antenna azimuth controller design

U N I V E R S I T I T E K N O L O G I M AR A C o n t r o l E n g i n e e r i n g ( M E C 5 2 2 )

F a c u l t y O f M e c h a n i c a l E n g i n e e r i n g

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1.0 Title: Antenna Azimuth Position Control System

2.0 Objective:

The objective, of the lab is to analyze and design a control system for the antenna

azimuth position using MATLAB and SIMULINK.

3.0 Introduction:

A position control system converts a position input command to a position

output response. Position control finds widespread applications in antennas,

robot arms, and computer disk drives. The radio telescope antenna in Fig. 1 is

one example. The purpose of this system is to have the azimuth angle output

follow the input angle. The input command is an angular displacement. The

potentiometer converts the angular displacement into a voltage. Similarly, the

output angular displacement is converted to a voltage by the potentiometer in

the feedback path. The signal and power amplifiers boost the difference between

the input and output voltages. This amplified actuating signal drives the plant.

The system operates to drive the error to zero when the input and the output

match, the error will be zero and the motor will not run.

Figure 2.1: An Antenna Azimuth Position Control System



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Figure 2.2: Schematic Diagram of Antenna Azimuth

Figure 2.3: Block diagram for the system



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Table 2.1: The Schematic Parameters

Parameter Configuration 1 Configuration 2 Configuration 3

V 10 10 10

n 10 1 1

K - - -

K1 100 150 100

a 100 150 100

Ra 8 5 5

Ja 0.02 0.05 0.05

Da 0.01 0.01 0.01

Kb 0.5 1 1

Kt 0.5 1 1

N1 25 50 50

N2 250 250 250

N3 250 250 250

JL 1 5 5

DL 1 3 3

By neglecting the dynamics of potentiometers the relationship between the

output voltage and the input angular displacement is given by:

The relationship between motor and load is given by:

=



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The equivalent inertia, Jm is

Similarly the equivalent viscous damping, Dm is

These quantities are substituted into the motor equation, yielding the transfer

function of the motor from the armature voltage to the armature displacement.

The gear ratio to arrive at the transfer function relating load displacement to

armature voltage is;

From parameter values in Figure 3, design a controller consisting of P-I-D actions

to improve the performance of the antenna system. The requirement is open

which means that you should try to achieve as good as possible performance for

transient, stability as well as signal tracking. Use a unit step signal

4.0 Solution

4.1 To find the transfer function of the system

The block diagram of the system

From the block diagram in figure 2:

Kpot K

Kg

Kpot

+

-



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Where:

Kpot=

= 0.318

=

0.25

0.13

So,

- Motor, load and gears



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Then the block diagram become

a. Original block diagram

b. Pushing input potentiometer to the right past the summing junction

c. Showing equivalent forward transfer function

d. Final closed loop transfer function

Transfer function for the system

K

+

-

+

-

+

-



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4.2 From the transfer function, it can be plotted the graph for the Root Locus,

Nyquist, Step Response and Bode.

Figure 4.2.1: Root Locus graph

Figure 4.2.2: Nyquist graph



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Figure 4.2.3: Bode graph

Figure 4.2.4: Step Response graph



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Step response info:

RiseTime: 55.2535 Overshoot: 0

SettlingTime: 99.1616 Undershoot: 0

SettlingMin: 0.9004 Peaks: 0.9995

SettlingMax: 0.9995 Peak Time: 189.6234

Find the value of K (preamplifier) from the transfer function above

The characteristic equation is:

s3 1 132 s2 101.32 5.09K s1 a1 b1 s0 a2 b2



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Then we need to tune the system with the range value of K to get the overshoot

close to 10%.

For K=23.95

Figure 4.2.5: Graph for K=23.95 (tuned)

Figure 4.2.6: MATLAB/SIMULINK diagram for standard system



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4.3 Design a PID Controller

Setting the Ti=∞ and Td=0

Gc(s)=Kp

Then,

Find the value of Kp

Characteristic equation of the system, q(s)

Find the value of Kp by using Routh Stability criterion

s3 1 132 s2 101.32 5.09+5.09Kp s1 a1 b1 s0 a2 b2

Gc(S) G(s) +

-

Kp

+

-



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The maximum of Kp or Kcr/Ku is 2626.55

Substitute the value of Kp to the characteristic equation

Then substitute s=j⍵

For PID Controller

Kp = 0.6Kp

= 0.6(2626.55)

= 1575.93

Ti = 0.5Tu

= 0.5(0.547)

= 0.2735

Td = 0.125Tu

= 0.125(0.547)

= 0.0684



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The transfer function for the PID controller is

PID Controller transfer function

The transfer function for PID Controller is

Gc(S) G(s) +

-

+

-

+

-



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4.4 From the transfer function of PID controller, it can be plotted the graphfor

the Root Locus, Nyquist, Step Response and Bode.

Figure 4.4.1: Root Locus graph for PID controller

Figure 4.4.2: Nyquist graph for PID controller



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Figure 4.4.3: Bode graph for PID controller

Figure 4.4.4: Step response graph for PID controller

Step response info:

RiseTime: 0.1065 Overshoot: 67.1068

SettlingTime: 3.6861 Undershoot: 0

SettlingMin: 0.5084 Peak: 1.6711

SettlingMax: 1.6711 PeakTime: 0.312



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Then we need to tune the system with the range value of Kp to get the

overshoot close to 10%.

Kp=72

Figure 4.4.5: Graph for K=50 (tuned)

Figure 4.4.6: MATLAB/SIMULINK diagram for standard system



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5.0 Discussion

After all of the analysis was completed the system was well understood and

possible solutions have been presented above. For the standard system, it will

unstable when K>2627.55. From my simulation, I’ve use K=26 to achieve my target

overshot for this system which is 10%. The overshoot that I’ve for K=23.95 is 9.93%

which is close to the target.

For the PID Controller, the stability range of the system is quite similar to the

standard system which is Kp below 2626.55. The target for PID Controller system

also 10% and after to be tuned the value of Kp=72 is to be the best overshoot that

for this system which is 13.57%.

6.0 Conclusion

As a conclusion, it can be said that the value of gain could be change for the standard

system and for the PID system. The value of K or preamplifier for the standard

system is lowest than the PID system that need to be tune to achieve the target. So, it

can be concluded that the objective of the project was achieved and successfully

with the own requirement.

antenna azimuth controller design

Documents

fac ul ty

ek nol og

step response graph

root locus graph

step response

root locus

angular displacement

characteristic equation