Compensator Design Questions and Answers

Answer: A

Both Statement I and Statement II are false.

Statement I is false: a phase lag network behaves as a low-pass filter. It passes low frequencies and attenuates high frequencies, which is the reverse of what the statement says.

Statement II is false: steady-state accuracy is improved by the lag network, which raises the low-frequency gain and so reduces the steady-state error. A phase lead network improves the transient response, increasing bandwidth and speed of response, not the steady-state accuracy. Since both statements are wrong, every option calling either one true is ruled out.

Answer: D

A PI controller increases the type and order of the system by 1.

A PI controller has the transfer function

\[ \begin{aligned} G_{c}(s) &= K_{p} + \frac{K_{i}}{s} \\ &= \frac{K_{p}s + K_{i}}{s} \end{aligned} \]

It adds a pole at the origin and a zero. The extra pole at the origin raises the type of the system by 1, which is why integral action removes the steady state error to a step. The extra pole also raises the order of the characteristic equation by 1.

Options naming only the type or only the order are each half of the effect, and the option saying both decrease has the effect backwards.

Answer: B

Derivative control is desirable when the value of the controlled variable changes rapidly.

Derivative action produces a controller output proportional to the rate of change of the error, \(K_{d}\,de/dt\). It anticipates where the error is heading, so it reacts strongly to fast changes, adds damping and reduces overshoot. This makes it useful in processes where the variable can change quickly.

An output that settles below the set point is a steady-state offset, which needs integral action, not derivative action, since derivative does nothing to a constant error. Environmental influences and cost do not call for derivative control in particular.

Answer: A

The Smith predictor is used to compensate for time delays in the system.

A process with dead time, \(G(s)e^{-sT}\), is hard to control because the delay adds phase lag that grows with frequency and forces the controller gain down. O. J. M. Smith's scheme (1957) runs a model of the process inside the controller. The model's output without the delay is fed back in place of the real measurement, and the difference between the real output and the delayed model output corrects for model error. The controller can then be tuned as though the delay were not in the loop.

Better transient response, less overshoot or improved frequency response can follow as consequences, but they are not the specific purpose. The predictor exists to deal with dead time.