Antenna Azimuth Controller Design 662a17

Contr ol Eng ineer ing ( MEC 52 2)

UNI V ER SIT I T EK NOL OG I M AR A Fac ul ty Of Mec ha nic al Engi neer ing

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 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

K

+ -

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

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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 s2 s1 s0

1 101.32 a1 a2

132 5.09K b1 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 Gc(S)

+

G(s)

-

Setting the Ti=∞ and Td=0 Gc(s)=Kp Then, Kp

+ -

Find the value of Kp Characteristic equation of the system, q(s)

Find the value of Kp by using Routh Stability criterion s3 s2 s1 s0

1 101.32 a1 a2

132 5.09+5.09Kp b1 b2

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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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Contr ol Eng ineer ing ( MEC 52 2)

UNI V ER SIT I T EK NOL OG I M AR A Fac ul ty Of Mec ha nic al Engi neer ing

The transfer function for the PID controller is

PID Controller transfer function Gc(S)

+ -

+ -

+ -

The transfer function for PID Controller is

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G(s)

Contr ol Eng ineer ing ( MEC 52 2)

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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 K p 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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Contr ol Eng ineer ing ( MEC 52 2)

UNI V ER SIT I T EK NOL OG I M AR A Fac ul ty Of Mec ha nic al Engi neer ing

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.

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