Design and Simulation of a Basic Controller for Unmanned Aerial Vehicle

Abolfazl Sheibani and Mohammad Ali Pourmina

Department of Mechateronics Engineering Islamic Azad University-Science and Research Branch (SRBIAU)

Tehran, Iran afshin_shei@yahoo.com pourmina@srbiau.ac.ir

Abstract—In this paper we discuss the design issues and the corresponding systematic sequence of events related to a basic controller for an Unmanned Aerial Vehicle (UAV). To this end, we first present the details of a basic PID controller, We then describe the equations and investigate the problems of how these equations will be approximated for determining the dynamic longitudinal movement of UAV. After specifying the model of the system and clarifying the details of the designed algorithms, we will identify the gains corresponding to the coefficients of the PID controller using the well-known AeroSim simulator software. The computed gains and the results drawn from the simulation process will be used to analyze the UAV stability against important metrics such as air speed and pitch angle.

Keywords- Unmanned Aerial Vehicle (UAV), PID Controller, AeroSim Simulator, Stability of flight, longitudinal controller, Gain Scheduling.

I. INTRODUCTION In order for an UAV to be automatically flied, all the flight

fixes need to be defined for the autopilot system. In this manner, the autopilot system will be able to control the heading, the altitude, and the speed of the UAV compared to the air speed. The autopilot also needs noticeable capabilities for accepting commands corresponding to maintenance of the roll and pitch angles. To achieve this goal, one needs to use a nested structure for the basic PID controller. The commands relevant to elevator, aileron, rudder and throttle will be controlled by an internal closed-loop PID controller in such a way that sufficient stability in roll and pitch axis could be met. The altitude and heading of the UAV will also be controlled by the external loops in such a way that the necessary values for controlling the internal loops of the basic PID controller will be provided.

In regard to above explanations, we can conclude that the autopilot exploits two independent basic PID controllers [1]: one is the lateral controller and the other is longitudinal controller. In this paper, we will investigate the longitudinal controller for the UAV. The rest of the paper is organized as follows: Section II presents the UAV longitudinal controller, Section III presents the experimental analysis of the system, and Section IV presents our conclusions.

II UAV LONGITUDINAL CONTROLLER In this section, we developed the model for UAV

longitudinal controller. This controller is used for controlling speed, pitch angle and the altitude of the UAV. The symbols

used in this paper are defined in Tables 1 and 2. For the sake of illustration, we have shown these specifications in Fig. 1.

Table 1. Definition of Parameters

Parameter Explanation

pk Proportional gain

ik Integral gain

dk Derivative gain

e∂ Detour angle of Elevator

Table 2. Used symbols

Roll axis Pitch axis Yaw axis Angular shift � Angular speed p q r

Speed components u v w

Aerodynamic force

components X Y Z

Aerodynamic moment

components L M N

Axis Energy moments IX IY IZ

Energy Multiples IYZ IXZ IXY

Fig. 1. The specifications and the effects of the various parameters on a

typical UAV.

2011 International Conference on Computational and Information Sciences

978-0-7695-4501-1/11 $26.00 © 2011 IEEE

DOI 10.1109/ICCIS.2011.126

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Fig. 2. The elevator control loop of PID controller.

Fig. 3. The throttle control loop of PID controller.

Fig. 4. The altitude control loop of PID controller.

The controller is composed of three internal loops and two external loops. The internal loops were designed to give directive instructions for the UAV elevator and the throttle, and the external loops were designed to adjust the pitch angle. The first internal loop, based on the created error in the UAV pitch angle, directs the UAV elevator. In addition, in order to maintain the pitch angle, the first internal loop will control the elevator. The second internal loop, according to the angle, will change the rate of pitch axis of the control elevator. Thus, using this loop one can control and eliminate turbulences in the UAV pitch axis. Finally, in the third internal loop the controlling of the air speed will be done by adjusting the instructions issued for the throttle. The output of this loop causes the throttle to increase or decrease the thrust. The first external loop according to the aggregated error in UAV altitude, directs pitch angle while the second external loop's task is to control the air speed in regard to the pitch angle. This loop is used for maintaining the air speed for ascending or descending mode of the UAV. In order to design the PID controller, we first needed to analyze the longitudinal model of the UAV and then proceed to specify the relevant gains [3, 5]. The state of the longitudinal model of the UAV is shown in Eq. (1), as follows:

0( ) 0( ) ( ). ( , ), 0, tt t f u t x= ≥ =X A X X (1)

The coefficients matrix ( )tA in Eq. (1) contains stability coefficients of the system (moment and aerodynamic force of the UAV) which can be estimated from Eq. (2):

1

2

0

0 0 0( )

0 0 0

0 0 1 0 0 0 0 0

u w q w e

u w w e

e

x x x x x

z z z z

qu w w

y y y y y

F F F g c F F

F F c F Ft MMM M M

I I I I I

δ

δ

δ

− −����== �����

A

�

�

�

(2)

Lewis and Stevens of [2] have shown that:

[ ]( )t u w q θ=X (3)

And,

( , ) Teu u w q uq wq wθ δ= � �� �F X � (4)

After identifying the dynamic equation of longitudinal movement of the UAV, the PID controller gains can be specified. Let the symbols ( pk , ik , dk ) denote these gains. Now, we can adjust the error rate and can stabilize the system by means of Eq. (5), as follows:

. . .dp i dtnew Input k error k error error= + +� (5)

Now the design process of control portion of longitudinal axis of the UAV is completed. Please note that the elevator is the control surface, the input of PID controller is the angle of detour of elevator ( eδ ), and the pitch angle will be the output. The rate of changes in the above equation can be given by Eq. (6), as following:

. . . d errorp i i dte k error k error k θθ θ∂ = + + (6)

In Eq. (6), the term errorθ results from both the difference of targetθ and the outputθ [7].

