+ [] Q2) (40p.) The state-space equations of the system are given as -102 -20001 i(t) = 1 0 0 X(t) + out) 0 1 LO y(t) =

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Q2 40p The State Space Equations Of The System Are Given As 102 20001 I T 1 0 0 X T Out 0 1 Lo Y T 1 (80.33 KiB) Viewed 147 times

+ [] Q2) (40p.) The state-space equations of the system are given as -102 -20001 i(t) = 1 0 0 X(t) + out) 0 1 LO y(t) = [0 0 1200] x(t). a) Is the system stabilizable? Explain. (5p) b) Design a state feedback controller to yield a 1X % overshoot and a settling time of (X+1) second via pole placement (equalizing coefficients). Place the third pole 10 times as far from the imaginary axis as the second-order dominant pair. (10p) c) Assume that the state variables of the plant are not accessible and design an observer to estimate the states via Ackermann formula. The desired transient response for the observer is a 17 % overshoot and a natural frequency 10 times as great as the system response above. As in the case of the controller, place the third pole 10 times as far from the imaginary axis as the observer's dominant second-order pair. (15p) d) Draw a block diagram of the closed-loop system including the observer and controller. (10p) X is the last digit of your student number. Y is the second last digit of your student number. Note: You are allowed to use MATLAB for mathematical calculations at Q1 and Q2, but you need to show all the formulations that you use step by step.