{\tilde{\theta }}_i}\end{array}$E19

Using Eq. (19) the following adaptive law is derived

$\dot{{\tilde{\theta }}_i}=-{{\eta }_i}^{-1}{s}_i{\xi }_i\left(\theta ,\stackrel{\text{.}}{\theta }\right)$E20

By replacing Eq. (20) in Eq. (19) and simplifying

$\stackrel{.}{V}=s\left(-e_f-K_{d}s-w.sgn\left(s\right)\right)$E21

It is assumed that ideally fuzzy compensating error e_f is approaching zero, and by choosing K_d > 0 it can be shown that

$\stackrel{.}{V}=-s{K}_{d}s\le 0$E22

3.1.2. Results and discussion

For simulations and validity of the proposed control scheme, the following parameters are used. Total inertia of the system is given as J = 0.04Kg/m², resistance R = 7.5Ω, inductance L = 1mH, motor torque constant k_t = 5.7325Nm/A, back emf constant k_b = 5.7325Nm/V, viscous coefficient B = 0.244Nm/rad/s, torque sensor stiffness K_s = 950Nm/rad, static friction f_s = 3Nm, coulomb friction f_c = 2.7Nm, σ₀ = 260Nm/rad, σ₁ = 2.5Nm − s/rad, σ₀ = 0.022Nm − s/radand Stribeck velocity α = 0.001rad/s. The parameters of the controller are given as fuzzy learning rate η_i = 0.0001, amplifier gain k_u = 10, k_d = 10, w = 1.5, λ = 15.

3.1.3. Loading motor torque tracking performance

The testing of actuator is performed under the loading torque T_r = 16θ_a where “C = 10”. From Figure 3, it is concluded that the output torque applied by the loading motor is exactly the same as the reference loading torque.

Figure 3.

Loading motor closed loop performance.

Figure 4.

Flight actuator closed loop performance with aerodynamics load.

3.1.4. Flight actuator angle tracking performance under load

Figure 4 presents the testing results and the qualification of the autopilots of the flight actuators under the aerodynamic loading shown in Figure 3, which is mechanically transmitted from loading motor. From the results provided, it is concluded that the flight actuator under can withstand the non-linear profile of the aerodynamic load supplied. Moreover, the autopilot position controller is also robust and the position tracking errors are small enough.

4. Conclusion

This chapter covers the basic working principle of the load simulator system for testing of the flight actuators. As a case study, a real test data was used as reference command to the flight actuators and the load calculator unit. The output of the load calculator system provides the reference loading torque command for the loading motor, which is working in closed loop. From the results presented in this chapter, it is concluded that the proposed hardware setup is feasible to be utilized for cost-effective testing and qualification of the flight actuation system.