The block diagram of a control system is shown below. 1. Rewrite the system into a state space description form shown below and simulate this continuous plant for a unit step input. y CX AX Bu dt dX?? ?? ?? (10 marks) 2. Discretize this system into a discrete time system in the form below ( ) ( 1) ( ) ( ) y CX k X k X k u k ?? ?? ?? ?? ?? ?? (20 marks) 3. Simulate this discrete time system and change T to observe the changes in responses. Select a proper sampling interval T based on your observation for the rest of the assignment. (10 marks) 4. Design a state variable feedback regulator for the closed-loop system with a pair of complex poles at 0.3??j0.4. Simulate this closed-loop system for a unit step input. (30 marks) 5. If the system state variables are not available. Design a dead-beat observer to provide state variables for your regulator. Simulate the complete system with regulator and observer in place and non-zero initial errors in state variables. (30 marks) Please note that marks will be awarded according to the solution presented presentation of results and reasoning. It is strongly suggested that all of the assignment should be typed. A listing of computer code should be required for verification purpose.
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