I am studying a paper on a control theory that deals with a multivariable system and does not use integrator in the designed controller. The author said in his study that he has avoided using integrator because it creates saturation which will lead to nonlinear effect and the control theory becomes invalid.
Can somebody explain the effect of an integrator in a control system and how and why it saturates the system response? what could be the measure to solve this problem in the control theory?
Dear Basim,
The practical integrator circuit is equivalent to an active first-order low-pass filter. Effectively the integrator creates saturation and this may adversely for control systems, so it is expected to add an anti windup element to mitigate the existence of this phenomenon.
Here are attached files as proof of this strategy
Remember that the integral part may remain doing this math operation for all time. In math/numerical environment this is certainly not a problem, However, in real life, actuators, OPAMPs (operational amplifiers), etc, saturates (they can not go beyond its own factory limit). For instance, OPAMPs are composed of transistors which can not consume more electric current than the allowed by the electric supply; actuators can not go beyond its physical limit, and so on.
I am fully agree with Ilhan Polat and Mohamed-Mourad Lafifi regarding integral saturatuion and to avoid it required anti-reset windup action.
Practically to avoid this saturated high output, the controller is first set to manual mode and operating the valve manually first bring the process value equal to the set point or desired value and then controller further switched to the AUTOMATIC Mode. This is popularly known as Bump-less transfer.
Just to add, saturation is considered a nonlinear effect since the transfer function (input-output relationship) changes depending on the value of the input. There is no linear representation for saturation hence making the system nonlinear. From a practical point of view, everything (motors, sensors, circuits) saturates that's the reason why most of the time the assumption of a "linear region" is taken.
Integrator usually eliminate steady state error in a system response. Saturation of integrator simply means the system does not follow it normal pattern with an integrator. and can simply be eliminated by using filter with the integrator.
An ideal integrator will continue to increase its output given a constant nonzero value since it basically finds the area under the curve of the input. However, a practical integrator will have limits or bounds in its output which results in saturation. As you may know, saturation is a nonlinear function which will cause nonlinearity in the system. The problem is that nonlinear terms make linear control development or analysis inapplicable. Maybe they are trying to build or develop a control technique using linear analysis and design techniques and so not using an integrator avoids the nonlinear effect.
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