Open access peer-reviewed chapter

# Loads Simulator System for Testing and Qualification of Flight Actuators

Written By

Nasim Ullah

Submitted: 17 October 2015 Reviewed: 25 February 2016 Published: 08 September 2016

DOI: 10.5772/62710

From the Edited Volume

## Recent Progress in Some Aircraft Technologies

Edited by Ramesh K. Agarwal

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## 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.

### Keywords

• Ground-based testing
• flight actuators
• mathematical modelling
• modern control

## 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 θa represents the reference command of flight actuator, then the output of the load calculator Tr is a where “C” represents the proportionality constant. The parameter Tr is set as reference command of the torque loading motor. From Figure 2, the reference command signal of the flight actuator θais constructed from a real test scenario of a flight vehicle.

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

ud=idRs+LsddiddtPLsiqwmuq=iqRs+Lsqdiqdt+PLsqidwm+PψmwmTe=3P2[ψmiq+LsdLsqidiq=Jdwmdt+Bwm+Tf+TLE1

In Eq. (1) [id iq] is the d-axis and q-axis current vector, [uduq] represents d-axis and q-axis voltage vector, wm is the angular velocity of torque motor, [Lsq Lsd Rs] represents inductances and resistances of ELS motor,[P , ψm] represents the number of pole pairs and magnetic flux of rotor, [J, B] represents inertia and damping coefficient, kt=3P2ψmis torque constant, kb = m is back emf constant, and [Te , TfTL] 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

TL=KsθmθaE2

Here, [θmθa] represents the angular position of loading motor and actuator, Ks 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 id 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 Lsq = L and Rs = R

diqdt=RLiqKbLwm+KvKiLE3

Here, ki 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

θmuq=KvKiKbStmteS2+tmS+1E4

In Eq. (4), tm=RJktkb is the electromechanical time constant, te=LR is the electromagnetic time constant. Replace Eq. (2) into Eq. (2), the simplified relation can be written as

From the numerator of Eq. (5), it is concluded that extra torque is caused by the effect ofθa, θ˙a and θ¨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

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

T¨L=aT.L+bucfTextraTfTLE7

In Eq. (7) the parameters are defined as

a=ktkbJR+BJb=KsktJRc=KsJfTextraTf=KsJTsft+TfE8

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

Tf=a0Z+a1Z.+a2Z.=va0|v|gvgv=fc+fcfsevvs2vE8

In Eq. (8) the parameter g(v) is the Stribeck effect, vs is the Stribeck velocity, fc is coulomb friction, fs 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 [1015]. This section provides an overview of derivations of torque control system for electrical load simulator’s system. Let TLbe the output load torque and Trbe the desired torque signal, we define tracking error vector as

e=TLTre.=T.LT.re¨=T¨LT¨rE9

Error surface vector is defined as

s=e.+λes.=e¨+λe.E10

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

s.=aT.L+bufTextraTfT¨r+λe.E11

The control law is given by

u=1baT.L+f^Textra,Tf|θ+T¨rλe.1bKd.sw.sgnsE12

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

u=uT+uf+uextraE13

Here, uT is the control effort for torque tracking, uf is the friction compensation control and uextra is the extra torque compensation control. The unknown function f˜Textra,Tf|θis 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

V=12s2+i=1nηiθ˜2iV.=ss.+i=1nηiθ˜iθ˜i˙E14

Hereθ˜i=θ^iθi . Combine Eq. (11) and Eq. (14)

V.=saT.L+bufTextraTfT¨n+i=1nηiθ˜iθ˜i˙E15

Define T˙n=T¨r+λe˙ and combine Eq. (12) into Eq. (15)

V.=s(aT.L+aT.L+f^TextraTf|θ+T¨nKdsw.sgnsfTextraTfT¨n)+i=1nηiθ˜iθ˜i˙E16

The fuzzy approximation error is defined as [3]

ef=fTextraTff˜TextraTf|θ*θiξiθ.=f^TextraTf/θf˜TextraTf|θ*E17

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

V.=sf^TextraTf/θfTextraTfKdsw.sgns+i=1nηiθ˜iθ˜i˙E18
V.=s(f^TextraTf/θf˜TextraTf|θ*fTextraTff˜TextraTf|θ*Kdsw.sgns)+i=1nηiθ˜iθ˜i˙E19

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

θ˜i˙=ηi1siξiθθ.E20

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

V.=sefKdsw.sgnsE21

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

V.=sKds0E22

#### 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 kt = 5.7325Nm/A, back emf constant kb = 5.7325Nm/V, viscous coefficient B = 0.244Nm/rad/s, torque sensor stiffness Ks = 950Nm/rad, static friction fs = 3Nm, coulomb friction fc = 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 ηi = 0.0001, amplifier gain ku = 10, kd = 10, w = 1.5, λ = 15.

The testing of actuator is performed under the loading torque Tr = 16θa 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.

#### 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.

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Written By

Nasim Ullah

Submitted: 17 October 2015 Reviewed: 25 February 2016 Published: 08 September 2016