Control Systems

Why is the Nyquist plot symetrical about the real axis?

The value at the negative frequency is the complex conjugate, and hence the plot is symmetric about the real axis

A lag compensator has what net impact on the phase of the system at the phase margin frequency?

No net phase impact, causes the phase margin to increase because it causes it to happen at a lower frequency

Does a lag compensator increase or decrease the overall magnitude of the system output?

Lag compensator decreases magnitude (dB) of the system output

Does a lead compensator increase or decrease the phase at the phase margin frequency and why?

Increases the phase margin, both by increasing the phase

To what temporal charateristic is phase margin most closely related?

Overshoot

What affects do lead and lag compensators have on the phase margin frequency?

Lag compensator decreases the phase margin frequency, lead compensator increases it

How would you design a controller for a non-linear system that operated over a range larger than a lineariastion model would be accurate for?

Frequency domain techniques can still be used to determine stability of non-linear systems

Why may you want to create a digital twin for a mechanical system?

The parameters for a digital twin would be simpler to manipulate than an actual mechanical system A digital twin can make the system more efficient. It also enables a better design of the system as the twin creates data about the likely performance outcomes.

What is a major limitiation in understanding a high order system if you only have the transfer function?

Harder to determine stability

When will the time domain formula for a 2nd order system step response have a cosine component?

if there is no s^1 component in the denominator. the denominator should have roots in the form (s+1)(s-1). if there is a zero in the X(s) then the f(t) will have a cosine component

How can a 3rd order system (with no delay) be made stable for all system gains?

s^2 coefficient * s coefficient larger than s^3 coeefficient * constant. Could make constant 0

What shape could the asymtotes of the root locus branches take if the system has 4 poles and no zeroes?

All heading off to different corners

When would a full PID compensator be used?

If both transient and steady state responses need to be manipulated

Why is it not always possible to get the exact calculated performance from a system, even with a PID controller?

Real life issues, like time delays and imperfections

How can a 2nd order system decrease the frenquency range the phase transition occurs over and what affect will this have on the magnitude?

Have repeated roots. Means the magnitude will go down 40dB/dec at that point

How does a time delay affect a system?

Time delay can degrade the performance of a control system or lead to system instability. Time delays can also reduce the information systems use to respond to the environment and requires the system to predict future states based on the past inputs.

Why did the proportial controller become unstable in practical 1 when the motor is a 1st order system?

The gain value input to the system was large which caused the error to become large and hence oscillation down to a negative amplitude and the back up with an even larger overshoot, as this repeats the system becomes unstable

Will the inclusion of a digital controller make a system more or less stable at high frequency and why?

Less stable because of the time delays inherent in digital systems

Without knowing the closed loop system poles what are two ways of determaning system stability and how do they compare?

Open loop poles are the same as the poles of the characteristic equation, Routh array?

How many capacitors would be required to build an op-amp based electronic circuit that functioned as a lead-lag compensator?

4. 2 for lead, 2 for lag