Design of Nonlinear Control Loader System for a ...

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for a Boeing 737-300 simulator. In that research; triple channeled PCL were developed according to the principles of Boeing 737-300 flight qualities.
Design of Nonlinear Control Loader System for a Flight Simulator (a Dynamic Inversion Approach) Sajad Azizi Graduate Program in Electrical Eng. Federal University of Minas Gerais Av. Antonio Carlos 6627, 31270-901 Belo Horizonte,MG, Brazil [email protected]

Saeb AmirAhmadi Chomachar AmirKabir University of Technology 424 Hafez Ave., Tehran, Iran [email protected]

Abstract-A

theoretical

study

regarding

column and gives the pilot a feel of real-environment human-machine interactions. The development of the so­ called peL subsystem requires the application of the well­ established control techniques available in the literature. The control techniques are then utilized to assist a position­ control or force-control scheme. There are limited papers available in the existing literature related to peL systems [l­ IS]. peL systems realm suffers from a lack of great contribution, roughly speaking, the literature rarely presents nonlinear models of aircrafts to generate the force-feel characteristics, and where nonlinear models are considered, the study lacks crucial effects such as friction that is certainly present in every mechanical sub-system as gear box of a peL device. The first control loading system was designed and operated in the NASA Ames research center in 1960. In this rather long history until the present time, the principal contribution to the analysis of control loading systems is restricted to design of linear control systems, with simple dynamics. Whereas in 1989 Durham [3] devised a procedure in designing a nonlinear model following control law that was adopted for the control loader system digitally controlled by a torque motor.

experimental

development of a nonlinear control loader system for a vertical flight motion simulator is presented. Coupled stick-aircraft dynamics during an active 3-DOF nonlinear maneuver in the vertical plane is simulated in the MATLAB

SIMULINKTM

software environment that facilitates a near-exact simulation of control column displacements in response to pilot's input, and is used as a mathematical model to actively produce the force-displacement characteristics.

SIMULINK™ model

of the

aircraft under study is run and free flight is considered in the atmospheric

A

environment.

position

control

strategy

is

devised by using nonlinear dynamic inversion technique to reproduce the relevant control loads on control column of the corresponding simulator cockpit. The simulator is assumed to simulate

the

aircraft.

The passive feel system of the plant includes a

nonlinear

vertical

spring

flight

and

a

motion

linear

of

a

general

damper.

The

aviation

mechanical

contacts of several parts of the control loading system give rise to the friction that is certainly inherent in almost every mechanical system. However, the friction is compensated by a frictional torque observer of the type proposed in the existing literature.

Results

of

computer

simulations

verify

the

robustness of our design plan.

T ABLE OF CONTENTS 1. INTRODUCTION

.................................................

2. ACTIVE STICK DVNAMICS

•.•.•.•.•.•.•.•.•.•.•.•.•.•.•.•.

3. AERODYNAMIC HINGE MOMENT 4. PLANT DVNAMICS

••••••••••••••••••••

In 1960, Walter [1] presented a brief review of the development of a variable control feel simulator. In 1983 Rinaldi and Beckham [2] presented a modular approach in analysis of digital control loading systems. The actuator used in that research was a hydrostatic one. In that study it was reported that by means of the day technology it was feasible to design a digital control loader to fulfill all specific design requirements. Effects of free play, cable stretch, hard stops, static and sliding friction, non-linear springs, and autopilot actuator engage/disengage forces, and boosted or un-boosted flight could be easily simulated using existing standard program modules. The superiority of the proposed digital system to analog systems was reported there.

1 2

.4 4

.•.•.•.•.•.•.•.•.•.•.•.•.•.•.•.•.•.•.•.•.•.•.

5. NUMERICAL SIMULATION ................................ 5 6. SUMMARY

.•.•.•.•.•.•.•.•.•.•.•.•.•.•.•.•.•.•.•.•.•.•.•.•.•.•.•.•.

9

ACKNOWLEDGMENT ............................................ 9 REFERENCES

•••••••••••••••••••••••••••••••••••••••••••••••••••••••••

9

BIOGRAPHY ........................................................ 1 0 ApPENDIX

•.•.•.•.•.•.•.•.•.•.•.•.•.•.•.•.•.•.•.•.•.•.•.•.•.•.•.•.•.•.

