Question: Many control systems must operate in two dimensions, for example, the x- and the y-axes. A two-axis control system is shown in Figure P3.10, where

Many control systems must operate in two dimensions, for example, the x- and the y-axes. A two-axis control system is shown in Figure P3.10, where a set of state variables is identified. The gain of each axis is K1 and K2, respectively.
(a) Obtain the state differential equation.
(b) Find the characteristic equation from the A matrix.
(c) Determine the state transition matrix for K1 = 1 and K2 = 2.
Figure P3.10
Two-axis system.
(a) Signal-flow graph.
(b) Block diagram model.

O Y K. X, R(s) K, lb)

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