post-lab

1

Sabanc University

Faculty of Engineering and Natural Sciences

Fall 2014

ME 303

CONTROL SYSTEM

DESIGN

LAB REPORT # 3

(Group Number1 & B)

PID Controller Design

Submitted by

Alp Gabay-15369

Doukan Er-15509

K. Selim Engin16429

on

19.11.2014

2

INTRODUCTION The main aim of this lab is to see the effects of control parameters on a real system. Our

equipment consisted of a D-space device, DC motor with an encoder and a computer for

software. First of all, whole devices connected to each other properly and software configuration

took place. After that MATLAB project is created for simulation purposes. We were giving a

constant as an input and we were multiplying it with our transfer function and gain. By changing

the control parameters we tried to observe the effects of these parameters on our system. We

drew some graphs from the data we collected from our encoder that is attached to our motor and

the results of the graphs and the experiment is discussed below.

PROCEDURE In this lab our task was doing some experiments on D-space in order to understand what is effect

of control parameters on the output. At first we installed our D-space device and made the

configurations accordingly. After that, we created a MATLAB project in order to download into

D-space for our experimental purposes. Creating another windows for our observations was

another part of our task. We drew 3 graph for input, output and error values. Finally, we

changed the control parameters' values in a specific order to see their effect on the system,

output.

RESULTS

Figure 1. The results with parameters Kp=4

0 5 10 15 20 2511

12

13Kp = 4

Outp

ut

0 1 2 3 4 5 6 7 8 9 10-5

0

5

Err

or

0 1 2 3 4 5 6 7 8 9 10-20

0

20

Contr

ol In

put

3

Figure 2. The results with parameters Kp=100

Figure 3. The results with parameters Ki=0.1

0 1 2 3 4 5 6 7 8 9 100

1

2Kp = 100

Outp

ut

0 1 2 3 4 5 6 7 8 9-5

0

5

Err

or

0 1 2 3 4 5 6 7 8 9-500

0

500

Contr

ol In

put

0 10 20 30 40 50 60-50

0

50Ki = 0.1

Outp

ut

0 10 20 30 40 50 60-50

0

50

Err

or

0 10 20 30 40 50 60-20

0

20

Contr

ol In

put

4

Figure 4. The results with parameters Ki=1

Figure 5. The results with parameters Kp=3 Ki=0.1

0 10 20 30 40 50 60-20

0

20Ki = 1

Outp

ut

0 10 20 30 40 50 60-20

0

20

Err

or

0 10 20 30 40 50 60-100

0

100

Contr

ol In

put

50 60 70 80 90 100 110 1205

5.5

6Kp = 3 Ki = 0.1

Outp

ut

50 60 70 80 90 100 110 120-1

-0.5

0Error

50 60 70 80 90 100 110 120-0.15

-0.1

-0.05Control Input

5

Figure 6. The results with parameters Kp=5 Ki=0.1

Figure 7. The results with parameters Kd=1

380 390 400 410 420 430 440 4500

0.01

0.02

Err

or

380 390 400 410 420 430 440 4500.06

0.08

0.1

Contr

ol In

put

380 390 400 410 420 430 440 450

4.985

4.99

4.995

5Kp = 5 Ki = 0.1

Outp

ut

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.5

1Kd = 1

Outp

ut

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.5

1

Err

or

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.5

1

Contr

ol In

put

6

Figure 8. The results with parameters Kp=3 Kd=1


0 1 2 3 4 5 6 7 8 90

5

10Kp = 3 Kd = 1

Outp

ut

0 1 2 3 4 5 6 7 8 9-5

0

5

Err

or

0 1 2 3 4 5 6 7 8 9-20

0

20

Contr

ol In

put

0 2 4 6 8 10 12 14 16 18 200

5

10Kp = 3 Kd = 2

Outp

ut

0 2 4 6 8 10 12 14 16 18 20-5

0

5

Err

or

0 2 4 6 8 10 12 14 16 18 20-20

0

20

Contr

ol In

put

7


Figure 11. Comparing the results of the output as the parameter Kd changes

0 2 4 6 8 10 12 14 16 180

5

10Kp = 3 Kd = 5

Outp

ut

0 2 4 6 8 10 12 14 16 18-5

0

5

Err

or

0 2 4 6 8 10 12 14 16 18-20

0

20

Contr

ol In

put

0 2 4 6 8 10 12 14 16 18 200

1

2

3

4

5

6Comparing PD Controllers (Output) Kp=3

R:

