Antenna Azimuth Position Control System using PIDController & State-Feedback Controller Approach

International Journal of Electrical and Computer Engineering (IJECE)
Vol. 8, No. 3, June 2018, pp. 1539~1550
ISSN: 2088-8708, DOI: 10.11591/ijece.v8i3.pp1539-1550  1539
Journal homepage: http://iaescore.com/journals/index.php/IJECE
Antenna Azimuth Position Control System using PID
Controller & State-Feedback Controller Approach
Aveen Uthman1
, Shahdan Sudin2
1
Departement of Communication Engineering, Sulaimani Polytechnics University, Iraq
2
Faculty of Electrical Engineering, Universiti Teknologi Malaysia, Malaysia
Article Info ABSTRACT
Article history:
Received Jan 9, 2018
Revised Mar 20, 2018
Accepted Mar 28, 2018
This paper analyzed two controllers with the view to improve the overall
control of an antenna azimuth position. Frequency ranges were utilized for
the PID controller in the system; while Ziegler-Nichols was used to tune the
PID parameter gains. A state feedback controller was formulated from the
state-space equation and pole-placements were adopted to ensure the model
design complied with the specifications to meet transient response.
MATLAB Simulink platform was used for the system simulation. The
system response for both the two controllers were analyzed and compared to
ascertain the best controller with best azimuth positioning for the antenna. It
was observed that state-feedback controller provided the best azimuth
positioning control with a little settling time, some value of overshoot and no
steady-state error is detected.
Keyword:
Azimuth position control
system response
MATLAB simulation
PID controlle
Pole placement
State-feedback controller
Zeglior-tunung method
Copyright © 2018 Institute of Advanced Engineering and Science.
All rights reserved.
Corresponding Author:
Aveen Utman,
Departement of Electrical and Computer Engineering,
Sulaimani Polytechnics University SPU,
Sulaimaniyah, Kurdistan Region, Iraq.
Email: aveen.hassan@spu.edu.iq
1. INTRODUCTION
The issue of antenna azimuth position control has become one of the many aspects that have drawn
the attention of researchers in the control of antenna placement [1]. These interests are due to the major roles
and enhance performances that would be derived from correct azimuth positioning of an antenna. Several
techniques were proposed to achieve an optimum control of the azimuth position but such positioning
remains a control challenging problem.
Hoi et al [2] conducted a research on satellite tracking using fuzzy proportional integral derivative
PID control techniques and the conventional PID controller to get the best in performance on satellite
tracking. Both the step response in the two techniques presented evidence of chattering phenomena which
may lead to poor and weak result and conclusion respectively. Xuan et al [3] introduced a discrete control
system using PID controller to achieve a better control on satellite antenna angle deviation. The shortcoming
of this work is lack of proper tuning of the PID gains for precise results. Soltana et al [4] considered the case
of overseas satellite telecommunication where the control system was applied to an on-board motorized
antenna; the separate controller was designed to detect a fault in the satellite control. Though the controller
was not robust enough to enable handle the detected fault in the controlled signal. The research of [5] and
that of [6] is basically using PID and Linear Quadratic Gaussian (LQG) for the antenna azimuth position
control system; both researchers were faced with similar shortcomings of degraded performance due to
system nonlinearities and delay in reaching setpoint. A much better settling time and less overshoot were
achieved by [7] where the Fuzzy logic controller (FLC) and a self-tuning fuzzy logic controller (STFLC) was
utilized in the design but chattering phenomena were reported as the setback. All these make the antenna

