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MMAN3200 Linear Systems and Control – Lab Report

Marcella Moniaga z3377465

Introduction The letters P, I, D stand for Proportional, Integral, and Derivative. It is a three terms controller which is used to calculate the error in a closed-loop system. In this experiment, the PID controller is planted on a small scale monorail which should be manually tuned by students. We are required to input the values for Kp, Ki, and Kd in certain manner to achieve the objectives given. Those objectives are: a. Rise time < 1.1 seconds b. Stationary error < 3% c. No overshoot (or marginal overshoot) The values for Kp, Ki, and Kd should be within the range of 0 to 2. Table 1: PID parameters

(increasing)

Rise Time

Stationary Error Values

Overshoot Values

Settling Time

Kp

Decrease

Decrease

Increase

Ki

Decrease

Eliminate

Increase

No definite trend Increase

Kd

No definite trend

No definite trend

Decrease

Decrease

Table 1 shows PID Parameters which affect the system dynamic. In this table, the change in Kp, Ki, and Kd could determine the change in rise time, stationary error values, overshoot values, and settling time.

Laboratory Results

Combinations

Trial 1 2 3 4 5 6 7 8

Kp 0.6 0.6 0.7 0.6 0.8 0.8 0.8 0.8

Ki 0.1 0.1 0.1 0.6 0.2 0.2 0.3 0.1

Position (volts) Kd 0.0 0.1 0.1 0.0 0.1 0.2 0.1 0.1

Initial -1.10 0.98 -1.02 1.20 -0.99 -0.99 1.01 -0.98

Final 1.20 -0.96 1.00 -1.10 1.06 1.05 -1.20 1.00

Rise Time (sec) 0.53 1.13 0.70 0.51 0.56 0.56 0.55 0.82

Stationary Overshoot Error Values (volts) (Volts) 21.10% 3.32% 1.37% 14.30% 6.40% 4.50% 17.20% 0.30%

0.56 1.18 -

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MMAN3200 Linear Systems and Control â&#x20AC;&#x201C; Lab Report

Marcella Moniaga z3377465

Laboratory Diagrams Trial 1 [Kp = 0.6, Ki = 0.1, and Kd = 0.0]

Trial 3 [Kp = 0.7, Ki = 0.1, and Kd = 0.1]

Trial 4 [Kp = 0.6, Ki = 0.6, and Kd = 0.0]

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MMAN3200 Linear Systems and Control â&#x20AC;&#x201C; Lab Report

Marcella Moniaga z3377465

Trial 5 [Kp = 0.8, Ki = 0.2, and Kd = 0.1]

Trial 6 [Kp = 0.8, Ki = 0.2, and Kd = 0.2]

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MMAN3200 Linear Systems and Control â&#x20AC;&#x201C; Lab Report

Marcella Moniaga z3377465

Discussion Trial 1

On the first trial of tuning the controller, we tried to put Kp, Ki, and Kd as 0.6, 0.1, 0.0 respectively. In this case, it is evident that there is a presence of overshoot. From table 1, it could be seen that the stationary error is 21.1% with overshoot value of 0.56 volts. Because of that, despite the fact that the rise time is less than 1.1 seconds, this trial did not produce the targeted result.

Trial 2

When the derivative value (Kd) is increased from 0.7 to 0.1 and the proportional (Kp) as well as integral (Ki) values are kept constant, the stationary error decreased by 84.3% and the overshoot values reduced to 0 volt. However, the stationary value is still more than 3%, which is not desirable.

Trial 3

In trial 3, we decided to increase the proportional value from 0.6 to 0.7 and kept the other values constant (Ki = 0.1, Kd = 0.1). The rise time and stationary error decreased until it became 0.7 seconds and 1.37% respectively. Since there is no presence of overshoot as well, all of the objectives are met.

Trial 4

Notwithstanding that trial 3 produces a desirable result; we tried to change the Kp, Ki, and Kd values to reduce the rise time and the stationary error. In this case, we altered the proportional, integral, and derivative values to 0.6, 0.6, and 0.0 respectively. However, the result was found to be worse with the rise time increased from 0.00 to 0.51, stationary error increased from 1.37% to 14.30%, and there is a presence of overshoot by 1.18 volts.

Trial 5

In trial 5, we increased all the values from trial 4 (Kp = 0.8, Ki = 0.2, Kd = 0.1). There is no presence of overshoot, on the other hand the stationary error is not favourable since it is more than 3%.

Trial 6

We change the derivative value from 0.1 to 0.2. The rise time value is constant, nevertheless the stationary error is reduced from 6.4% to 4.5%. Since not all of the objectives are met, the result is adverse.

Trial 7

In this trial, we slightly change the integral and derivative value into 0.3 and 0.1 respectively. Surprisingly, the stationary error increased greatly from 4.5% to 17.2%. We still need to alter the values to produce the targeted result.

Trial 8

To decrease the overshoot value in trial 7, we decided to reduce the integral value from 0.3 into 0.1. The result is: the rise time is 0.82 seconds, there is no presence of overshoot, and the stationary error decreased greatly into 0.3%. It is evident that this trial produces a better result than the previous ones.

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MMAN3200 Linear Systems and Control â&#x20AC;&#x201C; Lab Report

Marcella Moniaga z3377465

Conclusion In summary, the final best trial chosen is trial 8 with Kp = 0.8, Ki = 0.1, Kd = 0.1 given that the rise time is 0.82 seconds (less than 1.1 seconds), no existence of overshoot, and the stationary error is 0.3% (less than 3%). There are several difficulties and possible errors in undertaking this experiment. For example, the static friction between the beam and monorail could affect the activity of the monorail, thus affecting the rise time values. This could be reduced by properly lubricating the monorail and beam to increase accuracy. Another problem is the unstable result produced by the experiment, even though the values inputted are constant. For instance, there is a case where we tried to input the values for Kp, Ki, and Kd as 0.6, 0.1, and 0.1 respectively and ran the experiment twice. Nonetheless, the produced results are different although the values are constant. Lastly, there is only one PID controller available whereas there are more than five groups are undertaking the experiment. There are times where some groups did not inform others when they want to utilize the PID controller, thus resulting in conflict in system.

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