Contents
Abstract ................................................................ ................................ ......................................... ......... 2 Introduction .............................................................. ............................... ................................... .... 2 Objectives ..................................................................... 3 Theory ............................................................ ............................. .............................................. ............... 3 Experimental Procedure ............................................... 5 Sample of Calculation ................................................... 6 Results............................................................ ............................. .............................................. ............... 7 Discussion ................................................................... 12 Conclusion............................................................ ............................ ....................................... ....... 13 References ................................................................ ................................ .................................. .. 13 Appendices ................................................................. 14
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Abstract This report consists of proportional, integrator and derivative (P-I-D) controller designation. This P-I-D controller is used to improve the performance of the antenna system. From the layout and schematic diagram given, the schematic block diagram was come out. This block diagram then has been through the simulation process by using SIMULINKMATLAB. The simulation purpose is to obtain the t ransient response by using the parameter given. For the transient response, the values of P-I-D controller need to be found out in order to satisfy the system requirement which is have maximum overshoot, M p<15% and peak time, tp<0.5s.
Introduction Control system is a subsystem and processes that have been assembled together to obtained desired output and desired performance by using certain input. The performance of a control system is majorly measured from transient response and the steady state error. Transient response is the system response that shows the system performance in term of stability, the response time and the system error. This can be known from the system maximum overshoot, rise time, peak time, stability and steady state error. This entire factor can be controlled depending on the system functionality and customer requirements. Commonly, controllers were used in this control system in order to improve the system performance. The controllers that use are proportional, integrator and derivative. Each of these controllers has their own function and advantages as well as the disadvantages. Type of controller that need to use in each of system is totally depending on the desired output. These controllers commonly used as a combination of two or three types as to obtain the better system performance. As each of controller has its own advantages, the using of combination will increase the effect f or the system performance. Proportional controller is functional to reduce or increase the system stability. By varying the value, system stability also has changes. Integrator controller used in order to eliminate the steady state error. However, too high value of this controller will make the system be more unstable. Others than that, in order to make the system steady state more accurate and stable, the derivative controller need to be add up.
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Objectives i.
To design the block diagram of antenna azimuth system based on the layout and schematic diagram given.
ii.
To do the antenna azimuth system simulation by using SIMULINK-MATLAB software
iii.
To design the controller system consisting of P-I-D actions to improve the system performance.
Theory
Figure 1: An antenna azimuth position control system
Figure 2: Schematic diagram of antenna azimuth
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From the layout and schematic diagram of antenna azimuth given, the relationship between the output voltage and the input angular displacement is given by;
The relationship between motor and load is given by;
⁄ The equivalent inertia, J m is
The viscous damping D m is
The overall transfer function from the armature voltage to the armature displacement is;
Figure 3: Transient response Maximum overshoot is the maximum amount of under damped response over shoots the steady state response while the peak time can be defined as the time required for the 4|Page
under damped response to reach the first peak. As shown in figure above, transient is the combination of the under damped response with the steady state response. From the parameter given below, the P-I-D controller system needs to be design to achieve the requirement transient response that satisfied maximum overshoot, M p< 15% and peak time, tp < 0.5s. Parameter
Configuration 1
Configuration 2
Configuration 3
V
10
10
10
n
10
5
5
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
Table 1: Parameter values
Experimental Procedure i.
Block diagram has been designed to obtain the transfer function for each component based on layout and schematic diagram given.
ii.
The system transfer function has been design by using SIMULINK-MATLAB software to see the transient response.
iii.
From the response the P-I-D controller has been design to improve the system performance.
iv.
P-I-D controller value has been adjusted to satisfy the system requirement.
v.
The maximum overshoot and peak time has been calculated based on the system response.
