Question

Elevator motors require feedback control to avoid speed differences between up- ward and downward movement and when a different number of passengers ride the elevator car. Soft acceleration and deceleration is achieved with the same feedback control system. A possible feedback control system is shown in Figure 2. E(s) Motor R(S) H(S) w(S) S+5 10 S+10 Figure 2: motor. Suggested feedback control system for controlling the speed ?(s) of an elevator The motor speed is measured with an optical encoder, and the integration of the encoder slits causes a slightly delayed response that can be modeled with the tachometer function 10/(s10). To simplify the task, the steady-state gain of the motor is combined with the controller, and we can describe a PI controller with the transfer function s + where g is an adjustable gain parameter and k is the adjustable weight coefficient of the integral component. A. Formally prove that the steady-state tracking error vanishes in this feedback configuration when kl > 0 and the input R(s) Is bounded. Hint: The tracking error E(s) is defined as E(s)R(s)-s. It is sufficient to show with the final value theorem that ?(t ? oo) = R(1 ? ?), irrespective of the actual function R(s). If you insist, you may use R(s) 1/s. [5 points]

Answer 1

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3 apply lemtt ten ocf