Question: 5.1 A dynamic system has a plant: a. Define the state variables as x1(k) =y(k), x2(k) =y(k +1), and x3(k) =y(k + 2). Derive state

5.1 A dynamic system has a plant:

H(z) = Y(z) U(z) 10z (z+1)(z+0.4)(z+0.7)

a. Define the state variables as x1(k) =y(k), x2(k) =y(k +1), and x3(k) =y(k + 2). Derive state equation for this system.

b. By use of state feedback control u =-Kx, obtain the gain matrix K so that the closed-loop poles are at

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H(z) = Y(z) U(z) 10z (z+1)(z+0.4)(z+0.7)

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