Question

3- a. Use the Discretization concept to convert the given continuous state-space represented system to a discrete system. A = [0 1; -2 -3] B = [0; 1] C = [2 0] b. For the system described above (in a), after discretization, determine the state feedback gain matrix K such that the closed-loop system will exhibit the deadbeat response to any initial x(0). Verify your answer. c. Study the controllability and observability of the given system. d. Find the homogeneous solution of the state-space represented system for: i. a unit step input and ii. x(0) = [0 2]T. e. Determine the state feedback gain vector K such that the closed loop poles of the system are located at z1 = 0.2 + j0.4, and z2 = 0.2 – j0.4.

          3- a. Use the Discretization concept to convert the given continuous state-space represented system to a discrete system.

A = [0 1; -2 -3]

B = [0; 1]

C = [2 0]

b. For the system described above (in a), after discretization, determine the state feedback gain matrix K such that the closed-loop system will exhibit the deadbeat response to any initial x(0). Verify your answer.

c. Study the controllability and observability of the given system.

d. Find the homogeneous solution of the state-space represented system for:
i. a unit step input and
ii. x(0) = [0 2]T.

e. Determine the state feedback gain vector K such that the closed loop poles of the system are located at
z1 = 0.2 + j0.4, and z2 = 0.2 – j0.4.

Show more…

3- a. Use the Discretization concept to convert the given continuous state-space represented system to a discrete system.

A = [0 1; -2 -3]

B = [0; 1]

C = [2 0]

b. For the system described above (in a), after discretization, determine the state feedback gain matrix K such that the closed-loop system will exhibit the deadbeat response to any initial x(0). Verify your answer.

c. Study the controllability and observability of the given system.

d. Find the homogeneous solution of the state-space represented system for:
i. a unit step input and
ii. x(0) = [0 2]T.

e. Determine the state feedback gain vector K such that the closed loop poles of the system are located at
z1 = 0.2 + j0.4, and z2 = 0.2 – j0.4.

Added by Andrea V.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Audrey Fong

Step 1

To discretize the system, we can use the forward Euler method, which approximates the derivative of the state variables as a difference quotient. The discretized system can be written as: x(k+1) = Ax(k) + Bu(k) y(k) = Cx(k) where A = I + T*A_c, B = T*B_c, C = Show more…

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3- a. Use the Discretization concept to convert the given continuous state-space represented system to a discrete system. A = B = C = [2 0] b. For the system described above (in a), after discretization, determine the state feedback gain matrix K such that the closed-loop system will exhibit the deadbeat response to any initial x(0). Verify your answer. c. Study the controllability and observability of the given system. d. Find the homogeneous solution of the state-space represented system for: i. a unit step input and ii. x(0) = [0 2]T. e. Determine the state feedback gain vector K such that the closed loop poles of the system are located at z1 = 0.2 + j0.4, and z2 = 0.2 – j0.4.

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