Part A: Open Loop Control System and Ziegler Nichols PID design
1. Obtain the step response timed output data from an instrumented, linear and time invariant open loop control system.
2. Draw a block diagram of the measured system and describe its operation.
3. Model this system on Matlab or Simulink and test that the outputs response to a step input accurately mimics your real system.
4. Using Ziegler-Nichols open loop (process reaction) method, design a PID controller for your model.
5. Using your designed PID controller, model your system as a closed loop system.
6. Test your closed loop system's output response to a step input and verify that your controller is working as expected.
7. For the open loop system in Part (3), calculate the expected frequency response of this system, considering low and high frequencies, poles, zeros and dB/frequency.
8. Using the Simulink model of this open loop system. simulate the system to obtain output frequency response data in your preferred format (Nyquist plot. Bode plot or Nichols plot).
9. Compare the Simulink frequency response results with your calculated results and critically evaluate the accuracy of the model in terms of frequency response.
Consider the marking schedule on pages 3 and 4 and lay out your report accordingly. Note that marks will be lost for poor presentation, including poor grammar, poor spelling, incorrect citations and incorrect referencing.
Part B: Frequency Response Analysis and Root Locus PID Design
1. It is required to design a PID controller to meet the specification for output response to a unit step input, as defined in Table 1. The open loop system you should use for your design should be picked from the row appropriate to your surname 10 initial, as should the overshoot and peak time specifications, and all systems should be designed for zero steady state error.
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Surname 1" initial
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G(s) =
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Percentage overshoot (max)
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Peak time (max) (s)
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Steady State Error
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A, B, C.
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(s + 1)
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2
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0.1
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0
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D
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(s3 + 19s4 + 100s + 150)
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|
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|
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E, F, G,
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(s + 1)
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5
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0.2
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0
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H
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(s3 + 2052 + 105s + 155)
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|
|
|
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I, J, K, L
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(s + 1)
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8
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0.1
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0
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(.53 + 2052 + 1105 + 160)
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M, N, 0,
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(5 + 1)
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2
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0.3
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0
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P
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(s3 + 1852 + 90s + 120)
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|
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O. A, S,
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(s 4. 1)
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1
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0.2
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0
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T
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(s3 + 1852 + 85s + 100)
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|
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U, V, W
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(s + 1)
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2
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0.3
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0
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(s3 + 20s2+ 105s + 120)
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|
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X, Y, Z
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(s + 1)
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1
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0.2
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0
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(s3 + 20s2 + 100s + 130)
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|
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Table 1: Open Loop Transfer functions and Closed Loop design specifications, per surname 1st Final.
2. Using the root locus method, as defined in Nise's Control System Engineering book (module core book): Chapter 9, Example 9.5, design a closed loop system with PID controller, in Matlab, to achieve the specification in Table 1, specific to your surname 1st initial.
3. Test your closed loop system's output response to a step input and verify that your controller is working as expected.
4. Critically compare the two PID controller design methods: Ziegler Nichols process reaction versus root locus.
Consider the marking schedule on page 4 and lay out your report accordingly. Note that marks will be lost for poor presentation, including poor grammar, poor spelling, incorrect citations and incorrect referencing.