Transfer functions of the 2-phase servomotor

One of the most common electromechanical positioning devices for low-power applications is the 2-phase servomotor, several different . constructional forms being available. When used in a control application, various transfer functions of the machine are important and these have been investigated by previous workers using analyses of varying validity. For example, in early studies, it was common to regard the speed-torque characteristics of the machine as straight lines, and also to neglect the electrical energy storage elements in comparison with those of the mechanical system. Quite sophisticated mathematical studies using, for example, symmetrical components, were based on these assumptions, but the results obtained are obviously highly suspect in view of the doubtful basis from which they are established. Experimental verification of the results of the analyses were confined to steady-state. measurements, attention being devoted to establishing an equivalent circuit to provide steady-state characteristics. Recently, with the increasing use of powerful mathematical tools in engineering situations, several workers have attempted to obtain direct solutions of the nonlinear equations characterising the -operation of the servomotor. Thus, simulation and state transition methods, involving a step-by-step numerical solution, have attracted considerable interest. Although these approaches may provide useful numerical answers, they do not help in forming any understanding of the main factors affecting the transient performance of the machine. A recent paper used the complex convolution approach to provide analytical transfer functions, but unfortunately this paper contains a fundamental error which completely invalidates the work. The same formal approach is followed in this thesis, with the complex convolution technique being used to find time-domain expressions for the variations in speed which follow step changes in either the torque or the magnitude or phase of the control-winding voltage. As in the previous work, attention is confined to the practically important range of speed much lower than synchronous speed, Results obtained from the analysis are compared with experimentally obtained results and with results provided by earlier analyses, and an assessment is made of the usefulness and limitations of the various techniques.