Part 1: Phase Lead Controller Design  30%

1. Design a suitable phase-lead controller. You should explain in detail how your design has been developed. Your solution should include Bode plots constructed both manually and using an appropriate package such as MATLAB or Scilab.            (20%)
2. Using the design rules in the Control Engineering Data Sheets, obtain the TF of the “equivalent” 2nd order TF (including controller). (5%)
3. Compare the unit step responses of the equivalent 2^nd order TF and the actual closed loop system, and comment on the accuracy of the equivalent. (5%)

Part 2: Digital Controller Implementation 35%

1. Using the phase lead controller transfer function obtained above as a prototype, design a digital controller using Bilinear Transform or any other method of your choice (10%)
2. Select a suitable sampling increment, T, given the following constraints:

• the minimum value for T is, T= 1mS
• the value of T should be as large as possible, but must provide a unit step response that is within a 5% error band around the unit step response obtained from the ‘ideal’ closed loop system designed in Part 1. (15%)

3. Compare the performance of the digital controlled system with the analogue controlled system obtained in Part 1 (this should include consideration of both time domain and frequency domain responses). (10%)

Part 3: PID Controller 35% 

With reference to the following journal paper:

 H. Heong, G. Chong and L. Yun, (2005), PID Control System Analysis, Design, and Technology, IEEE Trans. On Control Systems Technology, vol 513, No. 4, pp. 559‐576.

 Discuss:

1. Reasons for the widespread use of PID control.-i.e. Why so popular
2. The range of applications that have adopted PID as the preferred control method.
3. The range of methods used to obtain suitable PID parameter settings. (i.e. tune)
4. The particular control problems caused by process dead‐time or transport delay.
5. The cause and effect of “integrator wind‐up”, and methods that have been developed to overcome this problem.

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