Control System Principles Flashcards

The Nyquist stability criterion states that the number of unstable closed-loop poles equals:

Answer: The number of encirclements of -1+j0 minus open-loop RHP poles

N = Z - P, where N is net clockwise encirclements of -1, P is open-loop RHP poles, and Z is closed-loop RHP poles; solving for Z gives stability information.

Which of the following describes a marginally stable system?

Answer: Poles on the imaginary axis with no repeated poles there

Marginal stability occurs when poles lie on the imaginary axis (non-repeated) and none are in the right-half plane, producing sustained oscillations.

For the transfer function G(s) = 100/[(s+1)(s+10)], what is the DC gain?

Answer: 10

DC gain is G(0) = 100/[(0+1)(0+10)] = 100/10 = 10.

In root locus design, where do the branches begin and end as gain K goes from 0 to infinity?

Answer: From poles to zeros (finite or at infinity)

Root locus branches originate at open-loop poles (K=0) and terminate at open-loop zeros or at infinity (K→∞).

An integrating element (1/s) in a control loop ensures zero steady-state error to which type of input?

Answer: Step

A single integrator (Type 1 system) eliminates steady-state error for step (position) inputs due to the infinite DC gain of the integrator.

What does the time constant τ represent in a first-order system G(s) = 1/(τs+1)?

Answer: The time to reach 63.2% of final value

For a first-order system, the time constant τ is the time required for the step response to reach 63.2% (1 - e⁻¹) of its final value.

Which frequency-domain specification directly measures the robustness of a closed-loop system to gain variations?

Answer: Gain margin

Gain margin indicates how much the open-loop gain can increase before the system becomes unstable, directly measuring gain robustness.