Optimal and pid controller for controlling camera’s position in unmanned aerial vehicles

International Journal of Information Technology, Modeling and Computing (IJITMC) Vol.1,No.4,November 2013

OPTIMAL AND PID CONTROLLER FOR
CONTROLLING CAMERA’S POSITION IN
UNMANNED AERIAL VEHICLES
MOHAMMAD ABDULRAHMAN AL-MASHHADANI
Department of Information System and Technology, Belarusian National Technical
University,Minsk ,Belarus

ABSTRACT
This paper describes two controllers designed specifically for adjusting camera’s position in a small
unmanned aerial vehicle (UAV). The optimal controller was designed and first simulated by using
MATLAB technique and the results displayed graphically, also PID controller was designedand
simulatedby using MATLAB technique .The goal of this paper is to connect the tow controllers in cascade
mode to obtain the desired performance and correction in camera’s position in both roll and pitch.

KEYWORDS
Unmanned Aerial Vehicles, System Control, Servo Motor, PID Controller, Optimal Control

1. INTRODUCTION
Unmanned aerial vehicle is remotely piloted or self piloted (without pilot) aircraftwhich can carry
many different types of accessories such as cameras. In many types of UAV’s servo motors are
using for adjusting movements, sensors and communications equipment [1].Control of the
movements and flying systems in the UAV is customarily done by using the microcontrollers
optimal controllers or conventional PID control techniques.The main objective of the work
reported in this paper is to evaluate the performance of each of optimal and PID controllers
separately and will show the characteristics of the each of PID and optimal controllers, and which
controller is better for obtaining the desired response.

2. SERVO MOTORS
Using the servomotor is helpful to correct the performance of a mechanism because it uses error
sensing feedback. The servo motors usually used in the systems where the feedback or error
correction signals help control mechanical position or other parameters[3]. Some servos also have
rotation limit of 360°, but servos do not rotate continually. The Servos are used for precision
positioning. They are used in many fields like toys, cars and UAVs. Servos are commonly
electrical or partially electronic in nature, using an electric motor as the primary means of
creating mechanical force. Other types of servos use hydraulics, pneumatics, or magnetic
DOI : 10.5121/ijitmc.2013.1403

25

principles [3]. Usually, servos operate on the principle of negative feedback, where the control
input is compared to the actual position of the mechanical system as measured by some sort of
transducer at the output.

2.1. Modeling a Simple Servo motor
DC servo motorhas an output shaft with an inertial load(J) on it.Theamount of frictions in the
bearings of the motor and load represented in our paper by the constant (b).The input voltage u(t)
is transformed by the motor into a torque T(t) in the motor output shaft. If we assume that (h) is
the angular position of the servo output shaft, then the torque balance can be written as:
J*ḣ+b*ḧ=T(t)

(1)

Where:
(ḣ)- Is the shaft velocity, (ḧ)-is the shaft torque
The control objective is to control the shaft position (h) or the shaft velocity (h) to be some desire
value. The input voltage u(t) is related to the torque T(t) by a gain (K) and the inertia load divided
by the friction coefficient is referred to as the system time constant (τ) where:
τ =J/b

(2)

So the system model becomes:
τ* ḣ+ ḧ=K.u(t)

(3)

The linear part of the servo system model can be put in the transfer function form:

y (s )  s (K 1) u (s )
s

(4)

Where y(s) is the output shaft position and u(s) is the motor input. K is the system gain and τ.
Where :(tau) is the time constant.
Let’s go now to the UAV and will show and explain the scheme for controlling the rotational
position of the camera for roll and pitch movements of an unmanned air vehicle (UAV).Roll error
and pitch error signals obtained from gyro systems in the UAV are subtractive combined with roll
and pitch position signals, to generated control signals to be applied to rotate the camera in a way
that compensates for the roll and pitch movements of the UAV, and effectively isolates the
camera from roll and pitch movements of the UAV and the camera will provide a good photo or
video without loss in information (Fig. 1).

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Figure1. Control system scheme for the camera in UAV

2.2. The Flight Controllers in UAV
The better method for controlling of a small UAV is to use the flight controller as consisting of
two cascaded controllers as shown in Fig.2.The firstcontroller, is designed to control the attitude
which takes desired attitude angles as inputs and generates the actuator commands that will result
in the desired attitude. The secondcontroller, which controls the slower translational rate
variables, takes desired velocity or position as input and generates desired angels to the inner
loop.

