LMI-based Sliding Mode Speed Tracking Control Design for Surface-mounted Permanent Magnet Synchronous Motors

Abstract -For precisely regulating the speed of a permanent magnet synchronous motor system with unknown load torque disturbance and disturbance inputs, an LMI-based sliding mode control scheme is proposed in this paper. After a brief review of the PMSM mathematical model, the sliding mode control law is designed in terms of linear matrix inequalities (LMIs). By adding an extended observer which estimates the unknown load torque, the proposed speed tracking controller can guarantee a good control performance. The stability of the proposed control system is proven through the reachability condition and an approximate method to implement the chattering reduction is also presented. The proposed control algorithm is implemented by using a digital signal processor (DSP) TMS320F28335. The simulation and experimental results verify that the proposed methodology achieves a more robust performance and a faster dynamic response than the conventional linear PI control method in the presence of PMSM parameter uncertainties and unknown external noises

Free (rational) derivation

By representing elements in free fields (over a commutative field and a finite alphabet) using Cohn and Reutenauer’s linear representations, we provide an algorithmic construction for the (partial) non-commutative (or Hausdorff-) derivative and show how it can be applied to the non-commutative version of the Newton iteration to find roots of matrix-valued rational equations

Solving matrix inequalities whose unknowns are matrices

This paper provides algorithms for numerical solution of convex matrix inequalities in which the variables naturally appear as matrices. This includes, for instance, many systems and control problems. To use these algorithms, no knowledge of linear matrix inequalities is required. However, as tools, they preserve many advantages of the linear matrix inequality framework. Our method has two components: ( 1) a numerical algorithm that solves a large class of matrix optimization problems and ( 2) a symbolic "convexity checker" that automatically provides a region which, if convex, guarantees that the solution from ( 1) is a global optimum on that region. The algorithms are partly numerical and partly symbolic and since they aim at exploiting the matrix structure of the unknowns, the symbolic part requires the development of new computer techniques for treating noncommutative algebra.17113

Solving Matrix Inequalities whose Unknowns are Matrices to appear

Abstract. This paper provides algorithms for numerical solution of convex matrix inequalities in which the variables naturally appear as matrices. This includes, for instance, many systems and control problems. To use these algorithms, no knowledge of linear matrix inequalities (LMIs) is required. However, as tools, they preserve many advantages of the linear matrix inequality framework. Our method has two components: 1) a numerical algorithm that solves a large class of matrix optimization problems; 2) a symbolic “Convexity Checker ” that automatically provides a region which, if convex, guarantees that the solution from (1) is a global optimum on that region. The algorithms are partly numerical and partly symbolic and since they aim at exploiting the matrix structure of the unknowns, the symbolic part requires the development of new computer techniques for treating noncommutative algebra