Control Systems

What is system sensitivity and how is it different between open- and closed-loop control?

System sensitivity is the ratio of change in the system TF to the ratio of change in plant TF. Open: 1, Closed: 1/(1+CG)

Why is it sometimes good to have a high controller gain, irrespective of system dynamics?

to determine when the system becomes unstable, or to have a faster system response. To amplify the system response, which can be useful when passing it into another system.

If you can use MATLAB to find system roots why would you need a Routh Array?

Useful for determining unknown design parameters while maintaining stability and without solving the characteristic equation

What is an operation you can perform to determine system stability without finding system roots?

Routh Array

As the system gain gets larger what happens to the branches of the root locus?

Head to infinity or to system zeros

How can a root locus be used to determine the system gains for stability?

System is stable so long as the poles are on the left half plane

How can required performance be achieved in a system if the goal point is not on the root locus?

Add poles/zeros

How many brances will the root locus of a system have?

The number of branches on the root locus will be equal to the number of open loop poles in the system

Is an open loop stable 2nd order system (with no delay) always stable for all system gains?

Yes. Poles of the open loop system are not dependent on K

What can a root locus be used for?

The root locus can be used to qualitatively describe the performance of a system. transient properties, systems stability

What is the root locus angular requirement?

The sum of the angles between the poles and zeros must be equal to 180.

What shape could the asymtotes of the root locus branches take if the system has 3 poles and no zeroes?

Single pole heading to negative infinity, complex conjugate pair heading away to infinity 60 degrees above and below the real axis

When will a segment of the real axis be on the root locus?

Left of an odd number of poles

Why is the root locus always symetrical about the real axis?

Because the branches of the roots diverge away from each other. This results in branches acting symmetrically about the real axis as they have to move away from each other at the greatest angle (180 degrees).

What does pole, or zero, placement mean in the context of designing a control system?

It affects the transient response of the system, the direction of the root locus, whether or not desireable characteristics of a response to a step input are observed, and if the system is stable or not.

What effect will increasing the D component of a PID compensator have on: rise time, overshoot, settling time and steady-state error?

Small decrease in rise time, decreased overshoot and tss, minor change to steady state error, improves stability

What effect will increasing the I component of a PID compensator have on: rise time, overshoot, settling time and steady-state error?

Small decrease in rise time, increase in overshoot and tss, large decrease in steady state error, decreases stability

What effect will increasing the P component of a PID compensator have on: rise time, overshoot, settling time and steady-state error?

Decreases rise time, increases overshoot, small increase in tss, decreases steady state error and stability

What is pole cancellation and why is it rarely done in practice?

Placing a zero exactly on a pole to cancel its effects on the system. Rarely done in practice because it has to be perfect otherwise it introduces undesired system dynamics

When would a PD be a good compensator to use?

Gives shorter Tss, reduces steady state error (doesn't get rid of it)