Question

Problem 3 Consider the dynamical system $\frac{dx}{dt} = \begin{bmatrix} -4 & -3 \\ 1 & 0 \end{bmatrix} x + \begin{bmatrix} 1 \\ 0 \end{bmatrix} u \implies \dot{x} = Ax + Bu$ y = $\begin{bmatrix} 1 & 3 \end{bmatrix} x$ y = Cx Select the state controller $u = -k_1x_1 - k_2x_2$ that would place all closed loop poles at -4

          Problem 3 Consider the dynamical system
$\frac{dx}{dt} = \begin{bmatrix} -4 & -3 \\ 1 & 0 \end{bmatrix} x + \begin{bmatrix} 1 \\ 0 \end{bmatrix} u \implies \dot{x} = Ax + Bu$
y = $\begin{bmatrix} 1 & 3 \end{bmatrix} x$
y = Cx
Select the state controller $u = -k_1x_1 - k_2x_2$ that would place all closed loop poles at -4

Problem 3 Consider the dynamical system
(dx)/(dt) =
< b m a t r i x >
x +
< b m a t r i x >
u ẋ = Ax + Bu
y = < b m a t r i x >
x
y = Cx
Select the state controller u = -k1x1 - k2x2 that would place all closed loop poles at -4

Added by Leroy M.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Gregory Devenport

Step 1

The closed-loop transfer function is given by: G(s) = K / (1 + GK) where K is the controller gain and G is the open-loop transfer function. Show more…

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Problem 3: Consider the dynamical system dx/dt = -3x + x^2 + 10x^3, x(0) = 3 y = Cx Select the state controller K = -x - x^2 that would place all closed loop poles at -4.