11

1. INTRODUCTION

In 1989 Durham [3] proposed a nonlinear model following control law to achieve precision control of a certain simulator control loader system. The effect of the motor commutation ripples on the error dynamics was discussed by Durham. Increased feedback gains were seen effective in eliminating both ripple and measurement errors but could result in noisy tracking. Nonlinear behavior was faithfully reproduced in the simulation results [3]. The remaining researches in this field were mainly performed in the years after 2000. In 2003 Davis and Hildreth [4], presented a work

Simulators are one of the most noticeable breakthroughs in aerospace engineering. Due to threats in real-environment trainings for piloting military or civil flight vehicles, simulators are widely used. A high-level fidelity simulator is required to efficiently train the pilots and depends upon the available technologies. One of these technologies is applied to pilot control loader (peL) subsystems. peL subsystems are an indispensable part of the simulators that help the pilot control loads to be realized on the control 978-1-4799-5380-6/151$31.00 ©2015 IEEE

1

acceleration feedback is a technique that can be used to remove all inertia effects from the differential transducer output, yielding a true pilot force measurement. The control loader system was a typical McFadden wheel and column system, which has a relatively high mass. Since the technique does not involve strain gauges near or in the pilot grip or gloves, the pilot could handle the control column in a normal fashion. Good compensation can be obtained even when the accelerometer is not exactly at the correct location. In 2008, Mueller [11], proposed an algorithm for optimizing the performance of the PCL's analog controller operated at the NASA vertical flight motion simulator of the Ames research center.

considering the problems in validating control feel in simulators. It was reported that the structural flexibility of the mechanical linkages used in the control loading systems were more serious than previously addressed. The stretching of the connecting cables in an aircraft control feel system had to be faithfully simulated. In 2004 Nam and Hong [5], developed an active stick using frictional torque compensation. The force feel characteristics of the active stick might be easily changed to give a soft or strong control feel to the pilot trainee. A two axis built-in force sensor was used to measure the force felt by the operator. A combined position and force control strategy was mechanized by a two-axis built-in force sensor and LVDT (Linear Variable-Distance Transducer). Nam and Hong observed that the frictional torque inside the stick generated due to mechanical contact of several parts caused the experimental frequency response to be dependent on the magnitude of the excitation signal hence achievement of a precision closed loop control was difficult. A type of frictional torque observer was designed and applied to the closed-loop control system. The efficiency of the frictional torque observer was verified through experiments and numerical simulations.

Friction compensation techniques which are central to the PCL systems development were discussed in [12-15]. As stated earlier, the PCL systems research realm is limited to analysis of simple linear dynamics; however, in this paper we address all of the issues relevant to an efficient PCL system design as a simulator subsystem. The Rockwell S-500 Shrike Commander is chosen as the aircraft whose force-feel characteristics is to be faithfully reproduced on the associated simulator control column that should be a copy of that existing in the real aircraft. The theoretical development of the so-called active stick is focused on solving three technical problems. One of those is that the force-feel characteristics should be accurately defined. This problem is taken away by using a 3-DOF nonlinear mathematical model of the selected aircraft dynamics developed by the MATLAB SIMULINK™ software. The second concerns how to pick up the grip force on a stick. This problem has been considered in [10]. The last problem concerns the performance degradation of the active stick due to an existent frictional torque. This comes from the mechanical contact of several parts, i.e. mainly from the reduction gear box. To overcome this impediment, a pre-defmed look up table was used. The look-up table should be constructed by the use of experiments performed on the active stick in open loop conditions. It facilitates the evaluation of frictional torque in a wide range of the stick rotational speeds inspired by the research in [5].

In 2005 Garretson et al [6], compared the effect of position­ loop, velocity-loop and force-loop based control loading architecture on quantitative performance characteristics of the subsequent control system. It was reported that the force-loop provided the designer with the best performance characteristics of the system, and although velocity-loop was also reliable but the position-loop became unstable in certain conditions and provided the worst performance of the three architectures. In 2006 Park et al [7], presented a systematic control parameter tuning for an actuator in a control loading system. By considering the Bode plots, they attempted to optimally tune the parameters of the control loading system for a reliable and faithful performance. In 2007 Shutao et al [8], designed a control loading system for a Boeing 737-300 simulator. In that research; triple­ channeled PCL were developed according to the principles of Boeing 737-300 flight qualities. Mathematical model of computed forces was derived for the considered PCL system. Passive force control system was developed. Experiments demonstrated that PCL had less than 4% error between computed force and good tracking performance.

