PID Control
Researchers:
Karl Johan Åström, Olof Garpinger, Tore Hägglund, and Per-Ola Larsson
This project has been in progress since the beginning of the
eighties, and resulted in industrial products as
well as several PhD theses. Three monographs on PID control
that are based on experiences obtained in the project have
also been published. The last is "Advanced PID
Control", published in 2005. It is also translated to Spanish 2009:
"Control PID avanzado". The research is currently focused on the
following topics:
A simple dead-time compensator
In this part of the project we are considering an ordinary PI(D) controller extended with a dead time compensator structure similar to a Smith predictor. The motivation for the project is that this new controller structure may be as easy to tune as a PI(D) controller, provided that model-based tuning rules are used. The performance of the new controller will be compared with the performance of the PID controller. The closed loops will be required to fulfill certain degrees of robust stability and performance and have a limit on control signal variance induced by measurement noise. The minimization criteria at the controller design is the integrated absolute error (IAE).
Relation between control signal properties and robustness measures
In a realistic setting, fast response to load upsets are restricted by
e.g. limitations on actuator devices, noise characteristics of
measured signals, and process variations. Thus, this should be
incorporated in the design of a controller. An analysis concering the
optimization constraint in the PID design in this project and in the
project ``Decentralized Structures for Industrial Control'' has been
performed. It has shown that analytical expressions relating the M_S
and M_T circles and the control signal magnitude
and activity exist to a certain extent. Large robustness margins give
small control signal activities and the opposite holds for small
robustness margins. Thus, the proposed PID
parameter optimization do take required control signal
properties into consideration.
Software tools for design of PID controllers
"Surface plot from the PID design tool"
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A new, interactive and easily modifiable software tool for robust
PID design has been developed at the department. The tool has been
programmed in Matlab and the goal is to find the controller that
minimizes the IAE value during a load disturbance, while applying
robustness constraints in terms of M-circles. The program has been
made with focus on being user-friendly as well as robust and will
hopefully be included in an educational autotuner in the future. The
figure on this page shows a plot from the program, depicting the IAE
cost as a function of the integral time and the derivative time in a
PID controller. The minimum is shown by the yellow mark in the figure.
The research is currently aimed at making the software suitable for control of real plants. This is achieved by tuning the time constant of a lowpass filter acting on the measurement signal. The purpose is to set a bound on the variance of the control signal, induced by measurement noise. By this modification, it becomes safe to include the D-part without fear of receiving a noisy control signal, wearing on the actuators. The new method will, however, only use a D-part if it is justified. In many cases, a PI controller has been shown to be quite sufficient. Tests have also been carried out to give a more general idea for which types of processes a PI or PID controller are performing well compared to more advanced controllers. Just as well as examining when a PID controller is prefered to a PI controller. The conclusion was that this will be related both to the dynamics of the process and to the maximum allowed control signal activity.
2008-07-01 - Robust PID Design Software available to download
We have decided to make the software tool, that was presented on IFAC World Conference in 2008 (article download), free for anyone to download.
The Matlab files contained in the zip-file will make you able to design a
robust, optimal PID (or PI) controller within seconds. The main
function to run is designpid.m and you can use the Tutorial that is
included as an introduction on how the program works. The software
has been tested on Matlab 7 and may need some changes if it is not run
under that version. However, this is just a first release and if you
have any comments, bug reports or questions please contact Olof
Garpinger and he will try to answer them.
PID Design Tool for Matlab: Download
Interacting learning modules for PID control
We are also developing interactive learning modules for
PID control. The modules are designed to speed up learning and to
enhance understanding of the behaviour of loops with PID controllers.
The modules are implemented in SysQuake, and the work is done in
collaboration with professor Sebastián Dormido at UNED, Madrid, and
José Luis Guzmán at Universidad de Almería. The tools can be
downloaded at
Download ILM.
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