Question: 9.1 Let the state-space equations for the level 1 electrostatic system be Use the control law shown in Equation 9.26 with the feedback gain matrix

9.1 Let the state-space equations for the level 1 electrostatic system be

x(k+1)= 1 y(k) 1 [0.9798 0 5] v(k) 0.4574 14.9315

Use the control law shown in Equation 9.26 with the feedback gain matrix given

image text in transcribed

a. Show the evolution of the states for xd¼[550 100]T and x(0)¼
[588 87]T with respect to 10 pitch numbers.

b. Show that the steady-state error is held to zero, even when one of the elements of the Jacobian matrix, say b22, is lowered by 20%.

c. Calculate the steady-state values of the actuator vector, v(k), for (a)
and (b).

x(k+1)= 1 y(k) 1 [0.9798 0 5] v(k) 0.4574 14.9315

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