 ISSN: 2088-8708
Int J Elec & Comp Eng, Vol. 8, No. 3, June 2018 : 1539 – 1550
1540
azimuth positioning a challenging control problem. There is need for a high-performance controller; hence
the motivation of this paper is to come up with a better solution to the mentioned problems.
In this paper, the concept of PID and feedback controller will be presented to handle the issues
related to the antenna azimuth positioning as well as to prevent the said lapses experienced in literature. The
two controllers will be compared to enable justify the best controller with high azimuth positioning with less
possible positioning, overshoot settling time and chattering. Section 2 of this paper describes the
mathematical modeling of the proposed controllers. An analysis on the controllers is shown in Section 3.
Section 4 concludes with the obtained results.
2. MODELING OF THE SYSTEM
Two potentiometers are included in aforementioned system for controlling the position of telescope
antenna; one is utilized at input and one at output as transducer, a power amplifier, a preamplifier, a load and
a motor. The overall system includes 5 subsystems, and each subsystem has a related transfer function.A
more detailed of provided schematic diagram is shown in Figure 1. As well as, Figure 2 represents the system
block diagram for controlling the position of antenna azimuth.
Figure 1. Schematic diagram of antenna-azimuth position controlling system
Figure 2. Block diagram of antenna-azimuth position controlling system
The process starts with the turning of input angular rotation by the potentiometer in to a voltage.
Similarly, in the output region, the potentiometer converts the rotation angle to voltage, and returned back to
the input with a feedback. The alteration between the input and output voltage is increasing with the effect of

Int J Elec & Comp Eng ISSN: 2088-8708 
Antenna Azimuth Position Control System using PID Controller & State-Feedback … (Aveen Utman)
1541
gain and signal. While mistake or error becomes zero, the motor is not receiving any voltage and will not
start [8].
Figure 3. Block diagram in detail of antenna azimuth control system
Figure 3 describes the comprehensive block diagram of the system for controlling the position of
antenna.Gears as well as the load are attached to the motor, in this system the antenna is considered as a load.
The deep derivation of the motor transfer function could be found in [1], and the final model transfer
function:
⁄
Where, Ra is the motor resistance, Kt and Kb are the back EMF and torque constant of the motor respectively.
The components of the system including (dampening and inertial) are linked to the motor by gears sets. This leads
to changing of their operative values which is realized with the motor and have to be inserted within the
mathematics.
Kg=N1/N2=0.1
In the above equation, N1 and N2 represent the gear teeth.
Where = is the load inertia at Ɵo. The equivalent viscous damping, , at the armature is:
Where is the load viscous damping at Ɵo. From the problem statement, = 0.5 N-m/A, Kb = 0.5 V-s/rad, and
the armature resistance Ra = 8 ohms. So, So, motor and load the transfer function would be:
(1)
Next step of determining motor transfer function, the gear ratio need to be multiplied with equation 1 in
order toget the ratio of load displacement to armature voltage:
(2)
Parameters for preamplifier, power and gears of above block diagram are given in Table 1.
In Table 1, gain value “K” is unknown which represents the preamplifier gain. The result block diagram
is shown for each transfer function in Figure 4. Consecutively, the final closed-loop system model will be

 ISSN: 2088-8708
1542
as Equation (3):
(3)
Table 1. Parameters of Antenna Block Diagram
Parameters Configurations
K ----
Kpot 0.318
Ra
K1
Kg
100
100
0.1
Routh-Herwitz criterion could be utilized in to obtain the preamplifier gain value “K” which makes the
system reaching stability. According to this this criterion, system will could be considered as stable in term of
response if the value of gain “K” taken in the range 0-262.3 [9]. Depending on [10], better value of “K” within the
mentioned range is 31.6 since best response is gotten with that value.
Figure 4. The related model of every subsystem of antenna azimuth control system
3. PID CONTROLLER
Proportional-integral-derivative (PID) controllers could be considered as a common used controller
in practically manufacturing control applications [11], [12]. This controller offers simplicity, versatility,
reliability, flexibility and speed, which makes this controller very popular [13]. The classic PID block
diagram is represented in Figure 5:
Figure 5. The classic block diagram of a process under PID

