Fuzzy control theory: A nonlinear case

Abstract

We prove theoretically that a nonlinear fuzzy controller is a nonfuzzy proportional-integral-derivative (PID) controller with proportional gain, integral constant, and derivative constant changing with error, rate change of error, and rate change of error rate about a setpoint of a process. The nonlinear fuzzy controller consists of the following parts:1. The linear defuzzificat ion algorithm 2. The linear fuzzy control rules 3. Zadeh's AND and OR fuzzy logics for evaluating the fuzzy control rules The nonlinear defuzzification algorithmThe nonlinear fuzzy controller is a linear fuzzy controller which is precisely equivalent to a nonfuzzy PID controller if the linear defuzzification algorithm is used instead of the nonlinear one listed above.

fuzzy PID control synthesis for Takagi–Sugeno fuzzy systems

“…The fuzzy PID controller, whose fuzzy rules are shown in (5), is implemented here to control the inverted pendulum. Assuming that the H ∞ performance 1 γ = , we will use Procedure 1 to design the fuzzy PID controller.…”

“…Significant efforts have been made to investigate the Mamdani fuzzy PID control systems. To mention a few, the analytical structure analysis results are reported in [5][6][7], the stability analysis problems are considered in [8,9], and the controller design methods are proposed in [10][11][12][13][14][15]. For the T-S fuzzy PID control systems, the analytical structure analysis is explored in [16,17], where the results show that a T-S fuzzy PID controller is a nonlinear PID controller with variable gains.…”

Takagi-Sugeno Fuzzy Control Based on Robust Stability Specifications

“…In the design of modern and classical control systems, the first step is establish a suitable mathematical model to describe the behavior of the controlled plant (Takagi & Sugeno, 1985;Ying et al, 1990). However, in practical situations, such a requirement is not feasible because in practical control systems the plants are always nonlinear systems, which makes this task analytically unfeasible for complex systems (Cetin & Demir, 2008;Dong et al, 2009;Park et al, 2007;Pelladra et al, 2009).…”

Design and Implementation of Fuzzy Control for Industrial Robot

“…A practical alternative would be the use of fuzzy logic. It has been reported that fuzzy logic controllers performed better, or at least as good as, a conventional controller and can be employed where conventional control techniques are inappropriate Sugeno, 1985;Ying et al, 1990). In contrast to adaptive control, fuzzy logic algorithms do not require a detailed mathematical description of the process to be controlled and therefore the implementation of fuzzy logic should, theoretically, be less demanding computationally.…”