Circuits for P, PI and PID controllers

[garvind25]

Hi there,

I wanted to know how to actually implement the P, I and D sections of of controllers in hardware? What is the actual electronic circuitry behind it? If possible pls. point me to a relevant textbook as well.

Thanks and Regards,
Arvind Gupta

 

[asdf44]

P is just a gain stage
I is an 'integrator' google for examples of opamp integrators
D is a 'differentiator' google for examples of opamp differentiators


Also understand how PID maps to common power supply control terminology:
I: Type I compensator
PI: Type II compensator (Type II has additional pole)
PID: Type III compensator (Type III has two additional poles)

Each of the above can be googled to find a corresponding circuit


Note a point of confusion: PID is more often used in industrial type control. In other areas you'll find less reference to PID. One reason: No system wants PID (two zeros, one pole) for compensation. In industrial environments there are usually additional poles in the system (thermal time constant of an oven for example) which provide the needed additional poles (but may not be mentioned).

 

[garvind25]

Thanks for your response. I also wanted to know the following:

1. What is meant by 'control system tuning'. is it related to tuning P, PI and PID controllers or something more? I need to know from astronomical application point of view (for an upcoming interview)

2. I have heard of P, PI and PID controllers being used. Are I, D, PD controller configurations also used? Where should I read about all these controller configurations and about their tuning pls?

Thanks again,
Arvind Gupta

 

[KlausST]

Hi,

Especially for PID controllers, how to design them, how to tune them...there are countless design notes, application notes, discussions, even a lot of videos.There are many good ones. Look for documents from semiconductor manufacurers, universities or other reliable sources.

Klaus

 

[garvind25]

OK. But my basic query remains. What is meant by control system tuning? Is it related to tuning P, PI and PID controllers? Or is there something more? And do the other combinations exist... I, D, PD controller configurations?

Regards,
Arvind Gupta.

 

[asdf44]

Control system 'tuning' may mean tuning the individual coefficients. It may also mean general control design. There is a lot more to control design than just tuning the bode plot of the compensator (where is feedback taken, control topology, limits, anti-windup, feed forwards etc)

Yes other combinations exist. I is the same as a Type I compensator and is very common (also called dominant pole compensation).

D or PD would be rare.

It all depends on the system. Understand the basic goal is to create an open loop transfer function which is very roughly a single pole system with 90 degrees of phase shift (<135 degrees is ok). If the system has a pole you add a zero in your compensator. If your system has a zero you add a pole in your compensator. So you choose a control topology that gives the poles and zeros you need to do that.

 

[garvind25]

Thanks for the insights. This has risen few more queries in my mind. Hope you will address them.

1. How to introduce a pole (or a zero) in a given system? Suppose I have a system with closed loop transfer function (with unity feedback) as T(s) = 10/[(s+100)*(s+200)]. I want to introduce a pole at s=-2. How do I do physically do that? I understand I will have to do so with a capacitor. But how to I calculate the value of ‘C’?

2. What is dominant pole theory? Where to read it from?

3. For a given transfer function (say T(s) in the above case) how to calculate phase margin (and gain margin) numerically? Is there any short cut method? Graphically doing so with bode plot can lead to errors due to drawing etc.

Regards,
Arvind Gupta

 

[asdf44]

1) You'd want to choose a compensator topology that has 'enough' poles or zeros.

TypeI: One pole
Type II : 2 poles, one zero
Type III: 3 poles, two zeros

I: One pole
PI: One pole, one zero
PID: One pole, 2 zeros

If you have a type II compensator but need a second zero move to TypeIII. You can also cascade multiple compensators in series if you actually need more than the above (however its unlikely you do).

2) Google "TypeI compensator" or "Dominant pole compensation". Dominant pole compensation places a single 'dominant' pole at a frequency that's lower than all the other poles and zeros in the system. This makes the rest of the poles and zeros irrelevant and can be a very simple way to compensate even a complex system. But it may be lower performance than other options.

3) You can do all the math if you really want. Usually simulating is fine. Ltspice has a cursor tool which lets you accurately see values. Other tools may calculate gain and phase margin for you.

 

[garvind25]

Thanks for the previous answers. I wanted to know the following pls:

** A single pole at origin is stable but a dual pole at origin is not. Why?
** What happens if there is single zero added to the origin?

Regards,

Arvind Gupta

 

[asdf44]

Two poles at the origin is stable. You can have 180 degree phase shift so long as it isn't at the crossover unity gain frequency.

See this thread:
https://www.edaboard.com/showthread...degree-when-gain-is-0dB&p=1670001#post1670001

And this thread:
https://www.edaboard.com/showthread...wo-Poles-at-Origin-Unstable-(even-with-Zero-)

And this link:
https://www.ti.com/lit/an/sboa015/sboa015.pdf

You could add a zero at the origin to cancel a pole at the origin but I doubt you need to.