Modeling and High Performance Control of Electric Machines
Book Preface
This book is intended to be an exposition of the modeling and control of electric machines, specifically, the direct current (DC) machine and the alternating current (AC) machines consisting of the induction motor, the permanent magnet (PM) synchronous motor, and the brushless DC motor. The particular emphasis here is on techniques used for highperformance applications, that is, applications that require both rapid and precise control of position, speed, and/or torque. Traditionally, DC motors were reserved for highperformance applications (positioning systems, rolling mills, traction drives, etc.) because of their relative ease of control compared to AC machines. However, with the advances in control methods, computing capability, and power electronics, AC motors continue to replace DC motors in highperformance applications. The intent here is to carefully derive the mathematical models of the AC machines and show how these mathematical models are used to design control algorithms that achieve high performance.
Electric machines are a particularly fascinating application of basic electricity and magnetism. The presentation here relies heavily on these basic concepts from Physics to develop the models of the motors. Specifically, Faraday’s law (< = [email protected]/dt, where @ = ss B . ds), the magnetic force law (F = ie‘x B or, I? = qv’xB), Gauss’s law ($B. dS = 0), Ampgre’s law ($H . d=i free)t,h e relationship between B and H, properties of magnetic materials, and so on are reviewed in detail and used extensively to derive the currently accepted nonlinear differential equation models of the various AC motors. The author made his best attempt to make the modeling assumptions as clear as possible and to consistently show that the magnetic and electric fields satisfy Maxwell’s equations (as, of course, they must). The classical approach to teaching electric machinery is to present their equivalent circuit models and to analyze these circuit models ad nauseam. Further, the use of the basic Physics of electricity and magnetism to explain their operation is minimized if not omitted. However, the equivalent circuit is a result of assuming constantspeed operation of the machine and computing the sinusoidal steadystate solution of the nonlinear differential equation model of the machine. Here, the emphasis is on explaining how the machines work using fundamental concepts from electricity and magnetism, and on the derivation of their nonlinear differential equation models. The derivation of the corresponding equivalent circuit assuming steadystate conditions is then straightforward. Electric machines also provide fascinating examples to illustrate concepts from electromagnetic field theory (in contrast to electricity and magnetism). In particular, the way the electric and magnetic fields change as one goes between reference frames that are in relative motion are vividly illustrated using AC machines. For this reason, optional sections are included to show how the electric and magnetic fields change as one goes between a coordinate system attached to the stator to a coordinate system that rotates with the rotating magnetic field produced by the stator currents or a frame attached to the rotor. Also given in an optional section is the derivation of the axial electric and azimuthal magnetic fields in the air gap This is also a book on the control of electric machines based on their differential equation models. With the notable exception of the sinusoidal steadystate analysis of the induction motor in Chapter 7, very little attention is given to the classical equivalent circuits as these models are valid only in steady state. Rather, the differential equation models are used as the basis to develop the notions of fieldoriented control, inputoutput linearization, flux observers, leastsquares identification methods, state feedback trajectory tracking, and so on. This is a natural result of the emphasis here on highperformance control methods (e.g., fieldoriented control) as opposed to classical methods (e.g., V/f,sl ip control, etc.). There are of course many good books in the area of electric machines and their control. The author owes a debt of gratitude to Professor W. Leonhard for his book [l] (see the most recent edition [a]), from which he was educated in the modeling and control of electric drives. The present book is narrower in focus with an emphasis on the modeling and operation of electric machines based on elementary classical physics and an emphasis on highperformance control methods using a statespace formulation. The books by P. C. Krause [3] and P. C. Krause et al. [4] are complete in their derivation of the mathematical models of electric machines while C. B. Gray [5] presents electromagnetic theory in the context of electric machines. A comprehensive treatment using SIMULINtKo simulate electric machinery is given in CM. Ong’s book [6]. The graduate level books by D. W. Novotny and T. A. Lip0 [7], P. Vas [8], J. M. D. Murphy and F. G. Turnbull [9], I. Boldea and S. A. Nasar [lo], B. Adkins and R. G. Harley [ll], A. M. Trzynadlowski 1121, M. P. Kazmierkowski and H. Tunia [13], B. K. Bose [14], and R. Krishnan [15] all cover the modeling and control of electric machines while the books by R. Ortega et al. [16], D. M. Dawson et al. [17], and F. Khorrami et al. [l8] emphasize advanced control methods. The introductorylevel books by S. J. Chapman [19], H. Woodson and J. Melcher [20], L. W. Matsch and J. D. Morgan [21], G. McPherson and R. D. Laramore [22], D. V. Richardson [23], P. C. Krause and 0. Wasynczuk [24], N. Mohan [25], G. R. Slemon and A. Straughn [26], J. Sokira and W. Jaffe [27], G. J. Thaler and M. L. Wilcox [as], V. Deltoro [29], M. ElHawary [30], P. C. Sen [31], and G. R. Slemon [32] are among the many books on electric machines from which this author has benefited.
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August 17, 2018 
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