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Choose as state variables: x,(t) =u,(1) and x,()-(1). Obtain the following state space model R, + R, L. y-l - +Ou and calculate the system matrices for L 0.5, R, = 1, R2 = land C = 1. From the state space model obtain the transfer function of the system. By using controllability gramian, check if the system representation R(A, B,C) is controllable Design a state feedback u(t) =-Kx(1), which will place the closed-loop poles on desired locations: 14 =-1 and 1f -2. By using observability matrix, check if the system representation R(A, B,C) is observable. Design a reduced-order state observer with desired poles 2d = -2.

Choose as state variables: x,(t) =u,(1) and x,()-(1). Obtain the following state space model R, + R, L. y-l - +Ou and calculate the system matrices for L 0.5, R, = 1, R2 = land C = 1. From the state space model obtain the transfer function of the system. By using controllability gramian, check if the system representation R(A, B,C) is controllable Design a state feedback u(t) =-Kx(1), which will place the closed-loop poles on desired locations: 14 =-1 and 1f -2. By using observability matrix, check if the system representation R(A, B,C) is observable. Design a reduced-order state observer with desired poles 2d = -2.

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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Consider the following electrical system: R L C= uc u R The equations describing the system dynamics are the following: u(1) = 1 di(e) dt 2+(R, + R, i() + u,(1) cdu, 0 - i(1) Choose as state variables: x,(1) = u,(1) and x,(t) = i(t). Obtain the following state space model R, +R, + Ou and calculate the system matrices for L = 0.5, R, = 1, R2 = land C = 1. From the state space model obtain the transfer function of the system. By using controllability gramian, check if the system representation R(A, B,C) is controllable Design a state feedback u(t) =-Kx(1), which will place the closed-loop poles on desired locations: 14 = -1 and 14 = -2. By using observability matrix, check if the system representation R(A,B,C) is observable. Design a reduced-order state observer with desired poles 24 = -2. 2.
Transcribed Image Text:Consider the following electrical system: R L C= uc u R The equations describing the system dynamics are the following: u(1) = 1 di(e) dt 2+(R, + R, i() + u,(1) cdu, 0 - i(1) Choose as state variables: x,(1) = u,(1) and x,(t) = i(t). Obtain the following state space model R, +R, + Ou and calculate the system matrices for L = 0.5, R, = 1, R2 = land C = 1. From the state space model obtain the transfer function of the system. By using controllability gramian, check if the system representation R(A, B,C) is controllable Design a state feedback u(t) =-Kx(1), which will place the closed-loop poles on desired locations: 14 = -1 and 14 = -2. By using observability matrix, check if the system representation R(A,B,C) is observable. Design a reduced-order state observer with desired poles 24 = -2. 2.
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