Control curve design for nonlinear (or fuzzy) proportional actions using spline-based functions (Q1298207)

The authors investigate a nonlinear design of proportional actions using spline-based functions. To be more specific, the controller uses Bézier curves to form the nonlinear mapping in order to emulate fuzzy PID systems. The paper is structured as follows. Section 2 motivates the use of proportional actions, and their properties (general for any fuzzy PID controller design, rather than process-dependent) are presented in Section 3. The definition of Bézier curves, which fall into a general form of spline-based functions, is introduced in the next section. Section 5 presents the procedures used to generate nonlinear functions using one, two or four parameters and the associated nonlinear flexibility of the system for each case of parameter selection. Procedures for using more parameters are described in Section 6, and it is followed by a discussion about nonlinear functions under symmetric considerations. Section 8 contains the linguistic representation.