Control System Principles Flashcards

Which of the following best describes the steady-state error of a Type 1 system subjected to a ramp input?

Answer: A finite constant

A Type 1 system has one integrator, which eliminates steady-state error for step inputs but produces a finite constant error for ramp inputs.

In a second-order control system, if the poles are located at -3 ± j4, what is the damping ratio?

Answer: 0.6

The poles are at σ ± jω_d where σ = 3 and ω_d = 4, giving ω_n = 5 and ζ = σ/ω_n = 3/5 = 0.6.

What is the primary function of a lead compensator in a control system?

Answer: Improve transient response and increase phase margin

A lead compensator adds positive phase at crossover frequency, increasing phase margin and improving transient response speed.

For a unity feedback system with open-loop transfer function G(s) = K/[s(s+2)(s+5)], what happens to closed-loop stability as K increases beyond a critical value?

Answer: System becomes unstable

As K increases, root locus poles migrate into the right-half plane, causing instability; the Routh criterion confirms a finite gain margin.

Which parameter is directly read from the Bode magnitude plot at the gain crossover frequency?

Answer: The magnitude is 0 dB by definition

The gain crossover frequency is defined as the frequency where the open-loop magnitude equals 0 dB (unity gain).

In state-space representation, what does the matrix C represent in the equation y = Cx + Du?

Answer: Output matrix relating states to outputs

The C matrix (observation matrix) maps the state vector x to the system output y.

A PD controller applied to a second-order plant primarily has what effect on the closed-loop system?

Answer: Adds a zero that increases damping ratio

The derivative term of the PD controller adds a zero to the open-loop transfer function, which increases damping and reduces overshoot.