Suppose that we wish to use a combination of feedback and feedforward control in the form qe = q∗ + Kf b(h − h^∗) + K^ffQ(t).

a. Show that you obtain perfect control (h = h* at all times) for Kff = 1. Show
that steady-state offset is reduced for K_ff ff never be greater than unity?)
b. Now suppose that some input disturbances are unmeasured, or there is unknown measurement error, in which case Q(t) = Q_m(t) + Q_u(t), where the subscriptsmand u refer to measured and unmeasured, respectively. The controller then has the form q_e = q∗ + K_fb(h − h∗) + K_ffQ_m(t). Obtain the equation for the response of the controlled system. How should K_fb be chosen if K_ff = 1? If K_ff c. In your physics course you may have studied the damped harmonic oscillator. If so, consider the case in which the feedback controller is proportional plus integral, or PI, control:

Show that the equation for the flow in the tank becomes identical to the equation for the damped harmonic oscillator, and that steady-state offset is eliminated for Q(t) = constant.

Transcribed Image Text:

qe = q* + Kƒb(h - h*) + K₁ | [h(t) – h*]dt. 0