Here is an excerpt from "G. Ellis, Control System Design Guide":

"Compensators are specialized filters ...designed to provide a specific gain and phase shift, usually at one frequency. The effects on gain and phase either above or below that frequency are secondary."

My opinion: There is no clear threshold between "compensators" and "controllers".

Some authors use one or the other term (or mixed). Am I wrong?

To be more precise: I think, each compensator (P, I, PI, PID) can be regarded as a controller - but not vice versa. The bang-bang controller certainly is not a compensator.

A controller aids the output towards its nominal set point and tries in reducing the error. The simplest example in this regard is a PID controller. On the other hand, a compensator is required in altering the entire system characteristics; it is operated beyond the control functions.

Controllers are in terms of magnitude perspective whereas the compensators are in terms of the phase perspective.

Design of controllers more concern with arrangement of system structure and the selection of a suitable components and parameters. A compensator is an additional component or circuit that is inserted into a control system to compensate for a deficient performance of the overall system.

The lead compensator plays the same role as the PD controller, reshaping the root locus to improve the transient response.

For the controller P,PI,PD, PID the design is used for not only filtering but controlling is the main function,and repeatedly it does. but for compensation is temporarily filtering activity. some times for controller compensation term may used.

I agree with Lutz von Wangenheim. In my opinion, a compensator is some type of Controller that is designed to shape the disired magnitude and phase plots of a closed loop controller by reshaping the open loop transference (G(jw)H(jw)). The term compensation is much linked to the Bode Design, a classic control controller design technique (e.g. lead, lag, lead-lag compensation) although it is also found in Root Locus design.

On the other hand, a Controller is much more general term which refers to the block (an analogue/digital processor) that is inserted to produce the desired behavioural closed-loop performance, be it in the frequency domain, or in the time domain. The term controller is not linked to any design technique in my opinion.

Thank you all for splendid answers... I think, now, i am clear about this point.

I think there is another difference: I, personally, associate with the term 'compensator' something that 'compensates' for the deviation from a set point or so. I would expect the 'compensator' to measure the deviation between a reference and and output signal, and its output, to additively enter the signal path of the closed loop. In particular, I would not use the term 'compensator' if the plant is eg a finite automaton. In contrast, a 'controller' is just a device the guarantees that the closed loop enforces some predefined specification. The term is appropriate even if the plant is purely discrete and the specification is more complex than, say, tracking or stabilization.

(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.

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, 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. Available from the following RG Link. https://www.researchgate.net/publication/3332273_Self-tuning_IMC-PID_control_with_interval_gain_and_phase_marginsassignment

(2) A larger phase margin indicates a more stable control system but more sluggish response. The following Automatica 2003 paper recommended 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. https://www.researchgate.net/publication/223504459_Relay_auto-tuning_of_PID_controllers_using_iterative_feedback_tuning

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

(3) 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)

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

(3) Recent 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

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

Nasser, then maybe the "compensator" is a "stabilizer"?

...it seems so.

Yang, I have the feeling that you should swap "PD controller will make the system more stable" with "PI controller will make the system response faster"; i.e., they should be "PD controller will make the system response faster" and "PI controller will make the system more stable", right?

BTW, it is interesting and funny for electronics people to see that the humble inverting amplifier is a "proportional controller"...

... when connecting a capacitor in parallel to the first resistor we obtain a "proportional-derivative controller"...

... or when connecting a capacitor in series to the second resistor we obtain a "proportional-integrating controller"...

... and finally, by cascading the last two circuits we obtain a "proportional-derivative-integrating controller"...

Hi Cyril - as your examples demonstrate, electronic engineers and control system guys very often have different terminologies to desrcibe the same properties of a device.

As another example: A P-T1 block (control theory) is identical to a simple 1st-order lowpass.

I have another example that sometimes can create problems between both parties:

To me, "loop gain" is simply the frequency-dependent gain of the complete feedback loop. In the past, I have met control system engineers using this term ("loop gain") for the DC part only.

Maybe the truth is somewhere between the two statements, i.e., there are two loop gains (DC and AC)?

Lutz, I think there is no problem if "electronic engineers and control system guys have different terminologies"; the problem is when they do not suppose these device are identical... I would give a funny example illustrating this phenomenon in the area of measurement and electronics...

All we dugouts:) remember the old black boxes - measuring potentiometers, in the classic measurement laboratories where we had to measure an unknown voltage (by compensating). Then, in the electronics laboratories, we had to investigate an op-amp non-inverting amplifier. Maybe some of us ("system guys") had to investigate a potentiometric servo system in the control laboratories. But remember no one said to us that all these devices were the same...

"I think there is no problem if "electronic engineers and control system guys have different terminologies".

Cyril, of course, I agree - however, one should be aware of this and - if possible - should know the terminology from the "other side". I remember very well that the mentioned example (loop gain) has caused a long discussion - until we noticed that we were using different definitions.

(By the way: I suppose, you forgot to include a smiley when you were saying that " the truth is somewhere between the two statements".)

Lutz:)

, A compensator is a type of controller

which is used to improve characteristics of the open­loop system so that

the compensator can be used with feedback control safely

a controller in a fixed configuration is a compensator...

A compensator is a component in the control system and it is used to regulate another system. Most of the time, it is done by conditioning the input or the output to that system.

Adjusting a control system in order to improve its performance might lead to unexpected behavior (e.g. poor stability or even instability by increasing the gain value). In order to make the system behave as desired, it is necessary to redesign the system and add a compensator, a device which compensates for the deficient performance of the original system. [Wikipedia]

Dear Deep Shekhar Acharya

The objective of a controller is to respond to the error, an example of a controller is the PID. On the other hand the objective of a compensator is to change the original dynamics of the plant, examples of compensators are the lead, lag, and lag-lead compensators

Best regards