The theory of vector control is applied to the nonlinear model of a permanent magnet synchronous motor to develop a linear model for controller design purposes. The operation and relevant mathematics of a pseudo-derivative feedback controller are presented. Controller designs for three different speeds are then considered, and a comparative evaluation is made on the basis of their large and small-signal behavior. In order to test the large-signal response, the detailed nonlinear model of the machine and a real-time model of the inverter switches are used. Results indicate that a critically damped design done so as to ensure that all control and power signals never saturate gives an extremely poor result. Much better small and large-signal responses are achieved by avoiding this constraint and using Zener diodes instead to limit the commanded input into the inverter. Two designs using this technique are presented, an underdamped design with low speed overshoot and an overdamped design with no speed overshoot. The response of the underdamped design was much quicker than that of the overdamped. However the overdamped design has application when speed overshoot is intolerable.>
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Pillay et al. (1990) studied this question.
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