Kd=

1,

G:

Kd=

2 B

: K

d=

5

8

Figure 12. Comparing the results of the error as the parameter Kd changes

Figure 13. Comparing the results of the control input as the parameter Kd changes

0 2 4 6 8 10 12 14 16 18 20-1

0

1

2

3

4

5Comparing PD Controllers (Error) Kp=3

R:

Kd=

1,

G:

Kd=

2 B

: K

d=

5

0 2 4 6 8 10 12 14 16 18 20-2

0

2

4

6

8

10

12

14

16Comparing PD Controllers (Control Input) Kp=3

R:

Kd=

1,

G:

Kd=

2 B

: K

d=

5

9

Figure 14. The results with parameters Kp=1.5 Ki=0.02 Kd=0.15

Figure 15. The results with parameters Kp=1 Ki=0.01 Kd=0.1

0 5 10 15 20 25 30 350

10

20Kp = 1.5 Ki = 0.02 Kd = 0.15

Outp

ut

0 5 10 15 20 25 30 35-20

0

20

Err

or

0 5 10 15 20 25 30 35-50

0

50

Contr

ol In

put

0 5 10 15 20 25 30 35 400

5

10Kp = 1 Ki = 0.01 Kd = 0.01

Outp

ut

0 5 10 15 20 25 30 35 40-5

0

5

Err

or

0 5 10 15 20 25 30 35 40-10

0

10

Contr

ol In

put

10

Kp=4 Kp=100 Ki=0.1 Ki=1 Kp=3

Ki=0.1

Kp=5

Ki=0.1

Kd=1 Kp=3

Kd=1

Kp=3

Kd=2

Kp=3

Kd=5

Kp=1.5

Ki=0.02

Kd=0.15

Kp=1

Ki=0.01

Kd=0.1

5 5 23.42 15.3 -0.08 0.02 [] 5 5 5 5 5

2.76 2.85 12.65 8.2 0.28 0.006 [] 2.45 2.12 1.73 7.93 2.37

20 500 14.44 58.3 -0.08 0.07 [] 15 15 15 23.05 7.56

11.04 285.05 10.31 43.9 0.08 0.06 [] 6.82 5.85 3.9 8.31 1.58

tr 389 570 7721 929 41297 39833 - 1962 2201 3742 5034 2697

MP% 68 128 39 485 9 0 - 0 0 0 17 10

ts 5181 4481 56693 50891 54583 48970 - 4013 6042 7823 25806 30893

DISCUSSION

K. Selim Engin:

In the first case, we have used a low Kp value. There was a little overshoot at the

beginning. As we increased the Kp the response got worse. When Kp was between 2-4 the

system was not satisfactory since there were overshoots and undershoots. However,

interestingly, when we increased the Kp value more, the transient response became better.

There was almost no OS when Kp was larger than 4.

Then, we removed the proportional controller and added pure integral control. We

started with a low Ki value. The response to it was not satisfactory, because the system was

unstable and there were oscillations. We kept increasing the Ki however the response did not

change too much and the results were similar when we used a high Ki in pure integral control.

When we added Kp, the system became stable again. However, the settling time was

large and the transient response was not fine enough. The steady-state error and the control

input were zero.

Later, we used pure derivative controller. Pure derivative control is impractical due to

the undesirable noise amplification. In the layout the system was unstable. Because of the

amplified noise, we cannot see anything in the plots of Figure 7.

