Post date: Mar 5, 2014 4:30:49 AM
Suppose this is the block diagram, where
e = r - y is the error
D = step disturbance, and it enters at the point shown (after the controller, before the plant)
r is a step input
r-->(r-y)--->[controller]--->(+D)-->[plant with integrators]-----> y
Question: We know integrator action gives zero steady state error in the presence of disturbances. Can we use a proportional controller K here since the plants have integrators already? How many integrators should the plant have so that we can use a proportional controller, one or many? Assume that the a proportional controller gives zero error for a step input in the absence of any disturbance.
Answer: If you evaluate the transfer function from Y/D, it can be seen that no number of integrators in the plant can make y(inf) --> 0 in the presence of D. Or otherwise, evaluate the transfer function from E/R, and the same can be observed. The integrator must be used before the point of entry of D. Hence, the controller should use a PI or PID.