Adaptive Proportional, Integral, Derivative (PID) Controllers
by Peter Raeth

A rather significant issue with adaptive control methods is implementing them so that they are fast enough to make a difference. Two fundamental roadblocks exist that can prevent effective implementation: accuracy and speed. Experience has shown that there are cases where the adaptive method exceeds the accuracy of an approach based on a deep knowledge of the application. However, although the adaptive approach is self-adjusting and very general, the specific model is smaller and potentially faster. Sometimes the need for speed will make a less accurate approach more desirable. We have approached this topic earlier:

Field-Programmable Gate Arrays from Conventional Software
Parallel Processing

This time, let's take a look at an approach to adaptive control that can be implemented via a specific device that might normally escape our attention because it is rarely, if ever, mentioned in the adaptive-systems literature. By drawing the two together, we can open the possibilities for speed through yet another device: Proportional, Integral, Derivative Controllers.

According to a tutorial by Richard Wynne, School of Engineering, Sheffield Hallam University:

The PID controller is the most widely used control strategy in industry. It is used for various control problems such as automated systems or plants. A PID controller is a three-term controller that consists of three different elements:

P Proportional control—a pure gain adjustment acting on the error signal to provide the driving input to the process; used to adjust the speed of the system

I Integral control—implemented through the introduction of an integrator; used to provide the required accuracy

D Derivative control—normally introduced to increase the damping in the system; also amplifies the existing noise, which can cause problems, including instability.

Vance VanDoren, Control Engineering OnLine, gives an introductory discussion that contains a succinct definition.

A PID controller performs much the same function as a thermostat, but with a more elaborate algorithm for determining its output. It looks at the current value of the error, the integral of the error over a recent time interval, and the current derivative of the error signal to determine not only how much of a correction to apply, but for how long. Those three quantities are each multiplied by a tuning constant and are added together to produce the current controller output. P is the proportional tuning constant, I is the integral tuning constant, D is the derivative tuning constant, and the error e(t) is the difference between the setpoint P(t) and the process variable PV(t) at time t. If the current error is large, or the error has been sustained for some time, or the error is changing rapidly, the controller will attempt to make a large correction by generating a large output. Conversely, if the process variable has matched the setpoint for some time, the controller will leave well enough alone.
See the other PID tutorial articles posted at the Control Engineering OnLine site.
Understanding PID Control
PID—The Basic Technique for Feedback Control
Fundamentals of PID Control

According to the Advanced Control Technology Club (Industrial Systems and Control Ltd), while the PID controller is by far the widest type of automatic control used in industry, and though it is a relatively simple algorithm, there are many subtle variations in how it is applied. This has resulted in confusion for plant engineers and operators, who are happy to leave control loops in a sub-optimal configuration. See their portal for a number of tutorials and related information.

Process Control Portal

Prashant Mhatre, Tata Consultancy Services, provides a set of organized links into process control, including PID controllers. The topics include Basics of Process Control, Advanced Process Control, Frequency Response Techniques, and Statistical Process Control.

PID Control Technical Notes

In business since 1946, ISE offers a brief practical discussion along with links to other sites.

Interactive Demonstrations

Tomas Co (Chemical Sciences and Engineering, Michigan Technological University) provides two dynamic illustrations of PID controllers: PID Root Locus Generator and PID Controller Tuning. Take a look at these and his other postings in related areas.

Process Control Virtual Lab

This site gives an introductory lesson in process control design and tuning. It guides process control students through control techniques and controller tuning. It provides two examples: control of a toilet tank and temperature control of a distillation column. Additionally, the site provides an interactive forum where students can tune their own controller and create a controller for their own process. Many thanks to the Department of Chemical Engineering, University of Texas at Austin. Certain examples are provided by S. Qin.

Application to Motion Control

Newport Electronics presents us with a multi-part tutorial on applying PID controllers to motion control. The sections include: Introduction, Mechanical Design, Feedback, Electronics Design, Terminology, and Tuning Principles.

Technical Reports on PID and Adaptive Controls

Several people have written papers and reports that are theoretical but very understandable.

R. Ghanadan, Institute for Systems Research, University of Maryland. Click here for a list of papers.
Backstepping-Based Adaptive PID Control, André Desbiens, Department of Electrical and Computer Engineering, Laval University.
Petros Cominos, Control Systems Center, UMIST. Click here for a list of papers.
Generalised Nonlinear PID Controller Based on Neural Networks, Yonghong Tan, Xuanju Dang, and Achiel van Cauwenberghe, Department of Electrical and Computer Engineering, Adelaide University.
Implementation of an Innovative Self-Tuning Adaptive Controller for Complex Industrial Processes, David Lyon, Bill Gough, and Malcolm Cameron, Universal Dynamics. Also see their other papers.
Modification and Application of Autotuning PID Controller, Nedjeljko Peric, Ivan Branica, and Ivan Petrovic, Department of Automatic Control, University of Zagreb.
An Optimal Fuzzy PID Controller, K.S. Tang, Kim Fung Man, Guanrong Chen, and Sam Kwong, Department of Electronic Engineering, University of Hong Kong.
PI and PID Controller Tuning Rules for Time Delay Processes: A Summary (2000), Aidan O'Dwyer, School of Control Systems, Dublin Institute of Technology.
Also have a look at the other papers listed on this page.

Specific PID Controller Devices

Fuzzy Temperature Controllers, Related Manual;
Omron Fuzzy DIN Controller 1, Fuzzy DIN Controller 2;
ISE Process Controller;
Armfield Dual Controller;
Eurotherm (Also go to their search page and enter the keyword pid);
Universal High-Performance Motion Controller/Driver;
Newport Electronics (enter the keyword pid in the search block on their main page).

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