Sliding Mode Control for Synchronous Electric Drives

This volume presents the theory of control systems with sliding mode applied to electrical motors and power converters. It demonstrates the methodology of control design and the original algorithms of control and observation. Practically all semiconductor devices are used in power converters, that feed electrical motors, as power switches. A switching mode offers myriad attractive, inherent properties from a control viewpoint, especially a sliding mode. Sliding mode control supplies high dynamics to systems, invariability of systems to changes of their parameters and of exterior loads in combination with simplicity of design. Unlike linear control, switching sliding mode control does not replace the control system, but uses the natural properties of the control plant system effectively to ensure high control quality. This is the first text that thoroughly describes the application of the highly theoretical control design approach to synchronous drives in practice. It examines in detail the different features of various types of synchronous motors and converters with regard to sliding mode control design. It further presents a detailed analysis of control issues and mechanical coordinate observation design for various types of synchronous motors, of power converters, and various drive control structures. It also discusses the digital implementation of control, observation and identification algorithms. The potential of sliding mode control and observation are moreover demonstrated in numerical and experimental results from real control plants. This work is intended for professionals and advanced students who work in the field of electric drive control. It is also recommended to experts in control theory application, who work with sliding modes for the control of electrical motors and power converters. Introduction 1 Problem statement 1.1 Mathematical models of the drive elements 1.1.1 Synchronous motors 1.1.2 Semiconductor power converters 1.2 Drive control problems and their existing solutions 2 Sliding mode in nonlinear dynamic systems 2.1 Plant features and sliding mode design 2.1.1 Sufficient existence conditions of a sliding mode 2.2 Sufficient existence conditions of sliding mode in systems with redundant control 2.3 Sliding mode design 3 State vector estimation 3.1 Information aspects of sliding mode design 3.2 Use of an asymptotical observer of the state variables 3.3 Nonlinear sliding mode observer 3.4 Physical significance of equivalent control 4 Synchronous drive control design 4.1 Single-loop control design 4.1.1 The two step decomposition approach 4.1.2 First step - design of fictitious discontinuous control 4.1.3 Second step - phase voltage control design 4.2 Cascade (subordinated) control 4.3 Static modes optimization 4.3.1 Problem statement 4.3.2 Keeping maximum efficiency and minimum stator current 4.3.3 Keeping cos φ=1 4.3.4 Realization of the offered dependencies 4.3.5 Using control task id z =0 5 Multidimensional switching regularization 5.1 Features of real sliding mode 5.2 Switching loss minimized control for VSI 5.2.1 Analysis of PWM laws 5.2.2 Comparative analysis of switching laws from the switching losses viewpoint 5.2.3 Comparing PWM switching laws - Numerical results 5.2.4 Switching loss minimizing PWM 5.3 Optimal switching losses in real sliding mode 5.4 Switching regularization of discontinuous control vector components 5.4.1 Control vector 5.4.2 Simplified control 5.4.3 Follow-up current vector control structure 5.4.4 Test simulation of a follow-up loop 6 Mechanical coordinates observers 6.1 General formulation of the observation problem 6.2 Observer design for permanent magnet salient-pole synchronous motor with constant magnets 6.2.1 Rotating coordinate system 6.2.2 Motionless coordinate system (α, β) 6.2.3 The simplified observer 6.3 Observer design for the synchronous reluctance motor 6.3.1 Rotating coordinate system 6.3.2 The simplified observer 7 Digital control 7.1 Main principles of digital control 7.1.1 Features of digital control 7.1.2 Digital sliding mode 7.2 Digital control design for the synchronous motor 7.2.1 Synchronous motor difference equations 7.2.2 Angular speed control 7.3 Digital drive mechanical variable estimation 7.3.1 Problem statement 136 7.3.2 Permanent magnet nonsalient-pole synchronous motor state observer 7.3.3 The filter-observer of mechanical variables 7.4 Parameter identification of linear digital system with variable factors and the limited memory depth 7.4.1 Statement of a parameter identification problem 7.4.2 Identification condition of matrix factors 7.4.3 Identification of physical parameters 7.4.4 Moment of inertia identification 7.5 The reference rate limiter 7.5.1 The general problem statement 7.6 Reference rate limiter 7.7 Digital control design for the electric drive with elastic connections 7.7.1 Control problem statement 7.7.2 Elastic mechanical movement difference model 7.7.3 Digital control design of elastic oscillations 7.7.4 State variable observer 8 Practical examples of drive control 8.1 High speed synchronous drive sensorless control 8.1.1 Features of the control system 8.1.2 Simulation model 8.1.3 Drive rating parameters 8.1.4 Sensitivity research to parameter variation 8.1.5 Influence of A/D converter discreteness on current measurements 8.1.6 The influence of VSI "dead time'' 8.1.7 Conclusions on the simulation 8.2 Digital control system of the electric drive with elastic mechanical connections 8.2.1 Control plant features 8.2.2 Main principles of control design 8.2.3 Dry friction and backslash compensation 8.2.4 Closed loop simulation Index