What are the main differences between PID controller and lead/lag compensators? When and were are they implemented?


I am working on position control of a DC motor connected to a pulley and getting position feedback by means of a potentiometer. The motor is given a square wave for obtaining a step response. I deduced the transfer function and designed a PID using the Manual Method and ZN. Now I need to design a phase lead and phase lag compensator. thanks

 

What are the main differences between PID controller and lead/lag compensators? When and were are they implemented?

These just have different pole and zero locations. Generally, the PID is good if you don't have a detailed system model and just want a flexible controller that can be tuned to get good operation. The lead/lag would usually be used if you have a detailed system model and determine that you would like to modify the system response. Without a system model, it might be difficult to know how to tune the lead/lag compensator, although it could be tuned by trial and error experimentally.

Sometimes, you might want to combine methods. I sometimes use a lead/lag or lag/lead to modify the system response, and then put a PI controller on the new system.

 

A lead-lag circuit can be considered a part of a PID loop. The lead is the D (differentiator) part and the lag is the integrator (I) part. The P is the proportional part, of course.

 

I assume the final bandwidth of the system cascaded with lead/lag compensator is the whole CLTF not the OLTF.. is that correct? Do you have any idea of the matlab commands required? thanks

 

The practical PID controller provides "knobs that can be twiddled" to adjust a system response. Hence the evolution of tuning algorithms such as Ziegler-Nichols to optimize the response of systems fitted with PID controllers.

One thing that was overlooked in earlier comments is that Integral control is introduced to remove steady-state offset error from the closed loop input-output response. If steady-state error is not a problem then one would be disinclined to add potentially destabilizing Integral control.

A Lead-Lag compensator is probably less accessible in the sense of having twiddle knobs at one's disposal. The L-L compensator is normally designed with a good understanding of the uncompensated control system's open loop behaviour. The Bode plot is often a tool employed in conjuction with the compensator design. Generally one is attempting to control the open loop phase margin without sacrificing DC ['zero frequency'] gain.