In this paper, we formulate an optimization problem of establishing a fuzzy neural network model (FNNM) for efficiently tuning proportional-integral-derivative (PID) controllers of various test plants with under-damped responses using a large number P of training plants such that the mean tracking error J of the obtained P control systems is minimized. The FNNM consists of four fuzzy neural networks (FNNs) where each FNN models one of controller parameters (K, Ti, Td, and b) of PID controllers. An existing indirect, two-stage approach used a dominant pole assignment method with P = 198 to find the corresponding PID controllers. Consequently, an adaptive neuro-fuzzy inference system (ANFIS) is used to independently train the four individual FNNs using input the selected 176 of the 198 PID controllers that 22 controllers with parameters having large variation are abandoned. The innovation of the proposed approach is to directly and simultaneously optimize the four FNNs by using a novel orthogonal simulated annealing algorithm (OSA). High performance of the OSA-based approach arises from that OSA can effectively optimize lots of parameters of the FNNM to minimize J. It is shown that the OSA-based FNNM with P = 176 can improve the ANFIS-based FNNM in averagely decreasing 13.08% error J and 88.07% tracking error of the 22 test plants by refining the solution of the ANFIS-based method. Furthermore, the OSA-based FNNMs sing P = 198 and 396 from an extensive tuning domain have similar good performance with that using P = 176 in terms of J.
- Fuzzy neural network (FNN)
- Optimal design
- Orthogonal experimental design (OED)
- Proportional-integral-derivative (PID) controller
- Simulated annealing