1543
The PID controller in parallel form [14] is represented in the following equation:
∫ (4)
Where Kp is proportional gain, Ki is integral gain, Kd is derivative gain and e(t)= error. The PID model in
Frequency domain or transfer function is represented in the following equation:
(5)
3.1. Ziegler Nichols tuning method
In 1942, Ziegler-Nichols introduced a rule which could be followed in order to tune PID controller
and has named as Z-N tuning rule [15]. Ziegler-Nichols algorithm has the best performance with fastest rise
time, settling time and was able to restore the system back to normal operating condition in a short time when
subjected to disturbance compare to Cohen & Coon controller and Hagglund-Astrom algorithm settings.
Values of PID controller gain could be tuned according to zeglior tuning rule table [16]. The presented values
might be optimal values and further adequate tuning is required in some case in order to gain better
performance for the system. Depending on the system purpose and application, The PID-controller type is
selected to be applied to any system.
3.2. Finding the transfer function of overal system after PID control
As mentioned earlier the overall model.
(6)
By taken K =31.6 according to [10]. Assuming process transfer function, Gp(s)= (Ɵo(s))/(Ɵi(s)) and the
controller transfer function is Gc(s), so:
(7)
(8)
Figure 6. The closed-loop system diagram after adding controller block
Figure 6 illustrates the closed loop system diagram after adding the controller.According to figure6, the
closed- loop model is going to be situated as Equation (9) below:
(9)
3.3. Design of the response the closed-loop using PID-controller
The simulation block is shown in Figure 8 bellow. This is represented in term of input signal (θi),
output signal (θo) and the error (e-theta). PID controller is used to decrease amount of overshoot in the
response. Figure 7 shows the complete system diagram after introducing PID-controller.

 ISSN: 2088-8708
1544
Figure 7. Closed-loop system design with PID
3.4. Tuning of PIDcController via Zieglior-Nichols method
Firstly, we increase the value of Kp until the system response reach instability point or it shows
sustained oscillation, this value of kp known as kc, which is equal to 80 in our case. Figure 8 illustrates the
response when kc=82 :
Then we found value of Tc in the graph by measuring the period from peak to peak which is equal
to 0.5 in our case. Then the value of Kp, Ti and Td are founded according to Ziegler table [16], by
substituting each of kc and Tc. We get, Kp=16.4, Ti=0.15 and Td =0.25.Worth mentioning that the obtained
values of Kp, Ti and Td could not be considered as optimal and in order to achieve best performance for the
sys-tem more tuning is needed. The PID controller type could be selected depending on the application of the
system and designer goal as well. Figure 9 shows result of the system response.
Finally the acceptable response with small amount of over-shoot has been acquired from Ziegler-
Nichols PID tuning method. More to the point, by substituting the value of kp, Ti and Td in Equation (9), the
final closed loop transfer function will be as shown in Equation (10).
(10)
Figure 8. The response of the system with PID
controller (kp = 82, kd = ki = 0)
Figure 9. Closed loop system response after applying
PID controller when Kp=16.4, Ti=0.15 and Td=0.25

1545
4. DESIGN OF STATE-FEEDBACK CONTROLLER USING POLE-PLACEMENT APPROACH
State space representation is very powerful techniques used in analyse and model varied systems,
since it could be applied to nonlinearities and multiple-input, multiple-output systems. The state-feedback
design technique is to create a compensator in the feedback path with the plant that has the correct additional
poles and zeros to meet a desired transient response and steady-state error. The plant's characteristics may be
required to change by using a closed-loop control system, in this process a controller is considered to locate
the closed-loop poles at looked-for place. The mentioned method is called pole-placement technique. The
state-space method using state feedback offers adequate number of parameters of the controller design to
transfer all the poles of closed-loop independently of each other [17].
4.1. Topology for pole placement
Normally the state space equation of a plant is:
Figure 10 displays the State-space map graph of a plant.
Figure 10. A plant State-space graph
In the topology of state-variable feedback, the state-variables are feedback to summing junction and
then to u through gains meaning that each state variable connects to a gain In order to harvest obligatory
closed-loop pole val-ues, could be adjusted. Figure 11 presents a plant state-variable feedback graph.
̇
Figure 11. A plant state-variable feedback graph
4.2. Controller design procedure
Many steps need to be followed in order to apply pole placement methodology; these steps will be
presented below.
First of all, the plant model transfer function need to be con-verted to state-space representation as illustrated
in [1]. Lets the plant given as:
The state-space representation will be as Equation (11) and the characteristics quationwill be as
Equation (12).

