# How does P and PI controller help in reducing load disturbance?

#### ASToonBlue

Joined Mar 19, 2016
8
In the lecture note that I have read , it said only the following

For P controller , it is simple and easiest continuous controller to tune , fast response , relatively stable and exhibits offset at steady state.

For PI controller , it eliminate the offset , total loop will be less stable and there are two parameters to tune.

How does it help?

#### Jony130

Joined Feb 17, 2009
5,183
The negative feedback build into P and PI controller reduce load disturbance. So to understand how, you need to study the negative feedback first.

#### ASToonBlue

Joined Mar 19, 2016
8
I know that both controllers reduce load disturbance but what is the effect of PI and P controller has on load disturbance?

PI controller reduces more load disturbance than P controller . hence more stable?

#### Papabravo

Joined Feb 24, 2006
14,420
A load disturbance creates an error signal. The error signal has a sign and a magnitude. The error signal is used to create a control signal whose purpose is to reduce the magnitude of the error signal.

A P controller creates an error signal which is proportional to the difference between the input and the output. Depending on the dynamics of the system there may be a range of error signals that are small enough that they require no change in the control input. This residual error can persist for an infinite amount of time.

A PI controller combines the proportional term and an integral term. The purpose of the integral term is to eliminate small residual errors by accumulating them, and when they get large enough, generating a control signal to eliminate them.

Both systems are stable according to the standard definition. Stable does not mean static and unchanging. Stable only means that the output does not grow without bound for a bounded input. In particular it is allowed to execute small oscillations in the phase plane about a stable point.

#### ASToonBlue

Joined Mar 19, 2016
8
May I know what is residual error? Is it steady-state error?

Never really heard or see it before in my lecture note

#### ASToonBlue

Joined Mar 19, 2016
8
A load disturbance creates an error signal. The error signal has a sign and a magnitude. The error signal is used to create a control signal whose purpose is to reduce the magnitude of the error signal.

A P controller creates an error signal which is proportional to the difference between the input and the output. Depending on the dynamics of the system there may be a range of error signals that are small enough that they require no change in the control input. This residual error can persist for an infinite amount of time.

A PI controller combines the proportional term and an integral term. The purpose of the integral term is to eliminate small residual errors by accumulating them, and when they get large enough, generating a control signal to eliminate them.

Both systems are stable according to the standard definition. Stable does not mean static and unchanging. Stable only means that the output does not grow without bound for a bounded input. In particular it is allowed to execute small oscillations in the phase plane about a stable point.
So PI controller eliminates the residual errors that have resulted from P controller?

#### Papabravo

Joined Feb 24, 2006
14,420
So PI controller eliminates the residual errors that have resulted from P controller?
It tries to do that, but it may not succeed because in doing a correction it might overshoot and have to come back the other way, overshooting again and so on. It does allow you to limit the magnitude of the average error.

#### crutschow

Joined Mar 14, 2008
25,432
Depending on the dynamics of the system you are trying to control, you may also have to add a derivative term to the PI controller (PID loop) for stable system response.

#### Papabravo

Joined Feb 24, 2006
14,420
Depending on the dynamics of the system you are trying to control, you may also have to add a derivative term to the PI controller (PID loop) for stable system response.
Stable -- as in bounded inputs give bounded outputs, or do you mean something else?

#### WBahn

Joined Mar 31, 2012
26,156
May I know what is residual error? Is it steady-state error?

Never really heard or see it before in my lecture note
The best way to get a handle on your questions is to do the math. Take one of the simple systems that your book or lecture notes contains and actually crank the numbers. Start with a P controller and how increasing the proportional gain affects the steady state error. Then make it a PI controller and see what happens to the steady state error and how the integral gain affects how long it takes to settle. Also look at what happens if the integral gain is too high.

#### crutschow

Joined Mar 14, 2008
25,432
Stable -- as in bounded inputs give bounded outputs, or do you mean something else?
I mean stable, as in no oscillations or significant ringing in the system closed-loop response.

#### Papabravo

Joined Feb 24, 2006
14,420
I mean stable, as in no oscillations or significant ringing in the system closed-loop response.
OK, so a bit more stringent than no real roots in the right half-plane.

#### crutschow

Joined Mar 14, 2008
25,432
OK, so a bit more stringent than no real roots in the right half-plane.
Sorry, no habla pole-zeros.

#### Papabravo

Joined Feb 24, 2006
14,420
Sorry, no habla pole-zeros.
Quelle domage!
or
Che peccato! If you prefer.

#### WBahn

Joined Mar 31, 2012
26,156

#### MrAl

Joined Jun 17, 2014
7,811
In the lecture note that I have read , it said only the following

For P controller , it is simple and easiest continuous controller to tune , fast response , relatively stable and exhibits offset at steady state.

For PI controller , it eliminate the offset , total loop will be less stable and there are two parameters to tune.

How does it help?

Hello there,

"offset" may not be the best choice of words here, i think "DC error" would be a better term for what it sounds like you are taking about.

The DC error is, after all, an error in the DC level of the output. If it is supposed to be 5v for example, then it should be 5v within some small tolerance. If it strays too far away from 5v, then we want to be able to detect that and send a signal to the amplifier so that the total output error is reduced over time. By integrating the error we can see it better because we are basically adding up small errors over time and seeing how they accumulate over time. Once we see that they accumulate we can then correct them. It would be much harder to correct a very very very small error than to correct a large error because there is less differential to work with, or to put it another way, less to detect. The integral also happens to average the errors so that if some small errors go negative and some go positive, they cancel out to some degree. This means we dont jump to the conclusion that at time t=10us when the output jumps up by 1mv that the whole systems is running amuck.

One of the main ideas behind using an integral is to reduce the steady state error to zero. That's after the system has stabilized and is fairly quiet. This means that the system would be able to conform to some specification that requires that the output be within a certain tolerance of some constant value. This doesnt help the ability of the system to meet other performance spec's though, which spawns other types of controllers.

The disturbance can be viewed as just another input, just entering the system at a different place. Thus we have two basic responses: the response to the main input, and the response to the disturbance. The analysis of each one tells us the most about how the system will perform.

#### Papabravo

Joined Feb 24, 2006
14,420
Hey, hey, you two -- English only! Stop speaking in code!
's not like we do it every day. Calm yerself.

#### WBahn

Joined Mar 31, 2012
26,156
's not like we do it every day. Calm yerself.
There, there, PB, note the emoticon....

#### Papabravo

Joined Feb 24, 2006
14,420
There, there, PB, note the emoticon....
Note the slang spelling. I'm just sayin': "what's a phrase now and then among friends"?
Maybe @blocco a spirale will give me a like

#### crutschow

Joined Mar 14, 2008
25,432
Quelle domage!
or
Che peccato! If you prefer.
I prefer "ignorance is bliss".