2. ACTIVE STICK DYNAMICS

Stick is a kind of command-generating device in light aircrafts and is connected to the control surface through several mechanical linkages. In the current study, we are concerned with the reproduction of the control loads on the stick of a light aircraft simulator. The simulator considered for this purpose is assumed to simulate the vertical flight motion of the selected aircraft. The simulator stick should be a prototype of the actual stick in the real system. Pilot is routinely grasping the control column and pushes or pulls the stick to make the airplane change altitude. Whilst displacing the control column, the control surface revolves to a new position and the states of the aircraft will change simultaneously and this will produce new aerodynamic

Coiro et al [9], presented a work regarding the reproduction of the control loads in a 6DOF flight simulation environment for a general aviation aircraft. Various open source program modules were used for a high fidelity simulation. Muller and Hardy [10], devised a plan for pilot force measurement in a control loader system. The inertia and gravity effects were compensated. It was shown that 2

loads and moments on the control surface that compels the pilot to resist for a rational control of the aircraft, Figure 1.

characteristics that are to be fmally tracked by a peL system. The general control strategy is illustrated in Figure 2. The design process is exercised in MatIab Simulink™ environment.

In this paper, a nonlinear 3-DOF dynamics model of a general aviation aircraft is used to generate the force-feel

true control feel

Aerodynam ic load Figure 1 - Schematic of the control feel in real-environment condition.

Fst

Half B ridge Signal AMP and Low Pass Filtering

I

K (S) force

st

F ( N)

LVDT GAI N LVDT

�--+----I

K

Strain gages

Force Sensor

3 DOF Model

AMP

Torque by user

p assive feel

Frictional Torque

Figure 2 - The general control loading strategy. (Courtesy of [5])

3

geometric specifications of the aircraft drawn from its maintenance manual was utilized to get the aerodynamic characteristics and parameters.

3. AERODYNAMIC HINGE MOMENT

The aerodynamic hinge moment which is generated on the hinge line of the control surface is a function of several parameters such as the air density, aircraft velocity, elevator deflection, aerodynamic angle of attack, downwash (£), and, is governed by the following equation:

1

2 . TAero =2P V SC(h.o.t-KhJb-Khbb-Khaa-KO)

4. PLANT DYNAMICS

The plant of the PCL system theoretically designed in this study, comprises a stick, exactly as that existing in the real aircraft, and a passive feel system including a linear damper and a nonlinear spring. The actuator is a DC motor that drives the pitch axis of the active stick. An amplifier is used to feed the required current to the torque motor.

(1)

All nonlinear effects, including those from aircraft equations of motion and as well aerodynamic nonlinearities such as the higher order terms in Eq. 1 could be simulated, using the SIMULINK™ model that was developed in this study.

As reported in [5], the mechanical contact of several parts in the mechanical system generates frictional torque, and this will pose a challenge on precision control of the active stick. For this reason a frictional torque observer must be applied to the closed loop system to compensate the frictional torque which inherently exists inside the stick. The frictional torque observer applied in this paper is based on the general experimental characteristics of that applied in [5]. Coupled closed-loop diagram of the plant and the model has been illustrated by Figure 3 and as well has been mathematically expressed by Eq. 4.

The effect of downwash (£) on changing the air current such that the control surface hinged to the horizontal wing ( horizontal stabilizer) would experience a different angle of attack from that felt by the main wing is considered in the current work as described by the following equation: a & (2) i i atai! awb - t - w - &0 awb aa =

All these parameters were simulated in the MATLAB The SIMULINK™TM software environment. aerodynamic parameters have been estimated by the DATCOM™ software. It should be noted that the

Fp ilot ��

Aircraft

� Stick

9ModeJ

--

Control

LA...

Surface .....

