1. (a) The equation below describes the output u(t) from P++D con (9 marks) troller. Briefly discuss the contribution of each term of the con troller to the overall system response. de(t) dt (b) A step input of magnitude 7.5% is applied to the input of a Pro- portional plus Integral (P+I) controller at time t 0. The output undergoes a sudden step change of 15% and after 3 minutes the total change is 30%. (6 marks) Plot the output from the controller. Indicate the contribution from both P and I aspects of the controller. Calculate The Proportional bandwidth. The Integral action time. (4 marks) (6 marks)