 ISSN: 2088-8708
1546
.
0
0
B;
0100
0010
A
0121



























 baaaa no





(11)
 001C 
(12)
Now form the closed-loop system by feeding back each state variable to u, forming Equation (13):
(13)
Where, The 's are the feedback gains,
(14)
Using Equation (11) with Equation (14), the system matrix A-BK for the closed loop will be:














 )()()()(
0100
0010
BK-A
130220110 nono kbakbakbakba 



(15)
The closed loop system characteristic equation is:
( )
(16)
And, the desired-characteristic equation is:
(17)
Where ’s are the desired coefficients so, from the two above Equations (16) and (17) , we find:
(18)
(19)
Now closed-loop state-space model could be determined easily and the response of it as well.
5. CONTROLLABILITY
The issue of system controllability has been lengthily introduced and discussed very earlier. Until
now, numerous principles have been established, counting different kinds of matrix rank settings and
considerable graphic materials [18], [19]. According to [20], for an nth-order plant whose state equation is:
̇
Considered as totally controllable when the matrix.
(20)
6. STATE-FEEDBACK CONTROLLER DESIGN FOR ANTENNA AZIMUTH POSITION
CONTROL SYSTEM
The block diagram of the system is shown earlier in Figure 3. Depending on [10], better value for
the preamplifier is 31.6 and the forward transfer function is going to as presented in Figure 12 after removing

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the existing feedback.
Figure 12. Antenna control system simplified block diagram with k=31.6
First of all, it is wanted to test system controllability to see whether the system is controllable or not.
Since the transfer function of the system is:
(21)
So, the state equation and signal flow graph could be obtained and written as shown below:
̇ [ ] [ ] (22)
y= [1 0 0] = C (23)
The system controllabolity could be checked as shown bellow:
[ ] B = [ ]
According to Equation (20);
CM= [ ]
The determinant of CM is -2.8519e+008, so the system is controllable. The rank of CM equals the
number of linearly independent rows or columns. The rank can be found by finding the highest-order square
sub matrix that is non-singular. The determinant of CM =-2.8519e+008. Since the determinant is not zero,
the 3 x3 matrix is non-singular, and the rank of CM is 3. We conclude that the system is controllable since
the rank of CM equals the system order. Thus, the poles of the system can be placed using state-variable
feedback design.
A=[0 1 0
0 0 1
0 -171 -101.71]
B = [0 ;0 ; 658.228]
Cm=ctrb(A,B)
Rank=rank(Cm)
Ans=3
Thus the system is controllable.
In fact, the selection of the locatoions of closed-loop poles is considered as a main difficulty in
designing the controllers based pole-placement technique [21]. According to [22], the eigenvalues of the state
feedback can be placed in any position as well as the feedback gain could be found directly by substitution.
Worth mentioning, this method does not tell the controllability condition in what way arise to the design
that’s why a further efficient approach is recommended.
At this time, for controller design specification and for getting better transient response, it is
required to produce overshoot around 4.3% and 1.4 second settling time. Ƹ = 0.7 and =4. Based on that,
the8 characteristic equation for the dominant poles is:
s2 + 5.66s + 16.4 = 0 (24)
Y(s)=ƟO(
s)
658.228
s(s+1.71)(s+100)
U(s)=E(s
)
)