I o elevator I

8plant

eO-

�� NOI

Controller �

Amplifier

Nonlinear 3DOF Model

Figure 3 - The modified pilot control loading strategy.

4

-

Actuator

-

Plant

{i::�::ees:6}

= ==

(3)

To verify the theoretical design process presented in this study, we performed some numerical simulations in the MATLAB SIMULINK™ software environment. The outcomes were satisfactory. The position output of the model was tracked by the plant with an acceptable performance. In cases where damping is low in elevator system, the control surface intensely oscillates as limit cycles (Figure. 4).

The closed-loop dynamics of the system is as given in Eq. 4: Xl =x2

=J;J(-K2 f -KI Tservo = Kt x

N

xI-C x2 + Tpilot + Tservo - Tlric)

(4)

i

The dynamic inversion approach as is presented in the follow, yielded Eq. 5 for the required control input (the required current):

i _NK1_t(JeqvtK2E3tKIEteE

Iv=-KdE-KpE =

V

.

5. NUMERICAL SIMULATION

E=iJ-iJd

x2

=

K ,Kd are proportional and derivative constants of the p virtual control subsystem. Kl 30;K2 5;C 4;Kp =400;Kd 1 2

The state variables and the error are expressed as given in Eq.3 :

t

- Tpilot Tfriction)

)

A weak pilot force, lasting for a short time interval, and exerted in the trim conditions of the aircraft, causes an almost strong chaotic oscillation of the control surface and finally settles down in a limit cycle, and is seen in Figure 5. In the case, the time histories of the control surface deflections are depicted in Figure 6. A strong pilot force, exerted in the same conditions as the previous case and for a short time interval duration, resulted in an initial weak chaos followed by a limit cycle and is seen in Figure 7. Figure 8 illustrates the associated time histories of the stick dynamics.

(5)

is the virtual control. 3 �--�--�---, 2.5

� '"



2 1.5

Q) ro a:

� �

"" £ a:

t3 i55

0.5 0 -0.5 ·1 -1.5

-

-

_ 2 �__L-__L-__�__�__�__�__-L__-L__-J -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 0.1 0.12

Figure 4

Slick Pitch Angle (rad)

o

0.02

0.04

0.06

0.08

0.1

0.12

Stick Pitch Angle (rad)

Figure 5 Weak, short-acting (transient) pilot force input initiates a strong chaos and ends in a limit cycle.

Low-amplitude limit-cycles of the stick dynamic response.

5

0.ro5 r------c--��--�--_,

0.04 0.03



'0



Q) 0>

0.02

Q) 0>



c

s:::

0.01



0

..:

s:::

;! ii:

;! ii: '" "

0.01

� ij)

0.005

-0.01

o

-0.005 L---- - '----------' '----------' --------: -------:: O:----------:" 4 2 12 1 8 6 0

-0.02

lime (sec)

Figure 6 - State trajectory for the stick pitch angle in response to a weak transient pilot force input.



� 0.5

c

;! ii: '" "

(7)

u Q) '" '0

0.4

Q) 1ij II: Q) 0>

0.2



0

c

..:

-0.5

s:::

;! ii: '" .S!

-1

Ui

8

10

12

0 -0.2 -0.4

-1.5 -2

6

lime (sec)

0.6

U Q)

s:::

4

0.8 �----�----�c-?--,

1.5

..:

2

Figure 8 - State trajectory for the stick's dynamic response to specific pilot force inputs (strong and short-acting inputs).

2

Q) 1ij II: Q) 0>

0

0

0.05

0.1

0.15

0.2

Stick Pitch Angle (rad)

0.25

0.3

- O -0:8 L----- _ - '- ------'O'--------O-'-'-- ----- '--=- ----0: .L.ro-=- ----:-: .04 02 .01 0.01 0.02

0.35

Stick Pitch Angle (rad)

Figure 7 - Strong, short-acting (transient) pilot force input initiates a weak chaos and ends in a limit­ cycle.

Figure 9 - Phase portrait for the stick's stable dynamic response to a weak force exerted during a considerable time interval.

