Question 10.25: Full-State Feedback Control of a Direct Current Motor–Driven...
Full-State Feedback Control of a Direct Current Motor–Driven Cart
Consider the full-state feedback control system discussed in Example 10.24, in which the state-space representation of the plant is
\dot{\mathbf{x}} = \begin{bmatrix} 0 & 1 \\ 0 & -16.883 \end{bmatrix}\mathbf{x} + \begin{bmatrix} 0 \\ 3.778 \end{bmatrix}u
y = \begin{bmatrix} 1 & 0 \end{bmatrix}\mathbf{x}
and the mathematical model of the controller is
u = −\mathbf{Kx}
with \mathbf{K} = \begin{bmatrix} 48.24 & 0.18 \end{bmatrix}. Build a Simulink block diagram of the feedback control system and find the closed-loop response if the cart is initially 1 \text{m} away from the equilibrium position.
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