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Q1 The following DC motor system is shown in cascade form. U(s) Y(s) 1 s +6 s + 10 S + 8 s +3 (a) Show that the open loop transfer function Y(s) may be considered a third order US system and hence transform the system to phase variable form, [10 marks] (b) Design a controller to yield a closed loop response to a unit step input with an overshoot (OS) of 10% and a settling time of 1 second based on a 2% settling criterion. In order to meet this performance design specification it is assumed the output response is dynamically dominated by a second order transfer function plus a lag transfer function with a root at s = -6. Design a suitable feedback gain vector using a pole placement technique to meet the above design specification. Assume all states are accessible. [10 marks] (c) Produce a MATLAB/Simulink block diagram for implementing the state variable feedback design and confirm that it meets the required design specification (10 marks] (d) Evaluate the controllability and observability of the above desired system in (b). [10 marks] (e) Comment on the output response in terms of the performance parameters. [10 marks]