Integral (Reset) Control Systems

Integral (Reset) control

Reset/Integral control describes a controller in which the output rate of change is dependent on the magnitude of the input. Specifically, a smaller amplitude input causes a slower rate of change of the output. This controller is termed to as integral controller because it approximates the mathematical function of integration. This integral control method is also known as reset control.

Defining Integral Control

A device that performs the mathematical function of integration is called an integrator. The mathematical result of integration is called integral. The integrator provides a linear output with a rate of change that is directly related to the amplitude of the step change input and a constant that specifies the function of integration.

In the Integral control example above, the step change has amplitude of 10 % and the constant of the integrator causes the output to change 0.2 % per second for each 1 % of the input.

The integrator acts to transform the step change into a gradually changing signal. You can clearly see the input amplitude is repeated in the output every 5 seconds. As long as the input remains constant at 100 %, the output will continue to ramp up every 5 seconds until the integrator saturates.

With Integral control, the final control elements position changes at a rate determined by the amplitude of the input error signal.

Error = Setpoint – Measured variable

A large error result, if a large difference exists between the setpoint and the measured variable. This causes the final control element to change position rapidly; but if only, a small difference exists, the small error signal causes the final control element to change position slowly.

Output rate of change = Integral constant x % Error

The Integral controller responds to both the amplitude and the time duration of the error signal. Some error signals that are large or exist for a long period of time can cause the final control to reach its ‘’fully open’’ or ‘’full shut” position before the error is reduced to zero. If this occurs, the final control element remains at the extreme position, and the error must be reduced by other means in the actual operation of the process system.

Related: What is a Controller?

Example of Industrial Application of Integral Control System

With integral control, the final control element’s position changes at a rate determined by the amplitude of the input error signal.

We know that:

Error = Setpoint – Measured variable

If a large difference exists between the setpoint and the measured variable, a large error results, this causes the final control element to change position rapidly. But, if only a small difference exists, the small error signal causes the final control element to change slowly.

The figure below shows a process using an Integral controller to maintain a constant flow rate and its equivalent block diagram.  

Initially, the system is set up on an anticipated flow demand of 50 gallons per minute (gpm), which corresponds to a control valve opening of 50 %. With the setpoint equal to 50 gpm and the actual flow measured at 50 gpm, a zero error signal is sent to the input of the integral controller. The controller output is initially set for 50 % or 9 psi, output to position the 6 inch control valve to a position of 3 in open. The output rate of change of this integral controller is given by:

Output rate of change = Integral constant x % Error

If the measured variable decreases from its initial value of 50 gpm to a new value of 45 gpm, a positive error of 5 % is produced and applied to the input of the integral controller. The controller has a constant of 0.1 seconds^-1. So the controller output rate of change is 0.5 % per second.

The positive 0.5 % per second indicates that the controller output increases from its initial point of 50 % at 0.5 % per second. This causes the control valve to open further at a rate of 0.5 % per second, increasing the flow.

The controller acts to return the process to the setpoint. This is accomplished by the repositioning of the control valve. As the controller causes the control valve to reposition, the measured variable moves closer the setpoint, and a new error is produced. The cycle repeats itself until no error exists.

The integral controller responds to both the amplitude and the time duration of the error signal. Some error signals that are large or exist for a long period of time can cause the final control element to reach its ‘’fully open‘’ or ‘’fully shut’’ position before the error is reduced to zero. If this occurs, the final control element remains at the extreme position, and the error must be reduced by other means in the actual operation of the process system.

Related article: Proportional Control Systems

Advantages of Integral Control

Integral controllers have the unique ability to return the controlled variable back to the exact setpoint following a disturbance.

Disadvantages of Integral Control

Integral control mode responds relatively slowly to an error signal and that it can initially allow a large deviation at the instant the error is produced. This can lead to system instability and cyclic operation. Because of this reason, the Integral control mode is not, used alone in most cases, but is combined with other control mode(s).