A new methodology for tuning the scaling factors, or gains, of fuzzy proportional-integral-derivative controllers, by taking explicitly into account the closed-loop system performance is proposed in this study. The solution is obtained by solving a nonlinear constrained optimization problem, considering a set of constraints on the scaling factors of the Mamdani-type fuzzy system, and on the plant's inputs and outputs. Two distinct approaches are presented, which are associated with the optimization being carried out offline or in real time. The offline tuning scheme assumes the system dynamics described by a nonlinear model, while for the real-time implementation, the plant's dynamics is locally approximated by a linear model, with the underlying parameters recursively updated. In order to cope with rather stringent sampling time requirements, the constrained online optimization problem is implemented based on the grid computing paradigm. Given the adaptive nature of the real-time scheme, time-varying dynamics and unknown disturbances can be accommodated in such a way that the closed-loop performance is effectively maximized, while avoiding wind-up phenomena induced by the integrator term. The proposed tuning methodologies are assessed on a benchmark threetank system and compared against a conventional-based tuning approach. Results from experiments illustrate the feasibility of the proposed approaches and also all the relevance in optimal control systems based on Mamdani-type fuzzy controllers.
- Constrained optimization
- Mamdani-type fuzzy controller
- offline tuning
- real-time tuning
- recursive system identification
- scaling factors tuning
Gil, P., Lucena, C., Cardoso, A., & Palma, L. F. F. D. B. (2015). Gain Tuning of Fuzzy PID Controllers for MIMO Systems: A Performance-Driven Approach. IEEE Transactions on Fuzzy Systems, 23(4), 757-768. https://doi.org/10.1109/tfuzz.2014.2327990