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Sample of Calculation From the parameter given and the theory formula, the data that want to use as input of the control system has been tabulated as below. By taking sample from the Configuration 1, the equivalent inertia (J m) is:
For the equivalent viscous damping (D m):
Therefore the parameters that has been calculated is: Parameter
Configuration 1
Configuration 2
Configuration 3
K1
100
150
100
a
100
150
100
Ra
8
5
5
Jm
0.03
0.25
0.25
Dm
0.02
0.13
0.13
Kb
0.5
1
1
Kt
0.5
1
1
N1
25
50
50
N2
250
250
250
Table 2: Parameter used as input to the controller system
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Results From the given layout, the block diagram was come out below: Input Vp (s)
Vi (s)
Ve (s)
+
Preamplifier
Ea s Power Amplifier
Motor and Load
θm (s)
θo (s)
Gears
Output
-
Potentiometer
By substituting value from the theory part, the block diagram becomes:
Motor and Load
Power Amplifier
Input
+
+ -
+
Gears
⁄ ( )
Output
10
Subsystem 1
By adding P-I-D controller, the block diagram becomes:
+ Input
+
+
+ 10
Kp
+
-
Subsystem
+ Ki
Kd
1
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Output
After the simulation process, the value for Kp, Ki and Kd to satisfied the requirement which maximum overshoot, Mp < 15% and t p < 0.5s has been obtained which is: transient - response for c onfiguration 1 (A) 18
16
14
12
10 ) t ( c
8
6
4
2
0
0
1
2
3
4
5 t (s)
6
7
8
9
10
Figure 4: Graph of Configuration 1 (A)
transient - response for c onfiguration 1 (B) 12
10
8
) t ( c
6
4
2
0
0
1
2
3
4
5 t(s)
6
7
8
9
10
Figure 5: Graph of Configuration 1 (B)
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Configuration 1
Maximum Kp
Ki
Kd
Peak time,
overshoot,
tp (s)
Mp (%)
A
1
1
1
74.5
9.3
B
300
1.5
39
8.6
0.47
Table 3: Value of K p, K i , K d, M p and t p for Configuration 1
transient - response for configuration 2 (A) 18
16
14
12
10 ) t ( c
8
6
4
2
0
0
1
2
3
4
5 t (s)
6
7
8
9
10
Figure 6: Graph of Configuration 2 (A)
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transient - response for configuration 2 (B) 12
10
8
) t ( c
6
4
2
0
0
1
2
3
4
5 t (s)
6
7
8
9
10
Figure 7: Graph of Configuration 2 (B)
Configuration 2
Maximum Kp
Ki
Kd
overshoot, Mp (%)
Peak time, tp (s)
A
1
1
1
70
9.5
B
400
6
50
11
0.45
Table 4: Value of K p, K i , K d, M p and t p for Configuration 2
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transient - response for configuration 3 (A) 18
16
14
12
10 ) t ( c
8
6
4
2
0
0
1
2
3
4
5 t (s)
6
7
8
9
10
8
9
10
Figure 8: Graph of Configuration 3 (A)
transient - response for configuration 3 (B) 12
10
8
) t ( c
6
4
2
0
0
1
2
3
4
5 t (s)
6
7
Figure 9: Graph of Configuration 3 (B)
Configuration 3
Maximum Kp
Ki
Kd
overshoot, Mp (%)
Peak time, tp (s)
A
1
1
1
74.7
9.2
B
400
8
55
8
0.47
Table 5: Value of K p, K i , K d, M p and t p for Configuration 3
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Discussion Before the simulation process can be done, certain parameter need to be calculated as a parameter input for the system. The system need to be done according to the block diagram that has been drawn earlier based on t he layout and schematic diagram given. Three type of controller were use in this system which is proportional (K p), integrator (Ki) and derivative (K d). The proportional controller functions to increase or reduce the response stability. By increase the value of K p, the system will be more unstable compared to lower value of K p. Integrator controller is added up to the system in order to reducing the error occur in the system which is steady state error. The increasing K i will eliminate the steady state error. However, the system will be more unstable when this controller value being increase. Besides that, the other controller use is derivative which is functional to increase the steady state accuracy and system stability. From the result obtained by simulation process, it is found that the default configuration where K p,Ki and Kd is 1 shows the high value in maximum overshoot as well as peak time. To improve the transient response of the system, the controller needs to be added in the system. This is in order to reduce the maximum overshoot, peak time and increase the stability. The result shows that for configuration 1, the value of maximum overshoot and peak time is 74.5% and 9.3s respectively. This is when the value of K p, Ki and Kd is 1. To increase the system performance, the value of K p, Ki and Kd is change to 300, 1.5 and 39 respectively. As a result, the maximum overshoot is reducing to 8.6% and peak time to 0.47s. Besides that, the system also shows the more stable response where less fluctuating graph. By using value 1 for all K p, K i and Kd controller, the response maximum overshoot is 70% and peak time is 9.5s. This controller value then being adjusted to satisfy the requirement and the value is 400,6,50 for K p,Ki,Kd respectively. For this value, the maximum overshoot and peak time is reducing to 11% and 0.45s. This is a result by using configuration 2.Same for configuration 3, the value of Kp,Ki and Kd also have been adjust to 400,8,55 respectively and make the maximum overshoot reduce from 74.7% to 8%. The peak time also reduce from 9.2s to 0.47s.
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Conclusion After completing the pre-simulation process and the simulation process, the objectives of this project has been achieved. From the layout and schematic diagram given, the block diagram successfully been drawn and use for simulation process. The way to insert and define the parameter by using SIMULINK-MATLAB software also has been known. The functions that have in the software is appropriately use to represent the system block diagram and designation of P-I-D controller has been done. From the result, the P-I-D controller design shows the positive feedback and functional. This is due to the system performance improvement that has been achieved by adjusting the value of these three controllers. The theory of these three controller function also has been approved which is by increasing value of K p, the maximum overshoot will increase but the peak time will decrease. Same effect will occur as increasing the K i value. As increasing of Kd, both of peak time and maximum overshoot will have minor decreasing.
References i.
Modern Control Engineering, 5 th Edition; Katsuhiko Ogata; Prentice Hall
ii.
http://en.wikipedia.org/wiki/PID_controller
iii.
KJM 597; Transient Response Analysis note
iv.
en.wikipedia.org/wiki/Transient_response
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Appendices
Figure 10: A SIMULINK block diagram
Figure 11: A subsystem component for the system
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