Plenary lecture 3: design of robust fuzzy logic controllers for complex non-linear processes with time delay
Snejana T. Yordanova · International Conference on Artificial Intelligence · 2009
The fuzzy logic controllers (FLCs) mark a considerable progress in controlling complex, non-linear, time-varying processes satisfying the high system performance demands. Since their emergence in the area of process control the FLCs design is constantly being improved laying it out on theoretical grounds and making it more general and simple. Different FLCs structures and approaches have been suggested for treating together fuzzy system stability and uncertainty for the purposes not only of analysis but also of design. The aim of the plenary lecture is to present some results from the research of the author and her team on development and implementation of various types PI-like FLCs for robust control of complex industrial plants with time delay. An effort has been made to treat together in the frequency domain the stability and the performance of a fuzzy control system of a plant with time delay and model uncertainties, provoked by plant complexity and shift of the operating point along the smooth non-linear plant characteristics due to disturbances, changes in the operating mode and time-varying plant properties. Robust stability and robust performance criteria are derived by extension of the Popov stability criteria for the case of a fuzzy control system and combining it with robustness considerations, using estimated by experts simple approximate nominal plant model and plant uncertainties model. On their basis a simple and objective FLC design and parameter tuning procedures are developed. First the approach is applied to the design of a single input fuzzy controller (SI FC). The SI FC, based on the signed distance as a sole input, is promising in ensuring the fuzzy system stability and robustness as they have 1-D uniquely determined rule base - that is, a reduced number of tuning parameters), a sector bounded non-linear control curve - this facilitates the application of Popov stability criterion and the Morari robustness approach, which suit the plant description with model uncertainty and time delay. Two types of process PI SI FC are investigated. They both consist of a input fuzzy unit (FU) - sector bounded static non-linearity, and a classical position PI controller - dynamic LTI part. The first type of PI SI FC is an incremental PI with the signed distance as a sole input and a LTI part - the augmented plant that includes the pre and post processing units, which together comprise a position PI controller. The second type of PI SI FC is a position PI controller with the system error as a single input and a classical position PI controller after the FU. It avoids the problems, related to the computing the derivative of error signal. In both cases the whole LTI - position PI and plant, is stabilised by a feedback via a gain, which is a basic requirement for application of the Popov stability criterion. Then the initial plant model multiplicative uncertainty is transmitted to uncertainty disks around the Nyquist plot of the LTI part with nominal plant model and the robust stability and the robust performance criteria are derived. Next, this approach is applied?to the simple two input FLC with incremental PI algorithm. First the equivalent incremental PI SI FC is designed on the basis of the du-e projection of the FLC control curve in the plain of the rate of control du as function of the system error e. Then the initial FLC's parameters are obtained - all equal to the parameters of the incremental PI SI FC except the denormalisation factor, which is decreased by ten to compensate the fuzziness of the du-e projection around the steady state point (e-0, de=o, du=0). Further improvements on the performance of the system with the FLC or the SI FC are searched designing a plant predictor in the feedback by the help of ANN in order to reduce the effect of the plant time delay. The design procedures are applied to various industrial plants - a laboratory furnace, a laboratory water heating plant and an anaerobic biological degradation process in wastewater treatment. Results from simulation and real time control using MATLABTM facilities allow to estimate the various fuzzy control systems performance as well as to compare it with the performance of designed ordinary PI and internal model controller systems.