Control Systems

When would a PI be a good compensator to use?

Very reduced steady state error with minimal impact on transient response characteristics

Algebraically how does a transfer system with a time delay compare to one without?

Time delay does not affect the magnitude of the response but introduces a linearly increasing phase shift (delay). This decreases the gain and phase margins, moving system closer to instability.

At the frequency of the pole in a 1st order system what will the magnitude of the output be?

-3dB

At the frequency of the pole in a 1st order system what will the phase of the output be?

-45deg

For 2nd order systems with complex poles where are the poles located on a Bode plot?

Corner frequency? Or 1?

How can you determine the order of a system by looking at the Bode plot?

Number of slope changes (down 20dB/dec for poles, up 20dB/dec for zeros)

How does the damping ratio of a 2nd order system affect the Bode plot?

As the damping ratio decreases, both the magnitude peak, and sharpness of the phase change, at critical (natural) frequency gets larger.

If a 1st order system has a pole at w over what frequency range will the phase transition occur?

1/w to 10w

If a LTI system was excited by a sinusoid what components of the signal could be different, and what must remain the same, at the output?

Same frequency, different amplitude and phase

If a time delay were inserted into a 2nd order system would the overshoot get larger or smaller?

Larger

What are the gain and phase margins of a system and how would you determine them?

Gain margin is the gain value when the frequency crosses the horizontal axis, phase margin is the phase value when the gain crosses the horizontal axis

What are the similarities and differences between an impulse and white noise in the frequency domain?

Both have all frequencies, but impulse has specific phases where white noise has random phases

What is aliasing and why is it detrimental for system analysis and control?

Aliasing occurs when the sampling frequency is less than double the frequency of the highest frequency component of the signal. It causes information to be lost and can produce a misleading analysis

What is the maximum phase change induced by a 3rd order system with 2 zeros?

neg 270 (from the poles, the zeros would act against it)

How can a Nyquist plot be used to determine the stability margins of a system?

Observe closeness to (-1,0)

What are the two main ways to calculate the stability of a system?

Routh Hurwitz Method and Root locus for time domain Nyquist criterion and Bode plot for frequency domain

What is Contour mapping and why would it be used?

Contour map is a contour in the s plane that has been mapped into the F(s) plane using a certain function. It is used to create a Nyquist plot

What is the Nyquist Stability Criterion?

N = Z - P = 0 for stability. Nyquist stability criterion states the number of encirclements about the critical point (1+j0) must be equal to the poles of characteristic equation

What is the procedure to create a Nyquist plot?

Find the open-loop transfer function, OLTF = G(s)H(s) Find the number of unstable open loop poles, P Set the Nyquist path in the s-plane Draw the Nyquist Diagram in the GH plane Count the number of encirclements of the point (-1,0), N Calculate the number of unstable closed loop poles, Z = N+P If Z=0 the system is stable

What is the relationship between Nyquist and Bode plots?

Bode plot shows the same information as the nyquist plot but separated into phase and magnitude, on a frequency scale