Dear Kranthi Kumar Deveerasetty, A compensator is a type of controller which is used to improve characteristics of the open-loop system so that the compensator can be used with feedback control safely.

See this link:

https://www.researchgate.net/post/Controller_Vs_Compensator

Thank you

there is no a big difference, but I think the compensators such as lead compensators oor lag compensators and lead lag have similar effects to controllers (PI,PD,PID) on the performance of the system, you can check that by plotting bode diagram for a second order system and see the effects of compensators and controllers on the stbility of systems (gain margin,phase margin).

(1) One goal of both controller and compensator is to achieve the control system stability. According to Nyquist stability criterion, positive phase margin indicates a stable closed-loop feedback control system.

Comments on Nyquist stability criterion by Hendrik W. Bode, Harvard University, USA, 1977.

"To control theorists, Nyquist is no doubt best known as the inventor of the Nyquist diagram, defining the conditions for stability of negative feedback systems. This has become a foundation stone for control theory the world over, applicable in a much wider range of situations than that for which it was orignally enunciated."

http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1101666 A larger phase margin indicates a more stable control system but more sluggish response.

The following Automatica 2003 paper recommendeded that the choice of phase margin between 30 degree and 60 degree can achieve a good trade-off between system stability and responsiveness.

By cooperating with his peer researchers including Stanford University researcher, H. Hjalmarsson integrated iterative feedback tuning with PID controller to solve controller tuning issues caused by plant uncertainty. H. Hjalmarsson was elected to the Class of 2013 IEEE fellow due to his fundamental contribution to iterative feedback tuning.

"Relay auto-tuning of PID controllers using iterative feedback tuning," Automatica 39 (1), January 2003, pp. 149-157.

(2) Usually a compensator is combined with a controller (such as PID controller) to tune the control system performance. A typical representation of a compensator in frequency domain is (s-z)/(s-p), where z is the zero, p is the pole, and the pole and zero are both typically negative. In a lead compensator, the pole is one the left of the zero in the complex plane, that is, |z||p|. A lag compensator will make the phase margin become smaller. Similarly, PI controller will make the system response faster.

The following IEEE TCST 2001 paper shows that a representation of PID controller can be K_c(1+1/sT_i)(1+sT_d), a combination of PI controller and PD controller, which can be regarded as a "pseudo" lead-lag compensator.

"Self-Tuning IMC-PID Control with Interval Gain and Phase Margin Assignment," IEEE Transactions on Control Systems Technology, 9(3), May 2001, pp. 535-541.

Only PID Control and Smith Predictor were listed in the “Leaders of the Pack” InTech’s 50 most influential industry innovators since 1774. Available from the following link.

http://archive.today/2RoSK

PID Control was listed twice (the dominant control method in the industrial application -- (1) John G. Ziegler and Nathaniel B. Nichols and classical PID Control; (2) Karl Johan Åström and modern PID Control (IEEE Medal of Honor, 1993) http://en.wikipedia.org/wiki/IEEE_Medal_of_Honor http://www.ieee.org/about/awards/medals/medalofhonor.html

The next popular method is Smith Predictor: Otto J.M. Smith and Smith Predictor. http://en.wikipedia.org/wiki/Otto_J._M._Smith

WK Ho, Y Hong, A Hansson, H Hjalmarsson, and JW Deng, "Relay auto-tuning of PID controllers using iterative feedback tuning," Automatica 39 (1), January 2003, pp. 149-157. Available from the following RG Link. https://www.researchgate.net/publication/223504459_Relay_auto-tuning_of_PID_controllers_using_iterative_feedback_tuning

W.K. Ho, T.H. Lee, H.P. Han, and Y. Hong, "Self-Tuning IMC-PID Control with Interval Gain and Phase Margin Assignment," IEEE Transactions on Control Systems Technology, 9(3), May 2001, pp. 535-541. Available from the following RG Link.

H. Nyquist (Sweden) --> K.J. Astrom (Sweden) --> W.K. Ho (Sweden)

     | Nyquist plot (published in 1932)

     |  Bell Labs

    V  Bode plot (published in 1940)

H.W. Bode (Harvard) --> K.S. Narendra (Harvard, Yale) --> T.H. Lee (Yale)

https://www.researchgate.net/publication/3332273_Self-tuning_IMC-PID_control_with_interval_gain_and_phase_marginsassignment

C.C. Hang, K.J. Astrom, and W.K. Ho, "Refinements of the Ziegler-Nichols tuning formula," IEE Proceedings on Control Theory and Applications, 138(2), March 1991, pp.111-118.

http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=67610

This paper and selected classic PID tuning methods (co-invented by K.J. Astrom and his student W.K. Ho) have been implemented by Maplesoft Inc. for MapleSim Control Design Toolbox  http://www.maplesoft.com/support/help/MapleSim/view.aspx?path=ControlDesign/GainPhaseMargin

K.J. Åström, T. Hägglund, C.C. Hang, and W.K. Ho, "Automatic tuning and adaptation for PID controllers - a survey," Control Engineering Practice, 1(4), August 1993, pp.699-714. http://www.sciencedirect.com/science/article/pii/096706619391394C K.J. Åström, C.C. Hang, P. Persson, and W.K. Ho, "Towards intelligent PID control," Automatica, 28(1), January 1992, pp.1-9. http://www.sciencedirect.com/science/article/pii/000510989290002W

Discussions on control system design

"What are trends in control theory and its applications in physical systems (from a research point of view)?" https://www.researchgate.net/post/What_are_trends_in_control_theory_and_its_applications_in_physical_systems_from_a_research_point_of_view2

Article Self-tuning IMC-PID control with interval gain and phase mar...

Article Relay auto-tuning of PID controllers using iterative feedback tuning

It appears to me that word, "compensator" would have been coined when cross field machines were popular. We do have compensating windings in cross field machines specially in case of Amplidyne. A compensator seems to compensate partially, 100%, and over 100% and called as partially compensated and level compensated and over compensated. The type of compensation depended very much on feed back signal - flux and also on number of turns on the compensating winding. The level compensated is perfect and can be regarded as controller.

In my opinion the classical control theory would have been derived from electrical machine technology, because when there were no electronic components invented, still the control practices were adopted using rotating machine as amplifier and controller.

We use the words compensator and controller interchangeably but i think we called the controller as compensator when the reference or the set point is constant with time (regulators= compensator) (regulation the system output about constant set point ) but when the reference is variable with time (tracking system ) the correct word is the controller

Yes! I agree with Nasser. In case of cross field machines number of turns in compensating windings were fixed and not changed with signals.

Thank you one and all

compensator is a unit that can be employed to help fix certain system metrics that are outside of a proper operating range.

Controller is a unit that manages or directs the flow of data between two entities.

Dear Kranthi Kumar Deveerasetty, I am again here:

"A compensator is a controller meant to improve characteristics of the open-loop plant so that it can safely be used with feedback control. There are a number of different compensation units that can be employed to help fix certain system metrics that are outside of a proper operating range. Consider to differentiate let us talk about a microphone; soundboard and the speakers. If microphone is near to speakers then the higher harmonics tone superimposed in the system with high gain it is then the engineer’s job to compensate sound system by adjusting the gain and phase characteristics around that particular frequency".