Teknillinen tiedekunta, 2013
Vladimir Bochko/Jarmo Alander
Sähkö- ja energiatekniikan koulutusohjelma (DI)
PID controllers performance depend on how they are tuned. Tuning a controller is not easy either and many use their experience and intuition, or automatic software for tuning. We present a way to test the quality of controllers using statistics. The method uses multivariate extreme value statistics with novelty detection. With the analyser presented in this paper one can compare fresh PID parameters to those that have been tuned well. This tool can help in troubleshooting with PID controller tuning. Conventional novelty detection methods use a Gaussian mixture model, the analyser here uses a variational mixture model instead. This made the fitting process easier for the user.
Part of this work was to create PID parameter configurations to test the analyser with. We needed both well tuned and poorly tuned parameters for testing the algorithm, as well as several examples of both cases. A genetic algorithm was seen as a tool that would meet these requirements. Genetic algorithms have previously been used for both test parameters generation and PID controller tuning in many applications. The genetic algorithm was written in Matlab. The reason for using Matlab is that the genetic algorithm uses a Simulink model of a PID control process in its fitness function.
The parameters were simulated and plots of their step response were drawn. The best configurations according to the genetic algorithm had little error compared to the reference value. The error seemed to rise according to the index of goodness used by the genetic algorithm. We set three criterions on the parameters: maximum overshoot, settling time, and sum of absolute error. Each of these criterions had a threshold. Each parameter configuration that crossed at least one of these thresholds were classed abnormal.
The performance of the analyser was assessed with these parameters. The analyser were first trained with a set of normal parameters, then tested with a set of normal and a set of abnormal parameters. The results showed 2 false alarms in both cases out of 104 possible. This gave us an accuracy of 98%, which is a very high one for a novelty detection method.
Novelty detection, multivariate extreme value statistics, PID controller, test data generation, genetic algorithms, variational mixture model