Hybrid Self-Learning Fuzzy PD + I Control of Unknown SISO Linear and Nonlinear Systems
Santana Blanco, Jesús
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A human being is capable of learning how to control many complex systems without knowing the mathematical model behind such systems, so there must exist some way to imitate that behavior with a machine. In this dissertation a novel hybrid self-learning controller is proposed that is capable of learning how to control unknown linear and nonlinear processes incorporating human behavior characteristics shown when he/she is learning how to control an unknown process. The controller is comprised of a Fuzzy PD controller plus a conventional I controller and its corresponding gains are tuned using a human-like learning algorithm developed upon characteristics observed on actual human operators while they were learning how to control an unknown process reaching specified goals of steady-state error (SSE), settling time (Ts), and percentage of overshooting (PO). The systems tested were: first and second-order linear systems, the nonlinear pendulum, and the nonlinear equations of the approximate pendulum, Van der Pol, Rayleigh, and Damped Mathieu. Analysis and simulation results are presented for all the mentioned systems. More detailed results are provided for a nonlinear pendulum as a representative of nonlinear systems and for a second-order linear temperature control system as a representative of linear systems. This temperature system is used as a comparative benchmark with other controllers shown in the literature  that use this temperature control system, showing that the proposed controller is simpler and has superior results. Also, a robustness analysis is shown that demonstrates that the proposed controller keeps acceptable performance even under perturbation, noise, and parameter variations.