- Question 1 Compulsory Controllability And Observability Transfer Function From State Space Model Stability Pole Pla 1 (70.13 KiB) Viewed 38 times
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please provide complete solution for part 3
and part 4 ?
Question 1 (Compulsory) Controllability and Observability, Transfer Function from State Space Model, Stability, Pole Placement by State Feedback Method, Steady State Error to Step Input. Consider a linear open loop system described by the following state space model: -12 [²] + • U y=[18] [¹] + + [0] u 1) (4 marks) Determine if the open loop system is observable and/or controllable. 2) (6 marks) Find the open loop system transfer function, Gopen (S) =), system poles and zeros. Is the open loop system stable? U(s)' 3) (5 marks) Choose the appropriate locations for the closed loop system poles so that the following specifications will be met: Percent Overshoot, PO, of the compensated closed loop system step response is 0%. • The Settling Time, Tsettle (+2%), of the compensated closed loop system step response is to be no more than 0.25 seconds. . Steady State Error for the unit step input to the compensated closed loop system step response is 0%; 4) (5 marks) Place the system in a closed loop configuration with the reference input r and assume the controller equation to be in the form: u-K-(r-k²-x) Compute the required values of the state feedback vector gains k and of the Proportional Gain K. HINTS: Start with placing one of the closed loop poles so that the pole-zero cancellation in the closed Joop occurs. Since the resulting system response will be of a first order model type, choose the second closed loop pole location based on the first order model time constant that will meet the specification. Next, use the Proportional Gain K in the above equation to calibrate for the zero Steady State Error.