ABSTRACT
Drive systems with AC machines are designed for applications with di¦erent requirements for a rotor speed control. In the closed-loop control systems, usually a torque has to be controlled and machine currents have to be limited. A general idea of designing the controlled drives is based on the application of a controller, which ensures required dynamical properties for the torque. In case of AC machines, the torque is generated as the result of mutual interaction between currents and ¹uxes formed by three-phase, or more general, multiphase systems. Models of AC machines derived as di¦erential equations for phase variables are complicated and not appropriate for the synthesis of control systems. že application of known methods of controllers synthesis and tuning requires, in case of AC machines, linear and nonlinear transformations of variables and derivation of models in form of di¦erential equations. At Ÿrst, a linear transformation of phase variables to orthogonal coordinates is applied. A space vector method is used to receive new variables expressed as components of vectors. As a³er such transformation, the variables in orthogonal coordinates are harmonic, and the next transformation is applied to receive variables that do not contain periodical components. In a classical control theory of electrical machines, a simple rotation of frame of references is used, which, if properly orientated, results in machine model in form of di¦erential equation with
27.1 Introduction .................................................................................... 27-1 27.2 Nonlinear Transformations and Feedback Linearization ........ 27-2 27.3 Models of the Squirrel Cage Induction Machine ...................... 27-4
27.5 Models of the Interior Permanent Magnet Synchronous Machine .......................................................................................... 27-12 Vector Model of the Interior Permanent Magnet Synchronous Machine • Multiscalar Model of the IPMSM • Feedback Linearization of IPMSM • E¢cient Control of IPMSM
27.6 Structures of Control Systems for AC Machines Linearized by Feedback ............................................................... 27-15
References .................................................................................................. 27-18
the constant values of variables in steady states. Unfortunately, a³er transformations based on space vector method, the di¦erential equations of AC machines remain nonlinear although in a few cases one of the equations takes the linear form. A rule is that di¦erential equation for the rotor angular velocity remains nonlinear because the machine torque is expressed as nonlinear dependence of the components of current and ¹ux vector.
