Question

Applied Instrumentation and Control

Describe the difference between saturation and non-saturation of outputs for a controller. Give examples of each one.

Answer 1

Applying the saturation on top of the PID controller makes the controller nonlinear, because the saturation is usually mathematically defined as a nonlinear and/or non smooth function.

This means that Linear control theory can not be applied to analyze the system. Nonlinear methods of analysis are complex and not popular in practical applications.

Moreover, during the saturation, the feedback loop is broken and the system operates in an open loop mode. This may lead to instability.

example: pi controller

The phenomenon of saturation in a PI controller is called reset windup. Saturation is a physical limitation of the system, which is actually the point where system reaches safe limits of operation.

Integral windup, also known as integrator windup or reset windup, refers to the situation in a PID feedback controller where a large change in setpoint occurs (say a positive change) and the integral terms accumulates a significant error during the rise (windup), thus overshooting and continuing to increase as this accumulated error is unwound (offset by errors in the other direction). The specific problem is the excess overshooting.

To deal with this problem, we have various approaches.

• If the maximum slew rate of the process variable (maximum rate of change of process variable) can be predicted, we can introduce a derivative control and tune the gain accordingly.This probably shows that PID control is required over just using PI.
• Another solution is disabling the integral control once the process variable increases above a certain limit
• Anti reset windup algorithms back calculate and change integral gains
• For really simple cases, even reducing gain of Integral control is enough.

non saturation means it is a ideal one without any deviations.