Control Engineering Answer the folloing questions for the system given by: dx = Ax + Bu, y = Cx, x = (x1, x?)T X dt A = [ 1] B =[i] C = [10] 0 -4 (a) Check the stability, controllability and observability of the system. (b) Obtain the gain for the state feedback controller u = Kx = = [k? k?]x so that the poles of the closed-loop system are -2 and

Question

Control Engineering

Answer the folloing questions for the system given by:
dx
= Ax + Bu, y = Cx, x = (x1, x?)T
X
dt
A =
[ 1] B =[i] C = [10]
0
-4

Answer the folloing questions for the system given by: dx = Ax + Bu, y = Cx, x = (x1, x?)T X dt A = [ 1] B =[i] C = [10] 0 -4 (a) Check the stability, controllability and observability of the system. (b) Obtain the gain for the state feedback controller u = Kx = = [k? k?]x so that the poles of the closed-loop system are -2 and -3. (c) Now, we add an obserber of the system as shown in the figure (distributed separately.) Show the equation of the entire system with respect to the estimate of the state variables using A, B, C, K, L. (d) Obtain the gain for the observer L = [112] so that the poles of the observer are -20 and -22.

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