6

0.04

0.6

,.----c---c---�--�--�

0.5

0.4 '0



Ql OJ

..:

0.3

co

.c:

'0 e1 a5

0.01

!,! a:

'""

(7)

0.2

0 0.1

-0.01

-0.02

-

0

0

2

4

6

8

-0.1

12

10

0.5

0

Figure 10 - Stick's stable dynamic response to a weak but long-acting pilot force input.

0.8

Ql 1ij II: Ql OJ

..:

W

0.6

a5

I

0.2

)

o 0.4 -0.2 0.2

1-

0.5

o

!,! a:

0

(7)

-0.2

'""

3.5

4

2.5

3

SIMULATOR AIRCRAFT 3.5

4

lime(sec) 200 100

1\

-=-

1:'

1!:J

()

-0.4

-0.6 -0.02

2

1.5

co

.c:

AIRCRAFT



0.4

'Cl



3

Figure 12 - Acceptable performance of the simulator. 0.6

"'

2.5

lime(sec)

lime (sec)

U Ql

2

1.5

SIMULATOR

-0.01

o

0.01

0.02

0.03

0.04

I

V

-100 -200

Stick Pitch Angle (rad)

\

0

o

0.5

r.li,

�� 1.5

'V�¥N

2

2.5

3

3.5

4

lime(sec)

Figure 11 - Phase portrait for the stick's stable dynamic response to a strong force exerted during a considerable time interval.

Figure 13a, 13b - The controller is robust against noises that were added to the measurement locations.

The frictional torque observer as was studied in [5], efficiently estimates the average of the Coulomb friction but is weak in estimating static and Stribeck effects as were observed in [5]; Figure 14. It is worthy of note that in contrast to what was expressed in [5] the frictional torque observer is rather precise in estimating the Coulomb friction in cases where all parameters are extensively tuned; Figure 15. The pilot torque and the servo generated torque for a linear plant are depicted in Figure 16. Error dynamics of the control system is unstable for large PD control gains, whilst a good PD parameters selection leads in a stabilized error dynamics and is shown in Figure 17.

In contrast to the transient forces (lasting for a short time interval), the forces, whether weak or strong, lasting for a longer time interval, result in an exponentially stable control surface and stick dynamic response as are depicted in Figures 9-11.

�he passive feel parameters in plant should be adequately

. sImIlar to those felt in the real situation; otherwise, poor performance is certain. By adopting accurate parameter tuning and considering all model-matching issues a precision control is reached and is illustrated in Figure 12.

Band limited white noises were added to the measurement locations. Meanwhile the controller was seen robust against these measurement noises, although the required current was affected as seen in Figure 13-a and 13-b.

7

15 10

5 � LL

1\

v -5

IL

�A

-10

-20

Estimated Friction

-- Real Friction

o

0.2

0.4

0.6

0.8

1.2

� a:



1--

-15

� a:

II �

)====,

lJ.J

1.4

1.6

lJ.J

1

1.8

-0.6

I -- Error stability I

_0.8 L--L---L---'----�"=======:l --0.01 0.015 o -0.015 0.005 0.01 -0.005

2

ERROR

lime (sec)

Figure 14 - Estimated friction versus real friction. Figure 17 - Stability of error dynamics

0.6,·---�---�--�---�--�--� 0.5 0.4 0.3

i

0.2 0. 1 0 -0. 1

- 100 L-�-�-�-�-�-�-�-�-�----' 1.2 1.4 1.6 1.8 2 o 0.2 0.4 0.6 0.8

\ � V

.

-0. 2L---�--�---�--�--�-----' 2 1.5 2.5 o 0.5 3

lime(sec)

Figure 15 - Estimated friction versus real friction (satisfactory coulomb friction approximation).

Figure 18 - Plant's open loop response to a step pilot force (no control input)

100 r----�---��---, so



60 40 20

0

Pilot torque (blue-up) Servo torque (green-down)

.-,. ::


eo fOJ

o

-SO'-------L­ o 5

If

-10

-15

15

-20 '---�-�'----�-�'--�-�--�-� 0.4 -O.S -0.2 0.2 O.S 0.6 -0.6 -0.4 o

Pitch Angle Rate (rad/sec)

Figure 16 - Time histories of pilot input torque and DC servo-motor generated torque (linear passive feel system)

Figure19 - Hysteresis in the plant dynamics.

