The permanent magnet synchronous motor (PMSM) is a highly efficient energy saving machine. Due to its simple structural characteristics, good heat radiation capability, and high efficiency, PMSMs are gradually replacing AC induction motors in many industrial applications. The PMSM has a nonlinear system and lies on parameters that differ over time with complex high-class dynamics. To achieve the excessive performance operation of a PMSM, it essentially needs a speed controller for providing accurate speed tracking, slight overshoot, and robust disturbance repulsion. Therefore, this article provides an overview of different robust control techniques for PMSMs and reviews the implementation of a speed controller. In view of the uncertainty factors, such as parameter perturbation and load disturbance, the H∞ robust control strategy is mainly reviewed based on the traditional control techniques, i.e., robust H∞ sliding mode controller (SMC), and H∞ robust current controller based on Hamilton–Jacobi Inequality (HJI) theory. Based on comparative analysis, this review simplifies the development trend of different control technologies used for a PMSM speed regulation system.

In this paper we propose a new three-step iteration process, called M iteration process, for approximation of fixed points. Some weak and strong convergence theorems are proved for Suzuki generalized nonexpansive mappings in the setting of uniformly convex Banach spaces. Numerical example is given to show the efficiency of new iteration process. Our results are the extension, improvement and generalization of many known results in the literature of iterations in fixed point theory.

We introduce a very general class of generalized non-expansive maps. This new class of maps properly includes the class of Suzuki non-expansive maps, Reich–Suzuki type non-expansive maps, and generalized $\alpha$ -non-expansive maps. We establish some basic properties and demiclosed principle for this class of maps. After this, we establish existence and convergence results for this class of maps in the context of uniformly convex Banach spaces and compare several well known iterative algorithms.

In this paper we propose a new iteration process, called AK iteration process, for approximation of fixed points for contraction mappings. We show that our iteration process is faster than the leading Vatan Two-step iteration process for contraction mappings. Numerical examples are given to support the analytic proofs. Stability of AK iteration process and data dependence result for contraction mappings by employing AK iteration process are also discussed.

In this paper, an efficient new iterative method for approximating the fixed point of Suzuki mappings is proposed. Some important weak and strong convergence results of the proposed iterative method are established in the setting of Banach space. An example illustrates the theoretical outcome.