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I term in PID controllers
the I term in PID controllers - integral time and/or reset time?
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i am again at it. let us talk about the I term.

i have seen "ti, tn, integral time, reset time" alternatively being used for the I parameter in pid controllers. what i believe reset time is tn and in all probability integral time is ti.

i want to forget ki now.

does anybody know the relationship between ti and tn. are they same?

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The terms are interchangeable. Typically you need to refer to the manufacturer to know exactly how your particular controller matches to one of several different forms of the general PID Algorithm. Which is a complex way of saying ... it depends, Read the Manual.

There are two commonly used ways of specifying integral - repeats per time period (eg minutes or seconds) or time period per repeat.

30 seconds per repeat = 0.5 repeats per minute, 2 repeats per minute = 120 seconds per repeat etc etc etc.

To know what Ti means for your controller you need to read your manual. But commonly, Ti = Integral Time i.e. the time taken to repeat. So a Ti of 30 seconds means 30 seconds per repeat.


now i realize why they taught so much of the uncertainty principle at college :)

thank you, Rob, R.Caro, Dave for all your help. these questions (also the thread for control parameters) must be trivial for you people, but they have been eating up my brain for quite some time.

now it seems, got some peace. let's see how long it lasts.

By whyAmImike on 25 April, 2015 - 9:54 pm

I can tune a PID better than the last guy. I get it. The only thing I don't get is the use of the terminology "reset time". Reset to what? zero integral accumulation? From what accumulated integral? With what magnitude of error? This must not be correct or even on the right track. Another poster on here called it repeat rate, which confuses the topic more. In a Rockwell RSLogix5000 processor, with an independent SP-PV configuration, if I set the integral term to 0.01, which makes the "reset time" 100 seconds, and watch the integral accumulator, it's recalculating at the frequency of the instruction update rate. It does not take 100 seconds to change the CV. Any intelligible teachers out there ready to set this straight once and for all?

By William Sturm on 26 April, 2015 - 2:08 pm

I think that the term "reset time" might refer to the time that it would theoretically take to eliminate 100% of the error. Reset implies eliminating the offset error. When the I term is in time units, typically a larger number results in a slower response.


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A step change in error, with a PI controller, will result in the controller output change having two components.

The first is a step due to proportional action, which is equal to the error multiplied by the gain, or to the error x (100/PB) - PB is the proportional band width in percent. Both gain and PB may be found as controller settings, depending on the manufacturer - they are equivalent as gain = 100/PB.

The second component is the one due to integral action. It has a value at any time which is the accumulated result of the error over time - in a digital system, this can simply be generated by taking the value of the error at a sample instant, multiplying it by the sample time, and adding the result to the previous integral term.

For a step change in error, the change in the integral term is initially zero. It will ramp up (or down, depending on error polarity and controller action) at a rate dependent on the error. The amount of integral action is set by finding how long it takes for the integral contribution to the total output change to equal the initial proportional step. This can be expressed simply as a time - the integral action time (IAT) is the time taken for the integral contribution to match the initial proportional action.

However, the integral contribution decreases as the IAT increases, which is the opposite of the way the gain value affects the contribution of the proportional term. So some controllers use the inverse of IAT, and call this the repeat rate, expressed as repeats per minute. A "repeat" is an additional contribution to the output change equal to the initial proportional step in output. The repeat rate is simply 1/IAT, and if IAT is measured in minutes will have units of 1/minute, or repeats per minute.

So, if a controller with a gain of 2.5 and an IAT of 4 minutes sees an error step of 2 %, the controller will show an initial step change of (2.5 x 2) = 5 %. The output will then commence ramping and over 4 minutes it will change by another 5 % to be at 10 %. After 8 minutes it will be at 15 %; after 12 minutes at 20%, and so on.

If the controller gain is halved, but the IAT (or reset rate) is left unchanged, the initial proportional step will still be "repeated" after 4 minutes, again after 8 minutes, and so on.

But this is for the standard PID controller. You may find some so-called "non-interactive"controller algorithms out there where the rate of integral ramping is not affected by a gain change. In this case, the best advice I can give is to "Read the Manual" - and note that, for these, Ziegler-Nichols tuning doesn't work.

The terms used come from the good old days of pneumatic controllers, and can best be considered as simply labels, without getting too hung up on what they actually mean. The term "reset" is because the original approach with purely proportional controllers was to manually adjust the controller output using a "reset" control to bring the controlled PV into line with the setpoint. Integral action was initially referred to as "automatic reset".

Hope this helps,


Bruce - you provide good example below for understanding integral action (IAT of 4 min) when using the dependent PID equation. I'm trying to understand what would happen if using the independent equation. I have a heating zone using allen Bradley independent equation with a reset value of 0.001 (1/sec). so IAT would be 1000 seconds. if "proportional" gain was 2.5 with a error step of 2% what is output at end of 1000 seconds. thanks for any help you can provide for more understanding as new with PID.

