Digital Control And State Variable Methods By M Gopal Pdf !LINK! Download
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The simulation result is shown below. Here it can be seen that in the first iteration, the initial controller, U(0) = 20, generates an initial controller impulse, u(0) = 40, and an initial state difference, e(0) = 10, to the plant. The initial controller impulse is added to the system from the plant.
If we choose x(k) = x(k) as the controller state variable, then we obtain, xc(k + 1) = xc(k), u(k) = xc(k) + e(k) = 41xc(k) + 50x(k), x(k + 1) = xc(k), and as the plant model, ps(k) = xc(k) + e(k).
For the disturbance x(k), we choose xc(k) as the controller statevariable. The corresponding controller model is given by xc(k + 1) = e(k), u(k) = 21xc(k) + 30e(k), y(k) = 41xc(k) + 50e(k) as state model of the controller. Theplant difference equations are given by (solution to Problem 6.16) y(k + 1) =
(c) If the control system is assumed to begin in equilibrium at x(0) = 0, y(0) = 0, d(0) = 0, then the state and output response of the plant to the control input u(k) = 41xc(k) + 50e(k) and u(k) = 41xc(k) + 50e(k) are given by the following equations. Let xp(k) = x(k) + x(k), xp(k) = x(k) + x(k), where x(0) = 0, y(k) = xp(k), y(k) = xp(k) for k = 0, 1, 2,....
(e) Use the state error equation to determine the equilibrium point x*, y* of the state space model of theplant. Using the plant difference equations and the output error equation, show that(x*, y*), (41xc + 50e, 0.7 x*), (0, 0), are all equilibrium points of theplant model, and that all other points are unstable.
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