Laplace Domain Analysis And Stability Flashcards
What are the five elements in the feedback control loop?
Process, Sensor-Transmitter,Controller, Current to Pressure Transducer,Control valve
The effect of increasing Kc where there is setpoint changes for proportional control
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
The effect of increasing Kc where there is disturbance changes for proportional control
Reduces the amount of offset for disturbance changes
Effect of adding integral action in PI control and disturbance changes
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
Effect of decreasing tauI or increasing Kc in PI control and disturbance changes
The response is sped up
When is the performance of a FB closed loop system considered to be satisfactory?
If the oscillations have a small amplitude and damp out quickly
When is a system stable?
When the output response is bounded for all bounded inputs
What is a bounded input?
An input variable that stays within the upper and lower limits for all values of time
Examples of bounded responses
Step and sinusoidal functions
Examples of unbounded responses
U(t)=t and exponential
What is the prerequisite of having a physically realisable system? Looking at the characteristic equation?
The number of poles must be greater than or equal to the number of zeros
When is the closed loop system unbounded looking at the poles?
If one pole is a positive real number. This makes the response unbounded
When is the closed loop system stable looking at the poles?
If all poles are negative or have negative real parts
State the general stability criterion
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.
Why is it that if the closed loop system is stable for disturbances, it will also be stable for set-point changes?
The characteristic equations occurs for both disturbance and set-point changes. In their denominators
Routh stability criteria limitation
It is not directly applicable to systems containing time delays
What advantage does the bode stability criterion have over the general stability criterion?
It provides a measure of the relative stability rather than merely answer yes or no to the quiz, “is the closed loop system stable”
Bode stability criterion
Consider an O-loop t.function that is strictly proper (zeros
Properties of the bode stability criterion
- It provides a necessary and sufficient condition for closed loop stability, based on the properties of the O-loop t function.
- The bode stability criterion is applicable to systems that contain time delays.
- 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.
What happens when a closed loop system is marginally stable?
The closed-loop response exhibits a sustained oscillation after a setpoint change or a disturbance. Thus the amplitude neither decreases or increases.
How does the Gain Margin (GM) provide a measure of relative stability
It indicates how much any gain in the feedback loop component can increase before instability occurs
What does the phase margin indicate?
How much additional time delay can be included in the FB loop before instability will occur.
Guideline for GM and PM
A well tuned controller should have a gain margin between 1.7 and 4.0 and a phase margin between 30 and 45 degrees
T/F
Increasing the controller gain speeds up the response for a set-point change
Always true. Care must be taken not to increase it too or oscillations will result.
