Laplace Domain Analysis And Stability

Question 1

What are the five elements in the feedback control loop?

Answer 1

Process, Sensor-Transmitter,Controller, Current to Pressure Transducer,Control valve

Question 2

The effect of increasing Kc where there is setpoint changes for proportional control

Answer 2

It will reduce offset. But if it is too large, it will result in oscillatory or unstable responses due to the effect of additional lags and time delays

Question 3

The effect of increasing Kc where there is disturbance changes for proportional control

Answer 3

Reduces the amount of offset for disturbance changes

Question 4

Effect of adding integral action in PI control and disturbance changes

Answer 4

Eliminates offset for a step change in disturbance and offset for step change in setpoint. But it does not eliminate offset for a ramp response

Question 5

Effect of decreasing tauI or increasing Kc in PI control and disturbance changes

Answer 5

The response is sped up

Question 6

When is the performance of a FB closed loop system considered to be satisfactory?

Answer 6

If the oscillations have a small amplitude and damp out quickly

Question 7

When is a system stable?

Answer 7

When the output response is bounded for all bounded inputs

Question 8

What is a bounded input?

Answer 8

An input variable that stays within the upper and lower limits for all values of time

Question 9

Examples of bounded responses

Answer 9

Step and sinusoidal functions

Question 10

Examples of unbounded responses

Answer 10

U(t)=t and exponential

Question 11

What is the prerequisite of having a physically realisable system? Looking at the characteristic equation?

Answer 11

The number of poles must be greater than or equal to the number of zeros

Question 12

When is the closed loop system unbounded looking at the poles?

Answer 12

If one pole is a positive real number. This makes the response unbounded

Question 13

When is the closed loop system stable looking at the poles?

Answer 13

If all poles are negative or have negative real parts

Question 14

State the general stability criterion

Answer 14

The FB control system is stable if and only if all roots of the characteristic equation are negative or have negative real parts, otherwise the system is unstable.

Question 15

Why is it that if the closed loop system is stable for disturbances, it will also be stable for set-point changes?

Answer 15

The characteristic equations occurs for both disturbance and set-point changes. In their denominators

Question 16

Routh stability criteria limitation

Answer 16

It is not directly applicable to systems containing time delays

Question 17

What advantage does the bode stability criterion have over the general stability criterion?

Answer 17

It provides a measure of the relative stability rather than merely answer yes or no to the quiz, “is the closed loop system stable”

Question 18

Bode stability criterion

Answer 18

Consider an O-loop t.function that is strictly proper (zeros

Question 19

Properties of the bode stability criterion

Answer 19

1. It provides a necessary and sufficient condition for closed loop stability, based on the properties of the O-loop t function.
2. The bode stability criterion is applicable to systems that contain time delays.
3. The bode stability criterion is very useful for a wide variety of process control problems. However, for any Gol(s) that does not satisfy the required conditions, the Nyquist stability criterion can be applied.

Question 20

What happens when a closed loop system is marginally stable?

Answer 20

The closed-loop response exhibits a sustained oscillation after a setpoint change or a disturbance. Thus the amplitude neither decreases or increases.

Question 21

How does the Gain Margin (GM) provide a measure of relative stability

Answer 21

It indicates how much any gain in the feedback loop component can increase before instability occurs

Question 22

What does the phase margin indicate?

Answer 22

How much additional time delay can be included in the FB loop before instability will occur.

Question 23

Guideline for GM and PM

Answer 23

A well tuned controller should have a gain margin between 1.7 and 4.0 and a phase margin between 30 and 45 degrees

Question 24

T/F

Increasing the controller gain speeds up the response for a set-point change

Answer 24

Always true. Care must be taken not to increase it too or oscillations will result.

Question 25

T/F

Increasing the controller gain always causes oscillations in the response to a set-point change.

Answer 25

False. If the open loop system is first order, increasing Kc cannot result in oscillations.

Question 26

T/F

Increasing the controller gain too much can cause instability in the control system

Answer 26

Sometimes true. With the exception of 1st order and 2nd order systems

Question 27

Selecting a large controller gain is a good idea in order to minimise.

Answer 27

Always true. Increasing controller gain will decrease offset