8

Plant's open loop response to a step pilot force (no control input) is seen in Figure 18. Hysteresis is observed in plant dynamics and is in agreement with the existing literature (Figure 19).

The simulator stick was excited with a constant force in trim conditions of the aircraft under study by use of SIMULINK™ STEP BLOCK. Precision closed-loop control performance was visited. Through an ergonomics viewpoint and by the virtue of this research, it has been figured out that both weak and strong short-acting (transient) pilot control inputs result in consecutively weak and strong chaos followed by limit cycle. This contributes to generating uneasy feelings on passenger seats. However, both strong and weak forces performed during a considerable time interval result in an exponentially stable dynamic response from the stick. The nonlinear controller was robust against the measurement noise. However, the measurement noise made the required current to exhibit a noisy trend. To be summarized is the great applied insight on a high-tech simulator control loading system, yielded by this study.

It should be noted that the pilot input forces through an on-line human machine interaction are complicated functions of time and we were unable to realize them in this theoretical study, where only step pilot forces were used for simulation purposes. However our PCL system is reliable in taking into account the most general pilot force inputs in a physical simulator system built on a base of this study. The required control currents that are to be applied to the torque-motor are seen in Figures 20-a and 20-b where it is observed that the intensity of measurement noise is in direct connection with the intensity of noisy trends in the required currents.

ACKNOWLEDGMENT

The authors would like to thank National Council for Science and Technological Development in Brazil (CNPq) because of its financial support for this paper to be published in IEEE Aerospace Conference.

200

'E g!"

()

100 0 -100 -200

(\

II

\

o

0.5

I

\)

k

� � ���'YVc/' 1.5

2

2.5

3

3.5

REFERENCES

[1] Walter J.F. "Development of a Variable Control Feel Simulator". Aerospace IEEE transactions on 1(2) Aug 1963, pp. 647-658.

4

lime(sec) 200 r---.----r---.--.---�--_.--r___.

[2] Rinaldi Beckham., "Digital Control Loading- a Modular Approach". American control conference 22-24 June 1983, pp. 803-806. [3] Wayne C Durham., "Nonlinear Model Following Control Application to a Flight Simulator Control Loader". AIAA -3308 1989.

1.5

Figures 20-a, 20-b - Required control current in cases of low-level of measurement noise (up) and high-level of measurement noise (down)

[4] T. Scott Davis Bruce Hildreth., "Problems in Validating Control Feel in Simulators". Science Applications International Corporation, Lexington Park, MD; AIAA­ AIAA Modeling and Simulation Technologies Conference and Exhibit, Austin, Texas, Aug. 2003, 1114.

6. SUMMARY

The theoretical challenges encountered in the design process of a nonlinear control loader system for a flight motion simulator were overcome. The design process was a modified and updated version of that considered by Nam and Hong. The results achieved by the numerical simulations are logical and in complete agreement with the researches in the existing literature. The limit cycle oscillations and as well chaotic dynamics of the control surface and the stick's non-minimum phase behavior were observed that commit to unease of passengers on the aircrafts seats. For fair tracking performance, the real stick and that belonging to the simulator should be of a similar passive dynamics. If this is violated, poor closed­ loop dynamics together with high required electric current results that damages the servo-mechanical subsystems.

[5] Yoonsu Nam, Sung Kyung Hong., "Active Stick Control Using Frictional Torque Compensation". Sensors and Actuators A (117) 2005, pp. 194-202. [6] Arno Gerretsen Max Mulde M Van Passen., "Comparison of Position-Loop, Velocity-Loop and Force-Loop Based Control Loading Architectures". Delft University of Technology, Delft; Delft University of Technology, Delft, AIAA Modeling and Simulation Technologies Conference and Exhibit, San Francisco, California, 15-18 Aug 2005, pp. 6300.

9

[7] Joon-Ho Park, Tae-Kue Kim, Tae-Sung Yoon, Gun­ Pyong Kwak and Seung-Chae Jeong., "Systematic Control Parameter Tuning for Actuator in Control Loading System". IEEE, 2006.

