A Simple Linearization Method of Nonlinear Systems Based on Fuzzy Logic

Abstract

Linearization is a powerful tool that enables the analysis and control of nonlinear systems by simplifying their dynamics and allowing the use of well-established linear control techniques. This paper presents a new methodology for the linearization of dynamic nonlinear systems that can be applied without the need to know their internal structure and parameters solely from measured input/output data. The proposed technique, based on fuzzy logic, simplifies a higher-order nonlinear system into a first-order nonlinear fuzzy system. This enables the design of control systems based on an inverse fuzzy model in the vicinity of the chosen operating point. The properties of the proposed methodology were first verified for less complex systems by simulation in MATLAB. This paper presents the application of this method for torque control of an induction motor, which is a complex nonlinear system of the fifth order. The results were experimentally validated by measurements using an IC inverter-induction motor system. The experimental measurements confirmed the correctness and quality of the proposed methodology. Compared to traditional methods, it does not require any knowledge of the mathematical model of the nonlinear system, use of complex differential algebra, or other additional transformations. The proposed non-analytical linearization technique is primarily designed for a class of mechatronic systems with electric drives. Its simple structure and design methodology minimize the complexity of implementation, thereby enabling it to be widely used in industrial practice for other nonlinear systems with comparable structures.

Keywords

• Fuzzy logic
• induction machine
• linearization technique
• nonlinear systems
• torque control