Afterwards, we added proportional controller to pure derivative control. The response of

it was quite satisfactory. As we increased Kd the settling time also increased.

At the end, we used PID controller. The responses were similar to the results in the pre-

lab. Thats why we picked parameter values that are close to the ones in the pre-lab. The

response of this controller was not the best. When we used PD control there was no OS. The

steady-state response was aloes satisfactory.

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Alp Gabay:

As it was given in the lab task we started with a very small Kp value and increased it

slowly. From our observations, I can say that small Kp creates some under and overshoot but

as we increase it the percentage of these under and overshoots increased and the quality of the

system got worse.(when Kp is between 2 and 4). Surprisingly, when we exceeded 4 for the Kp

value we did not observe any overshoot.

After that we were asked to remove Kp and add some pure integral control. As we

expected regardless of the Ki value system was unstable. Increasing or decreasing the Ki value

did not affect the output drastically.

As the third task, we added some Kp value to the system and it simply became a PI

controller. That actions stabilized the system however it increased the settling time and we are

having a bad transient response.

Afterwards, we just put some pure derivative control to the system and it amplified our

noises in the system and we could not read any output and could not draw any graph from the

data. As a conclusion, I think it is useless to use pure derivative controller.

Then, we inserted a PD controller to our system. Results were okay and increasing Kd

allowed us to have smaller settling time and by changing Kp according to Kd values it was

possible to decrease the overshoot percentage.

Lastly, we put PID controller to the system. This should be the best of all systems that

we simulated but we encountered something different. In PD controller we managed to have

almost zero percent overshoot but in PID we could not reach that.

Doukan Er:

First of all, we started to observe the effect of Kp value as it was mentioned. We gave

small values of Kp to the system and continued to increase it. In a specific interval (2 and 4)

our system had some over and undershoot. When we reach to 4, overshoot of the system was

gone.

Secondly, we use pure integral control instead of Kp. Our observation was that the

system was very unstable does not matter which Ki value we insert.

Thirdly, we were asked to insert a PI controller. Adding Kp to our Ki, system became

stable but due to the integral gain we had very long settling time.

Later, we only inserted pure derivative controller to our system. That Kd increased our

noise in the output dramatically. That is why we could not observe anything on the output. For

that reason using a pure derivative controller is not logical.

Afterwards, we used a PD controller for our system. It had a very short settling time

with some overshoot. However, we can control the settling time as we desire and decrease the

overshoot to some extent.

At last, we put a PID controller for our system. In PID controller we managed to

control both settling time and overshoot percentage at the same time. However, we could

decrease the overshoot in PD controller more than PID.

12

CONCLUSION Using pure derivative or pure integral control for any kind of system is useless because it

makes our system unstable and impossible to control. However, PI and PD controllers did a

great job. PI controller had a longer settling time than PD that is why PD controller is the most

suitable one for this system. In our experiments we could not make overshoot equal to zero in

PID controller. However maybe spending more time on the decision of the control parameters'

values can lead to zero overshoot.

APPENDIX

% %% Low Kp

figure(1)

subplot(3,1,1)

plot(kp4_output.X.Data, kp4_output.Y.Data)

title('Kp = 4');

ylabel('Output');

subplot(3,1,2)

plot(kp4_error.X.Data, kp4_error.Y.Data)

ylabel('Error');

subplot(3,1,3)

plot(kp4_input.X.Data, kp4_input.Y.Data)

ylabel('Control Input');

%% High Kp

figure(2)

subplot(3,1,1)

plot(kp100_output.X.Data, kp100_output.Y.Data)

title('Kp = 100');

ylabel('Output');

subplot(3,1,2)

plot(kp100_error.X.Data, kp100_error.Y.Data)

ylabel('Error');

subplot(3,1,3)

plot(kp100_input.X.Data, kp100_input.Y.Data)


