I have a question regarding the PI controller. Lets say I have an actuator via which I control some plant. The control signal at the output of the PI controller is at its maximal realizable value. So the actuator supplies 100% power into the plant. Despite this fact the time response of the control loop is sluggish. Does it mean that the actuator has been chosen in wrong manner for a given plant? Thanks for clarification.
If the control signal is at maximum and you are still not getting the system performance you want than the problem would be an under sized actuator.
Consider a controls engineer sitting in their car at a stop light that just turned green. The engineer would like to reach a speed of 40 Mph as soon as possible. So the engineer floors the peddle. You can consider a floored peddle a saturated command signal. At this point it is no longer up to the engineer to affect the acceleration of the vehicle. The only way to improve the cars performance is by changing the car it self. Not the control system (The driver in this case)
Does it mean that the actuator has been chosen in wrong manner for a given plant?
If the actuator is at a point where it cant give additional energy its called a saturation point. Saturation points are bad because:
it makes the system hard to analyze because it no longer behaves linearly.
it can make the system unstable because of integrator windup and other effects (the system is not longer linear).
A change to the system would need to be made to prevent saturation of the actuator which could be done by changing the gain or increasing the actuator so it can respond with more energy.