Figure 2.Overall control scheme

3. SYSTEM CONTROL REPRESENTATION
The transfer function of the servo motor used in our experiment as shown below:
firstwe will view the open-loop step response for the system, Then create a new m-file in Matlab
and add in the following code:
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num=1050; den=[1 30 0]; step(num,den)
The DC gain of the plant used the above transfer function is () , so 10.5 x 10^5 is the final value
of the output related to a unit step input. This corresponds to the steady-state error of 1.5x10^5,
quite large indeed. Furthermore, the rise time is equal to the settling time.The goal of this
problem is to obtain a controller to give the following parameters:
•
•
•

Fast rise time
Minimum overshoot
No steady-state error

Modeling the optimal controller
The optimal controller equation in the Z-domain is given in the equation below:

1 b 1

z

b 2

1

z

2

W ( z) K
0 (1 

)(1 a1

1

z

1

z

)

Where: K, b1, b2, a1 are coefficients defined as below:
ab

K 0

;

 (1 A )(1 B)
b1( A  B);

b2 AB;

bBaA( a  b ) AB
a1
( aB )(1 A )(1 B)
Ae

ah

;Be

bh

; h 0.001sec

The modeling of the controller using MATLAB Simulink is as shown in the Fig.3

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Figure 3.Optimal controller design simulink

After running this model we can see the output signal as shown in Fig.4:

Figure 4.Output signal of the optimal controller

3.2. The PID Controller modeling
The transfer function of the PID controller is:

G(S )  K p 

Ki
 K d .s
s

Where:
Kp = Proportional gain ,Ki= Integral gain ,Kd = Derivative gain
The proportional gain (Kp) will reduce the rise time and will reduce (but never eliminate) the
steady-state error. The integral gain (Ki) will eliminate the steady-state error, but it may make the
29

transient response worse. The derivative gain (Kd) will increase the stability of the system, reduce
the overshoot, and improve the transient response.Performance criteria were specified as:
Rise time tr0.1
Settling time
ts0.5
Maximum overshoot Mr0.5%
Steady state error (e) 0.5%
Running the program and we will get the needed parameters. From the parameters tuning we
can get:
Kd = 0.008672, Ki =0.008672, Kp = 0.114
Fig.5 shows the PID controller designed by using MATLAB Simulink where all of controller
coefficients were adjusted.

Figure 5.PID control system designed in MATLAB Simulink

30

After running this simulink, we can see the signal shown in Fig.6

Figure 6.Output signal in the case of PID

By comparing the signal output in case of optimal controller (Fig.4) and PID controller (Fig.6) we
obtain the signals shown in Fig.7.

Figure 7.output signals compared between the 2-controllers

We can summarize the performance of the optimal and PID controllers obtained by our
experiment as in the table.1 shown:

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Table 1. OPTIMAL AND PID OUTPUT SIGNAL CHARACTERISTICS

controller
optimal
PID

RISE OVERSHOOT SETTLING
S-S
TIME
TIME
ERROR
0.2
0.2

none
none

0.4
0.57

0.4%
0.53%

Let’s now campaign the 2-controller as we explain above in cascade mode to get the desired
output signal and the desired output voltage from the servo motor to give the right signal to the
camera position (Fig.8).

Figure 8.output signal for combining optimal and PID controllers

As we see in fig.8 the desired performance well obtained and this refer that the combined of the
optimal and PID controllers in cascade mode give the performance better than if they worked
separately.

4. Conclusions
• Flight control of UAV is done by using tow controllers instead of one and the tow controllers is
designed by using MATLAB technic .
• Optimal controller satisfies the performance requirements. But, PID controller was unable to
give fast rise time and it failed to satisfy the performance requirements.
• Combining the optimal and PID controllers as we suggested in this paper in cascade mode will
give the desired performance and this will make no loss in information in the cameras movements
in both roll and pitch.

32

ACKNOWLEDGMENTS
I would like to acknowledge my professor Alexander A.Lobaty and Mr.A.G.Streshnov for their
big assistants.

REFERENCES
[1]

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[2] Rahul Malhotra, Narinder Singh, Yaduvir Singh, SOFT COMPUTING TECHNIQUES FOR
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[4] Jyotsna’sBlog,SERVOMECHANISMS AND ITS APPLICATIONS,July 2009
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[6] Servo control systems: DC servomechanisms. Control-systems principles.co.UK.
[7] Downs, Stuart G., unmanned air vehicle servoing dipole, Northrop Grumman Corporation Los
Angeles, CA,2004
[8] PID control-National Instrument , http://www.ni.com/white-paper/6440/en
[9] Tsai-JiunRenand Tien-ChiChen, Motion control for a two-wheeled vehicle using a self-tuning PID
controller, Control Engineering Practice Volume 16, Issue 3, March 2008, P 365–375
[10] Wallén, A. (2000): “Tools for Autonomous Process Control”. PhD, Department of automatic Control,
Lund Institute of Technology, Lund, Sweden.
[11] Panagopoulos, H. (2000): “PID Control; Design, Extension, Application”. PhD thesis, Department of
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[12] ieniazek, J. Software-based Camera Stabilization on Unmanned Aircraft, Aircraft Engineering and
Aerospace Technology: An International Journal, Vol. 75, No. 6, 2003.

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Optimal and pid controller for controlling camera’s position in unmanned aerial vehicles

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