BIOGRAPHY

Saeb AmirAhmadi Chomachar

was born on July 1984 in Rasht. Iran. He is currently a PhD student in Mechanical Guilan at Engineering University. Rasht. Iran. He received an MSc. in Aerospace Engineering (Flight Mechanics) from the Center of Excellence in Flight Dynamics and Controls at the Aerospace Engineering Department of the AmirKabir University of Technology (AUT). Tehran , Iran. 2011. As well, he holds a B.Sc. in Mechanical Engineering (Mechanics of Solids) from the University of Guilan. Rasht. Iran. 2007. He served as a reviewer for the IEEE (Aerospace and Electronic Systems. Transactions on). AIAA (Journal of Guidance. Control and Dynamics) and ASME-IMECE2012. His research interests are Flight Dynamics and Controls in general and particularly the Aeroservoelasticity.

[8] Zheng Shutao, Huang Qitao_Cong Dacheng, Han Junwei., "Experiment and Study of Control Loading System in Flight Simulator Based on RCP". IEEE 2007. [9] Domenico P. Coiro_ Agostino De Marco Fabrizio Nicolosi., "A 6DOF Flight Simulation Environment for General Aviation Aircraft with Control Loading Reproduction". AIAA Modeling and Simulation Technologies Conference and Exhibit Hilton Head, South Carolina 20-23 August 2007, 6364. [10] Rodger A. Mueller Gordon H. Hardy., "Pilot Force Measurement with Inertia and Gravity Compensation". AIAA Modeling and Simulation Technologies Conference and Exhibit Hilton Head, South Carolina 20-23 August, AIAA Paper number 6563. [11] Rodger A. Mueller., 2008 Optimizing the Performance of the Pilot Control Loaders at the NASA Vertical Flight Motion Simulator AIAA Modeling and Simulation Technologies Conference and Exhibit, Honolulu, Hawaii 18-21 August 2007, paper number 6349.

Sajad Azizi

is currently a PhD student at Federal University of Minas Gerais (UFMG) and his research activity is in nonlinear systems and control. He has passed his undergraduate and graduate studies at Amirkabir University of Technology in Flight dynamics and control. Before starting his PhD he worked more than 4 years at Amirkabir research center where he was a control expert and the director of control division. He is currently a reviewer of ISA Transaction journal. His research interests include Modeling and simulation of rigid body dynamics. Linear and nonlinear control. Optimal control. Fuzzy system. Optimization. System identification. Actuator design. Estimation. Genetic algorithm. Aircraft and spacecraft design. 3 DoF spacecraft simulator laboratory.

[12] A. Ramasubramanian, L. Ray., "Adaptive Friction Compensation Using Extended Kalman-Bucy Filter Friction Estimation: a Comparative Study", in: Proceedings of the American Control Conference, 2000, pp. 2588-2594. [l3] 1. Amin, B. Friedland, A. Harony., "Implementation of a Friction Estimation and Compensation Techniques", IEEE Control Syst. Mag. 1997, pp.71-76. [14] B. Friedland, Y. Park., 1992. "On Adaptive Friction Compensation", IEEE Trans. Automatic Control 37 (10) pp. 1609-1612. [15] M. Feemster, P. Vedagarbha, D.M. Dawson, D. Haste., "Adaptive Control Techniques for Friction Compensation", in: Proceedings of the American Control Conference, Philadelphia, Pennsylvania June 1998, pp. 1488-1492.

10

ApPENDIX

awb = Wing body angle of attack a

= Angle of attack

C

= Elevator aerodynamic mean chord = Linear damping coefficient of the plant = Elevator deflection angle = Downwash

&0

= Downwash constant

G

= Gearing ratio

It

= Tail incidence angle

lw

= Wing incidence angle

Jeq ,stick

= Pilot stick moment of inertia

K1 K2

= Linear spring constant = Nonlinear spring constant

Kt

= Torque constant of BLDC motor

KhJ = Damping coefficient of the control surface

Lstick = Length of stick LVDT= Linear variable distance transducer N = Gear reduction ratio S = Control surface wet area

T pilot = Pilot torque Tservo = Servomotor generated torque TAero = Aerodynamic torque on the hinge-line of the control surface

. . Tpric =FnctlOnal Torque V = aircraft velocity relative to wind

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