>So, if a controller with a gain of 2.5 and an IAT of 4
>minutes sees an error step of 2 %, the controller will show
>an initial step change of (2.5 x 2) = 5 %. The output will
>then commence ramping and over 4 minutes it will change by
>another 5 % to be at 10 %. After 8 minutes it will be at 15
>%; after 12 minutes at 20%, and so on.
>If the controller gain is halved, but the IAT (or reset
>rate) is left unchanged, the initial proportional step will
>still be "repeated" after 4 minutes, again after 8 minutes,
>and so on.

By Roy Matson on 1 May, 2015 - 4:43 pm

> The only thing I don't get is the use of the terminology "reset
> time". Reset to what? zero integral accumulation? From what

The time it takes to increase the output due to error x gain

E.g. you have an error of 10% and a gain of 0.2 = 2
Each reset interval the output will change by 2%

At least that's how it's supposed to work, many control system vendors have a different interpretation.

Any time you work on an unfamiliar system set up a loop with a fixed error and watch what the output does in automatic, I have seen several systems where the reset rate is independent of the gain.

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I see that a history lesson is required. I include this history when I teach the ISA CAP Exam Preparation course, EC00.

The RESET term and its definition as REPEATS comes from the fact that the basic Proportional Control equation is expressed like this:

M = Kp * error + bias

error is defined as Setpoint - Pv (process variable measurement)
bias is calculated when the loop is initialized (switched to AUTO)

but M (Output) will be forever wrong at any other Pv. We call this "offset" and is the result of Proportional-only control. To correct for offset error, the operator may manually change the bias term, or they may RESET the bias term. Long ago, very clever mechanical engineers created a way to automatically "reset" the bias term, and called that "integral control" since they did it by using pneumatic energy to integrate error over time. The dimension of the tuning factor for this reset term was the equivalent number of times (repeats) an operator would manually reset the bias term to keep the Proportional-only controller from exhibiting offset.

Another factor also taught in my CAP course - why are there two different forms of the basic PID algorithm?

Non-interactive form: M = Kp * e + Ki * (integral of error) + Kd (de/dt)

Interactive form: M = Kp [e + Ki * (integral of error) + Kd (de/dt)]

The 3-independent terms of PID were developed many years ago as the method to be used for servomechanisms. Most mechanical controllers such as used for machine tool positioning, rocket thrust vector control, etc. use this form, and it is the form of the PID found in most PLCs and VFDs (Variable Frequency Drives).

Many years ago, when mechanical engineers attempted to build a PID using pneumatic computing elements, they found it too difficult to keep the terms completely independent, so they created the interactive form of the PID. In my past efforts, I have run a few digital simulations of both forms, and they each produce valid closed loop control values, but they are somewhat different. You cannot say that one is better than the other. In Process Control, we have used the interactive form originally developed for pneumatic instruments. There is a large body of empirical tuning methods that have been created based on the responses of these pneumatic controllers. The Process Control industry has elected to implement computer controls, electronic analog and digital controllers, DCS, and Foundation Fieldbus based on the interactive equation form so that the tuning methods of Ziegler-Nichols and Cohen-Coons can still be used.

I thought you might like to know.

Dick Caro

A nice description, Dick.

One interesting item about the difference between the "interactive" (conventional process control PID) and "non-interactive" algorithms is that, on a frequency response chart, the three terms of the so-called "interactive" algorithm are in fact independent - so a change in gain setting affects the gains at all frequencies equally, without altering any of the frequency break-points. The integral setting will alter only the lower break frequency (fl = Ki/(2*pi) , and the D setting will affect only the upper one (f2 = Kd/(2*pi). In this model, the PID controller acts as a band-stop filter.

With the so-called "non-interactive" controller, changing gain will also alter the break frequencies - f1 = K1/(2*pi*Kp). An interesting side-effect of this is that under the right setup, reducing gain can make a loop less stable and possibly lead to cycling.

By pvbrowser on 6 May, 2015 - 2:55 am

What you need to know is the transfer function of the controller in the frequency domain. The transfer function can be expressed either as a sum or as a product of terms.

Here i post 2 tiny URLs to our controller classes that use the sum or product version of the transfer function.

Please note that the differential term includes a limiting low pass also.

Detailed Description

class for closed loop control
According to: F. Doerrscheid/W. Latzel, Grundlagen der Regelungstechnik, B.G. Teubner Stuttgart
Page 436-437, Regelalgorithmen mit der Trapezregel


By Peter Nachtwey on 7 June, 2016 - 7:37 pm

I understand the confusion.

I agree with those that don't like the term repeat or reset. It is misleading and doesn't give one a clue as to how the system will react. I use time constants which is what they really are.

The integral gain can be expressed in two ways. In motion control it is just a gain that is multiplied by the accumulated error. The gain has units of output/(error*time) so the gain must be multiplied by the sample interval. Motion controllers usually use frequency or the inverse of time constants because the time constants are so short.

In process control the integrator gain is usually express as an integrator time constant and a controller gain.

If the integrator time constant is 1 minute the system will get close enough in 5 integrator time constants.

It is important to know the type if PID and its units for each of the gains. There are many type of PID.