Many control systems must operate in two dimensions, for example, the x- and the y-axes

Chapter 0, Problem P3.10

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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 Ki 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 Ki = 1 and K2 = 2.

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