%% Low Ki

figure(3)

subplot(3,1,1)

plot(ki01_output.X.Data, ki01_output.Y.Data)

title('Ki = 0.1');

ylabel('Output');

subplot(3,1,2)

plot(ki01_error.X.Data, ki01_error.Y.Data)

ylabel('Error');

subplot(3,1,3)

plot(ki01_input.X.Data, ki01_input.Y.Data)


%% High Ki

figure(4)

subplot(3,1,1)

plot(ki1_output.X.Data, ki1_output.Y.Data)

title('Ki = 1');

ylabel('Output');

subplot(3,1,2)

plot(ki1_error.X.Data, ki1_error.Y.Data)

ylabel('Error');

subplot(3,1,3)

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plot(ki1_input.X.Data, ki1_input.Y.Data)


%% Low Kp + Low Ki

figure(5)

subplot(3,1,1)

plot(kp3_ki01_output.X.Data, kp3_ki01_output.Y.Data)

title('Kp = 3 Ki = 0.1');

ylabel('Output');

subplot(3,1,2)

plot(kp3_ki01_error.X.Data, kp3_ki01_error.Y.Data)

title('Error');

subplot(3,1,3)

plot(kp3_ki01_input.X.Data, kp3_ki01_input.Y.Data)

title('Control Input');

%% Higher Kp + Low Ki

figure(6)

subplot(3,1,1)

plot(kp5_ki01_output.X.Data, kp5_ki01_output.Y.Data)

title('Kp = 5 Ki = 0.1');

ylabel('Output');

subplot(3,1,2)

plot(kp5_ki01_error.X.Data, kp5_ki01_error.Y.Data)

ylabel('Error');

subplot(3,1,3)

plot(kp5_ki01_input.X.Data, kp5_ki01_input.Y.Data)


%% Pure Kd (NO GRAPH)

figure(7)

subplot(3,1,1)

plot(kd1_output.X.Data, kd1_output.Y.Data)

title('Kd = 1');

ylabel('Output');

subplot(3,1,2)

plot(kd1_error.X.Data, kd1_error.Y.Data)

ylabel('Error');

subplot(3,1,3)

plot(kd1_input.X.Data, kd1_input.Y.Data)


%% Kp(3) + Kd(1)

figure(8)

subplot(3,1,1)

plot(kp3_kd1_output.X.Data, kp3_kd1_output.Y.Data)

title('Kp = 3 Kd = 1');

ylabel('Output');

subplot(3,1,2)

plot(kp3_kd1_error.X.Data, kp3_kd1_error.Y.Data)

ylabel('Error');

subplot(3,1,3)

plot(kp3_kd1_input.X.Data, kp3_kd1_input.Y.Data)


%% Kp(3) + Kd(2)

figure(9)

subplot(3,1,1)


title('Kp = 3 Kd = 2');

ylabel('Output');

subplot(3,1,2)


ylabel('Error');

subplot(3,1,3)



14

%% Kp(3) + Kd(5)

figure(10)

subplot(3,1,1)


title('Kp = 3 Kd = 5');

ylabel('Output');

subplot(3,1,2)


ylabel('Error');

subplot(3,1,3)



%% Comparing PD Controllers

figure(11)

hold on;

title('Comparing PD Controllers (Output) Kp=3');

ylabel('R: Kd=1, G: Kd=2 B: Kd=5')

plot(kp3_kd1_output.X.Data, kp3_kd1_output.Y.Data,'r')

plot(kp3_kd2_output.X.Data, kp3_kd2_output.Y.Data,'g')


figure(12)

hold on;

title('Comparing PD Controllers (Error) Kp=3');


plot(kp3_kd1_error.X.Data, kp3_kd1_error.Y.Data,'r')

plot(kp3_kd2_error.X.Data, kp3_kd2_error.Y.Data,'g')


figure(13)

hold on;

title('Comparing PD Controllers (Control Input) Kp=3');


plot(kp3_kd1_input.X.Data, kp3_kd1_input.Y.Data,'r')

plot(kp3_kd2_input.X.Data, kp3_kd2_input.Y.Data,'g')