 ISSN: 2088-8708
1548
Where, dominant poles location at -2.83 ±j2.9. The third pole is about 10 times distant from the imaginary
axis, at -40.eventually, the closed-loop system desired characteristic equation be:
(25)
And then,
[ ]
In consequence, the closed loop characteristic equation is:
(26)
By comparing Equation (25) with Equation (26) and matching the coefficients of both of them, the 's could
be evaluated as follows:
=0.997, =0.1091 and = -0.0852
The direct matlab coding for the controller design and applying it to the system is:
num=658.228
den=[1 101.71 171 0]
g=tf(num,den)
[a,b,c,d]=tf2ss(num,den)
a=[0 1 0;0 0 1;0 -171 -101.71]
b=[0;0;658.228]
c=[1 0 0;0 1 0;0 0 1]
d=[0;0;0]
plant=ss(a,b,c,d)
p=[-40 -2.83-2.9j -2.83+2.9j]
k1=place(a2,b2,p1)
k1 =0.9978 0.1091 -0.0852
cl_sys=feedback(plant,k1)
step(cl_sys)
It’s noted that the value of s which has been calculated earlier is the same that obtained in matlab code
running
7. RESULT AND DESCUSSION
After the design of state-feedback controller for antenna azimuth position system, the overall system
with the controller has been simulated. The response is accepted and desired since it has zero steady-state
error and small value of settling time and overshoot as well, the graph is presented in Figure 13.
Furthermore, the system step response with PID controller is compared to system step response
using state-feedback controller to find the performance. As a result, it has been observed that, in spite of
small rise time and fast response in case of using PID controller but still the response is considered as not
good, due to high overshoot and much settling time value. While, very minor overshoot, small settling time
value as well as zero -steady-state error is gained after applying state-feedback controller to the system. The
comparison of both cases is presented in Figure 14. Figure 15 presents the system steady error after applying
both controllers.

1549
Figure 13. The system step response after applying
state feedback controller
Figure 14. The system response with state-feedback
controller
Figure 15. The system steady-state error after applying PID & state-feedback controller
8. CONCLUSION AND FUTURE WORK
As a conclusion, the overall antenna azimuth position control system in this work is well described
then analysed in term of modeling of each subsystem and figure out how it is operate. The transfer function is
obtained for each part and overall system as well. In order to prove the result, Matlab simulink has been used.
First of all, the closed-loop system response was found without applying any controller, the result indicates
that the system response is unstable and it has a high overshoot. Later on, PID controller has been designed
and applied to the system by following Ziegler-Nichols tuning method in order to provide ample stability and
good response characteristics. The response with the existing controller is much better than without using it,
since the stability and the characteristics of the response is enhanced, but still it has overshoot problem. In
order to come out with a good transient response specification, a state-feedback controller using pole
placement assignment is introduced and designed for the system. The result response shows a perfect
response with only some overshoot percentage, little settling time as well as no steady state error is observed.
Future work: For the future study, it is suggested to design other kinds of intelligent controllers for
this system like robust controllers as well as discrete PID controllers in order to reduce the disturbance and
come out with more efficient and stable response. Further analysis can be done with using different range of
K value and then the exact point of stability can be determined. Finally, it would be interesting if this system
going to be implemented physically in real life.
REFERENCES
[1] N.S. Nise, “Control System Engineering”, 6th Ed., John Wiley & Sons, 2000.
[2] T.V. Hoi, N. T.Xuan and B. G. Duong, “Satellite tracking control system using Fuzzy PID controller”, VNU Journal
of Science: Mathematics and Physics, vol. 31, pp. 36-46,2015.

