# 63 integral control the contribution from the

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Chapter 30 / Exercise 30
Welding: Principles and Applications
Jeffus
Expert Verified
6.3 Integral Control The contribution from the integral term is proportional to both the magnitude of the error and the duration of the error. Summing the instantaneous error over time (integrating the error) gives the accumulated offset that should have been corrected previously. The accumulated error is then multiplied by the integral gain and added to the controller output. The magnitude of the contribution of the integral term to the overall control action is determined by the integral gain, Ki. The integral term is given by: Where D out : Derivative output
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Chapter 30 / Exercise 30
Welding: Principles and Applications
Jeffus
Expert Verified
742 K d : Derivative Gain , a tuning parameter e : Error = SP PV t : Time or instantaneous time (the present) 6.3.1 Limitations Windup A basic knowledge of the concept of windup is useful before describing a specific type. Windup is defined as the situation when the feedback controller surpasses the saturation (i.e. maximum) limits of the system actuator and is not capable of instantly responding to the changes in the control error. The concept of the control variable reaching the actuator’s operation limits is reasonable considering the wide variety of operating conditions that are possible. When windup occurs the actuator constantly runs at its saturation limit despite any output the system might have. This means that the system now runs with an open loop instead of a constant feedback loop. Integrator Windup The most common type of windup that occurs is integrator windup. This occurs when the input into the system receives a sudden positive step command and causes a positive error when the system first responds to the actuator. If the rate of integration is larger than the actual speed of the system the integrator’s output may exceed the saturation limit of the actuator. The actuator will then operate at its limit no matter what the process outputs. The error will also continue to be integrated and the integrator will grow in size or “wind up”. When the system output finally reaches the desired value, the sign of the error reverses (e.g. ) and causes the integrator to “wind down” until things return back to normal. Through the wind down the control signal is still maximum for a long period of time and the response becomes delayed. The integrator takes a long period of time to fully recover to the operating range of the actuator. Integrator windup may occur from large set point changes, significant disturbances, or equipment malfunctions.
743 The illustration is a flowchart showing the specific steps that take place through the integrator controller. It shows the input ( ) and output of the system ( ) , along with the integrator, the actuator, the system, and sensor involved in the process. The sigma used in each flowchart is used to represent the summation of all variables inputed to it.