Multivariable PID Controller


Thread Starter

Mohsen Arezoomand

I am a student of control in I.U.T
My research is multivariable pid controller.
Can you help me in this subject?
Can you send me any document about this subject?

Johan Bengtsson P&L Automatik AB

What do you want to know?

Controlling more than one thing can be done in more than one way, some examples:

Cascade, one controller is the main controller, but in order to do it's work it can delegate part of the responsibility to another controller.
Classical example:
Consider level control, for example water in a tank. Without controllers in cascade you would measure the level, feed the PID with that, and take the output directly to the valve changing the input flow. Consider this after it have reached a stable state and think of what could need a change of control output (and valve position). they are:
1. Change in setpoint.
2. Change in output flow.
3. Change in input pressure.

1 and 2 are not affected by this, but 3 can be handled better with two controllers put in cascade like this:
Measure the level, as before and feed it to the level control.
Take the output from the level controller and feed it as setpoint to another controller. This one is controlling the flow. Measure the flow and of course feed that to this new controller. the output from this controller are then used to change the valve.
When a change in input pressure occurs the level doesn't have to be changed (not by very much at least) since the flow controller now tries to maintain the desired flow and (almost) immediately changes the valve to get the same flow regardless of pressure.

In some cases you have not only two controllers connected in that way, in for example a servo positioner it is quite common to have three controllers in cascade.

Point 2 above can be solved by another solution called feed-forward. Measure the output flow and directly open the valve to reflect the new load. This is sometimes combined with cascaded controllers.

In some cases you have two, as you view it, independent control loops, but they unfortunately affect each other. Such interaction are also considered a case for multivariable control and have to be taken into consideration when tuning the controllers. In some cases you have to make special solutions to handle this.

In yet some cases you want two (or more) individual control loops to follow each other, for example the fuel and air flows to a burner need to follow each other to get the best

Multivariable PID control is not one thing, but rather many different.
Is this what you wanted? if you need more you might want to consider this:
or make a more detailed question.

/Johan Bengtsson

P&L, Innovation in training
Box 252, S-281 23 H{ssleholm SWEDEN
Tel: +46 451 49 460, Fax: +46 451 89 833
E-mail: [email protected]

Edgar F. Hilton

Take a look at H_infinity controllers. Both Matlab and Scilab have nice tools to get you going.

An optimally tuned SISO PID is nothing more than a SISO H_infinity controller.


Edgar F. Hilton FSMLabs, Inc.
voice: 850.893.0300
fax: 206.350.4EFH

Kiel-1, Larry

Hello. You don't specify what depth of research you are doing but here are a couple of suggestions.

The Instrument Engineers Handbook/Process Control, edited by B*ela G. Lipt*ak, has several references to multivariable PID control. You will find information in the following sections: Optimizing Controls, p88, Stability Analysis p129, and Tuning PID Controllers p152. Most of this is theory and not real world application. I don't know if this source is available in your area.

Below are 2 web sites that talk about PID controls in general. Neither site talks about multivariable control but, both sites have references that you might be able to explore further with a little digging. Sorry I don't know
of a dedicated site to your question.

Larry Kiel
Space Gateway Support
Kennedy Space Center
I got a method for designing the multivariable PID controller. It is a frequency domain method, almost analytical(the last step is numerical), optimal/suboptimal. Because it has not been published, I cannot send it to u.

[email protected]