## Abstract

The dynamics of any motor consist of two parts, the mechanical and the electrical dynamics. The mechanical dynamics are given by Newton’s laws relating the force (or torque) to the acceleration. The electrical part is governed by Kirchoff’s laws and can be derived using an equivalent circuit model. The mechanical and electrical subsystems are coupled through the force (or torque) which depends on the currents and the inductances which depend on the position. The derivation of the dynamics of linear and rotary motors are similar. For simplicity, we consider a rotary motor to illustrate the basic principles. Although models of various motors have common features, we pursue modeling of stepper motors in this chapter. Modeling of brushless DC motors and induction motors are postponed to Chaps. 11 and 12, respectively.

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## References

- 1.These permeances Pl and P4 are equal because of the symmetry of the motor.Google Scholar
- 2.The flux linkage is an odd function of the current, and hence odd powers of current are used.Google Scholar
- 3.The derivation assumes two stator poles. However, an n-phase PM motor can be transformed to an equivalent 2-phase motor using an n-phase to 2-phase transformation. Therefore, the development given here and subsequent control design is applicable to the general n-phase PM stepper motor.Google Scholar
- 4.To simplify the dynamics of the motor, it can be assumed that all lengths are expressed as multiples of
_{2}so that -y can be taken as 1. In this case, the coefficients -y appearing in (3.61) can be eliminated.Google Scholar - 5.The reluctance functions for the air gaps under the second phase of the forcer are given
*by Rai,i = 5,...,8.*Google Scholar - 6.Saturation effects may be modeled by making
*Ro and Ra*functions of the flux.Google Scholar