%% Kp(1) + Ki(0.02) + Kd(0.15)

figure(14)

subplot(3,1,1)

plot(kp1bucuk_kd015_ki002_o.X.Data, kp1bucuk_kd015_ki002_o.Y.Data)

title('Kp = 1.5 Ki = 0.02 Kd = 0.15');

ylabel('Output');

subplot(3,1,2)

plot(kp1bucuk_kd015_ki002_er.X.Data, kp1bucuk_kd015_ki002_er.Y.Data)

ylabel('Error');

subplot(3,1,3)

plot(kp1bucuk_kd015_ki002_i.X.Data, kp1bucuk_kd015_ki002_i.Y.Data)


%% Prelab PID

figure(15)

subplot(3,1,1)

plot(prelab_o.X.Data, prelab_o.Y.Data)

title('Kp = 1 Ki = 0.01 Kd = 0.01');

ylabel('Output');

subplot(3,1,2)

plot(prelab_e.X.Data, prelab_e.Y.Data)

ylabel('Error');

subplot(3,1,3)

plot(prelab_i.X.Data, prelab_i.Y.Data)


%% System Responses to Step Input

stepinfo(kp4_output.Y.Data)

stepinfo(kp100_output.Y.Data)

stepinfo(ki01_output.Y.Data)

stepinfo(ki1_output.Y.Data)

stepinfo(kp3_ki01_output.Y.Data)

15

stepinfo(kp5_ki01_output.Y.Data)

stepinfo(kd1_output.Y.Data)

stepinfo(kp3_kd1_output.Y.Data)



stepinfo(kp1bucuk_kd015_ki002_o.Y.Data)

stepinfo(prelab_o.Y.Data)

%% MAX Values Of Errors

max(kp4_error.Y.Data)

max(kp100_error.Y.Data)

max(ki01_error.Y.Data)

max(ki1_error.Y.Data)

max(kp3_ki01_error.Y.Data)

max(kp5_ki01_error.Y.Data)

max(kd1_error.Y.Data)

max(kp3_kd1_error.Y.Data)



max(kp1bucuk_kd015_ki002_er.Y.Data)

max(prelab_e.Y.Data)

%% RMS Values Of Errors

rms(kp4_error.Y.Data)

rms(kp100_error.Y.Data)

rms(ki01_error.Y.Data)

rms(ki1_error.Y.Data)

rms(kp3_ki01_error.Y.Data)

rms(kp5_ki01_error.Y.Data)

rms(kd1_error.Y.Data)

rms(kp3_kd1_error.Y.Data)



rms(kp1bucuk_kd015_ki002_er.Y.Data)

rms(prelab_e.Y.Data)

%% MAX Values Of Control Inputs

max(kp4_input.Y.Data)

max(kp100_input.Y.Data)

max(ki01_input.Y.Data)

max(ki1_input.Y.Data)

max(kp3_ki01_input.Y.Data)

max(kp5_ki01_input.Y.Data)

max(kd1_input.Y.Data)

max(kp3_kd1_input.Y.Data)



max(kp1bucuk_kd015_ki002_i.Y.Data)

max(prelab_i.Y.Data)

%% RMS Values Of Control Inputs

rms(kp4_input.Y.Data)

rms(kp100_input.Y.Data)

rms(ki01_input.Y.Data)

rms(ki1_input.Y.Data)

rms(kp3_ki01_input.Y.Data)

rms(kp5_ki01_input.Y.Data)

rms(kd1_input.Y.Data)

rms(kp3_kd1_input.Y.Data)



rms(kp1bucuk_kd015_ki002_i.Y.Data)

rms(prelab_i.Y.Data)

post-lab

Documents

parameters kp

results figure

parameters ki

parameters kd

effect of control parameters

control parameters values

effects of control parameters

control input3 figure