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[3] L. Xuan, J. Estrada and J. Digiacomandrea, “Antenna Azimuth Position Control System Analysis and Controller
Implementation”, term project, 2009.
[4] M. N.Soltani, R. Zamanabadi, and R.Wisniewski, “Reliable control of ship-mounted satellite tracking antenna”,
IEEE Transactions on Control Systems Technology, 2010.
[5] M. Ahmed, S.B. Mohd Noor, M.K. Hassan and A.B. Che Soh, “A Review of Strategies for Parabolic Antenna
Control”, Australian Journal of Basic and Applied Sciences, vol. 8, pp. 135-148,2014.
[6] L.A. Alooa, P.K. Kihatob and S.I. Kamauc, “DC Servomotor-based Antenna Positioning Control System Design
using Hybrid PID-LQR Controller”, European International Journal of Science and Technology, vol. 5, pp. 17-31,
2016.
[7] H.İ. Okumus, E. Sahin and O. Akyazi, “Antenna Azimuth Position Control with Fuzzy Logic and Self-Tuning
Fuzzy Logic Controllers”, inElectrical and Electronics Engineering (ELECO), Nov. 8th International Conference
IEEE, pp. 477-481,2013.
[8] K. Ogata, “Modern Control Engineering”, Prentice-Hall Inc. USA, 5th Edition, pp. 95-96, 2010.
[9] A.R. Chishti, S.F.U.R. Bukhari, H.S. Khaliq, M.H. Khan and S.Z.H. Bukhari, “Radio Telescope Antenna Azimuth
Position Control System Design And Analysis In Matlab/Simulink Using PID & LQR Controller”, The Islamia
University of Bahawalpur, Pakistan, 2014.
[10] B. Temelkovski and J. Achkoski, “Modeling and Simulation of Antenna Azimuth Position Control System”,
International Journal of Multidisciplinary and Current Research, vol. 2, pp. 254-257, 2014.
[11] G. Franklin, F. Powell and A. Emami-Naeini, “Feedback Control of Dynamic Systems”, 4 th Ed., Addison-Wesley
Publishing Company, 2002.
[12] R. Babu, R. Samuel, S. Deepa and S. Jothivel, “A closed loop control of quadratic boost converter using pid-
controller”, International Journal of Engineering, vol. 27, pp. 1653-1662, 2014.
[13] M.A. Javadi Rad and A. Taheri, “Digital Controller Design Based on Time Domain for DC-DC Buck Converter”,
International Journal of Engineering, vol. 28, pp. 693-700, 2015.
[14] P.R.E Kumar, and V.N. Babu, “Position Control of Servo Systems using PID Controller Tuning with Soft
Computing Optimization Techniques”, International Journal of Engineering Research & Technology (IJERT),
vol. 3, pp. 976-980,2014.
[15] O. Ibrahim, S.A. Amuda, O.O. Mohammed and G.A. Kareem, “Performance Evaluation of three PID Controller
Tuning Algorithm on a process plant”, International Journal of Electrical and Computer Engineering, vol. 5, 2015.
[16] S. Anthony,Mc Cormack andR. G. Keith, “Rule-Based Autotuning Based on Frequency Domain Identification”,
IEEE Transactions on Control Systems Technology, vol. 6, 1998.
[17] T. Ashish, “Modern control design with Matlab and simulink”, Indian Institute of Technology, Kanpur, India, John
Wiley & Son, 2002.
[18] J. Ruths and D. Ruths, “Control profiles of complex networks”, Science, vol. 343, pp. 1373-1376, 2014.
[19] R.W. Shields and J.B. Pearson, “Structural controllability of multiinput linear systems”, IEEE Transactions on
Automatic Control, vol. 21, pp. 203-212, 1976.
[20] P.K.Sinha, “Multivariable control: An introduction”, Marcel Dekker, Inc. New York, NY, USA, 1984.
[21] M.H. Al-qatamin, “An Optimal State Feedback Controller Based Neural Networks for Synchronous Generator
Excitation Control System”, International Journal of Electrical and Computer Engineering, vol. 3, pp. 561-567,
2015.
[22] C.T. Chen, “Linear System Theory And Design”, Oxford University Press, 1999.
APPENDIX
Schematic parameters Parameters
V Voltageacross Potentiometer Kpot Potentiometer gain
N Turns of potentiometer K Preamplifier gain
K1 Power Amplifier Gain A Power Amplifier pole
JL Load inertial constant [kg-m2
] Km Motor and load gain
Ra Motor Resistance [ohms] am Motor and load pole
Ja Motor Inertial constant [kg-m2
] Kg Gear ratio
Da Motor Dampening constant [N-m s/rad]
Kb Back EMF constant [V-s/rad]
Kt Motor Torque constant [N-m/A]
N1 Gear teeth
N2 Gear teeth
N3 Gear teeth
N3 Gear teeth

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