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Question 4 System 1: A plant system is controlled with a discrete proportional (P) only controller. The sampling time, T, of the system is 0.1 seconds. The closed loop transfer function of the control system is: H(z) 0.3679z¹ +0.2642z 1-z¹+0.6321z² In this specific application, it is important that the transient response to a unit step input demonstrates zero steady state error, shows less than 15% overshoot and has a settling time (to within 2%) of less than 1 second. a) Determine if the proportional controller meets the required performance criteria. Hence, confirm whether this controller is appropriate, or not, for this application. [6 Marks] b) Discuss how you could improve the transient and steady state performance of the control system by implementing a proportional, integral and derivative (PID) controller. Specifically outline the benefits of each part of the PID controller. [4 Marks] c) When simulating a digital Pl control system, it is easy to forget the limitations of the actual control system hardware. Describe how the impact of maximum controller output and integrator anti-windup can be included in the modelling process to better represent the actual hardware system. You may wish to include diagrams to support your answer. [5 Marks] [Turn over