Abstract
This article proposed a novel optimal robust control design approach to solve the uncertain parameter problem in the permanent magnet synchronous motor (PMSM) system by integrating the fuzzy set theory and system control theory. First, we adopt the prescribed fuzzy number to describe the time-varying but bounded uncertain parameter in the PMSM system. Second, based on the estimated bound of the uncertain parameter and the nominal dynamical model, we design a deterministic robust control scheme characterized by model-based control and feedback control. The control objective is to guarantee the PMSM system with uncertain parameters satisfies the desired motion equation with deterministic system performance: uniform boundedness (UB) and uniform ultimate boundedness (UUB). Third, using the fuzzy uncertain parameter, a performance index relevant to the steady-state performance and control cost is constructed. A parameters design optimization problem is formulated by minimizing the performance index, whose analytical solution is successfully solved and proved to always exists and is unique. As a result, the resulting PMSM system under the proposed control approach has two-level system performance: the guaranteed deterministic performance and optimal performance. Finally, the results of numerical simulation and experiment are presented for demonstration.
Highlights
As the excellent performance characteristics of permanent magnet synchronous motor (PMSM) such as high efficiency, superior power density, high torque capability, and excellent controllability, PMSM systems are extensively applied in small and medium power drive fields, such as aerospace, robot, electric vehicle [1], [2]
Compared to the fuzzy logic theory, the fuzzy set theory application in control design is less, and more explorations are needed in this field. We explore another way of employing fuzzy set theory to robust control design, investigating the fuzzy description of VOLUME 9, 2021 uncertain parameters and optimization control design in the PMSM system
FUZZY NUMBER AND BASIC ARITHMETIC To describe the uncertain parameter in the PMSM system by fuzzy set theory, we introduce the fuzzy number with some properties and arithmetic operations [39], [40]
Summary
As the excellent performance characteristics of PMSM such as high efficiency, superior power density, high torque capability, and excellent controllability, PMSM systems are extensively applied in small and medium power drive fields, such as aerospace, robot, electric vehicle [1], [2]. We explore another way of employing fuzzy set theory to robust control design, investigating the fuzzy description of VOLUME 9, 2021 uncertain parameters and optimization control design in the PMSM system. As a further study of tracking control for PMSM system, we intend to combine the fuzzy set theory with a multi-parameter optimization approach for the deterministic robust control design for the fuzzy PMSM system. The robust control is constructed by tunable design parameters, nominal parameters of PMSM system, and the estimated value of uncertainty bound, which can guarantee the deterministic system performance of PMSM system, i.e., UB and UUB. For the uncertain parameters which inevitably exist in the PMSM system, we adopt the fuzzy number to describe the uncertainty bound by the membership function It provides an effective substitutive for the stochastic approach when the sampling data is insufficient to model the uncertain parameter. Mechanical systems, such as vehicles system, robotic system and aircraft system, etc
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