Finally, we can represent the behavior of UAV according to the amount of the changes in the coefficients of the PID controller. This behavior is shown in Table 3.

Table 3. The behavior of the UAV based on coefficients of PID controller

PID controller coefficient

Rise time overshoot Setting time Error

pk Decrease Increase Low changes Decrease

ik Decrease Increase Increase Increase

dk Low changes Decrease Decrease Low

changes

832

Fig. 5. Simulation of PID Controller.

Fig. 6. The simulated model for open loop of PID controller.

By simulating the designed UAV system with AeroSim software and also by using MATLAB toolboxes, we can obtain the rates of basic PID controller gains which adjust the air speed and the pitch angle. In addition, we can investigate the stability of the UAV from the simulation results [4].

III SIMULATING the UAV WITH PID CONTROLLER In order to simulate the system, we have used AeroSim

software. To this end, we have used the Aerosonde module which represents a real model of UAV. We have assumed that the thrust speed of the UAV is 25 m/sec and the pitch angle is assumed to be equal to 1.7 degree. At first, we design the open loop system. The simulated model for open loop of PID controller is shown in Fig. 6. The results of this simulation show that the system adjusts the pitch angle in 1.2 degree with a high vibration and swing. Also the air speed is adjusted in 25.5 m/sec. Based on the previous researches, these values are not desired outcomes at all.

By the help of our designed basic PID controller, we then performed the same experiment on a closed-loop system model. The acquired results revealed that the pitch angle is adjusted in 1.7 of target angle with a steady movement (without any vibration). The air speed was also adjusted to a proper speed of 25 m/sec.

Finally, the values of basic PID controller coefficient gains are shown in Table 4 according to the acquired results of the closed loop system simulation [4].

Table 4. The Gains of basic PID controller resulting from the closed loop

system

Gain type Value

pk -0.03

ik -0.005

dk -0.5

For the sake of clarification, we took the effects of wind into account in our simulation. We assumed that the wind is blowing at 25 m/sec from the South and 10 m/sec from the East.

A closer look at the literature revealed that we can illustrate the wind's effect as a sequence of noises and vibrations, and the swings in air speed and pitch angle charts [1, 7]. The results are shown in Fig. 13 and Fig. 14, respectively.

Fig. 7. Pitch Angle plot for open loop controller.

Fig. 8. Air speed plot for open loop controller.

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Fig. 9. Simulated model of closed-loop PID controller.

Fig. 10. Pitch Angle plot for closed loop UAV controller.

Fig. 11. Air speed plot for closed loop UAV controller.

Fig. 12. Simulated model of closed-loop UAV controller in the presence of

wind effects.

Fig. 13. Pitch Angle plot for closed loop UAV controller in the presence of

wind effects.

Fig. 14. Air speed plot for closed loop UAV controller in the presence of wind

effects.

IV CONCLUSIONS In this paper we investigated the major issues concerning

the design of an UAV with a PID controller. We provided closed-form expressions for the equations and using these equations conducted experiments to analyze the performance of the system both in closed and open-loop system architectures. The major contribution of this paper is that we took into account the environmental conditions, such as wind effect, in our simulations. We also investigated the stability of the UAV against important metrics such as air speed and pitch angle.

The experimental results showed that the gain coefficients of the PID controller were designed in such a way that lead to a better controlling of the UAV, even with optional air speed and pitch angle.

REFERENCES [1] D. pisano, "Linear Control Design for Osprey UAV Control System

Theory final Project", University of Florida, 30 Apr. 2009. [2] F. L. Lewis, and B.L. Stevens "Air Craft Control And Simulation, 2nd

Edition, vol.2. Wiley, 2003, pp. 143-327. [3] J. wang, and N. Sundararajan, "A non linear flight Controller Design for

Aircraft", Nan yang Technological University, 14 Feb. 2000. [4] L. J. HRNG, "AM25 Unmanned Air Vehicle Flight Control", National

University of Singapore, 2005, pp. 33-41. [5] R.S. Christiansen, "Design of an Autopilot for Small Unmanned Aerial

Vehicles", a thesis submitted to the faculty of Brigham Young University, Aug. 2004, pp.9-25.

[6] Y. Wu, "Development and Implementation of a Control System for a quad rotor UAV ", Thesis, University of Applied Science Ravens burg Weingarten Germany, March 2009, pp. 35-63.

[7] Electronic Publication: User guide Aerosim, www.u_anamics.com.

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