### Delta current control for vector controlled permanent magnet synchronous motors

P. Freere, D. Atkinson, P. Pillay
Conference Record of the 1992 IEEE Industry Applications Society Annual Meeting
To provide good torque control for a vector controlled permanent magnet synchronous motor (PMSM), delta current control cilll be used. It has the advantage compared to controllers such as hysteresis and ramp companson, that the maximum switching frequency of the inverter transistors is predetermined. Although investigations into the delta controller have been performed, little work has been done on the characteristics of the controller and its influence on the inverter design. For the delta
more » ... . For the delta controller, the delta frequency must be chosen with respect to the required characteristics of torque, peak current and the average switching frequency of the inverter transistors. These characteristics are studied experimentally, using computer simulation and with mathematical analysis, with respect to the variables of delta frequency, dc supply voltage and the reference current magnitude. At low delta frequencies, there is an exponential increase in the mean torque and peak current. A n approximate analytical expression is given to predict the delta frequency at which this operating region commences. The effect of the motor speed on the torque is shown to enable the minimum required supply voltage to be chosen and the upper bound on the delta frequency is shown to be determined by the maximum acceptable average switching frequency. Also investigated is the delta controller's transient response, torque harmonics, the effect of flux weakening and the effect of turn-off delays of the inverter transistors when bipolar darlington transistors are used as compared with IGBT's. Symbols Id =delta frequency (Hz) 1, = delta frequency for minimum torque. e = backemf (V) Vdc = rail voltage to supply zero( V) supply voltage = rail to rail voltage (twice vdd (V) i = phase current (A) I , = reference current amplitude (A) R = PMSM phase resistance (Q) L = PMSM phase inductancc (H) or = PMSM rotor speed (rpm) (om= PMSM rotor speed (rads/s) V, = PMSM common voltage (V) K = PMSM backemf constant (V/rpm) 1.0 Introduction Vector control of permanent magnet synchronous motors (PMSMs) [ I ] is used to provide the maximum torque per amp 121 and a fast operating performance 13) by maintaining the stator field at 900 spacially to the rotor licld 141. The vector control hardware has been implemented as shown in figure I [SI, and the equivalent circuit of figure 2 161 has been used as a basis for the computer simulations 171 and analytical results. The simulation takes into account the individual semiconductor device that is conducting in the inverter and its voltage drop. Unless specified, the simulations are based on a bipolar Darlington inverter transistor with a lops storage delay time. R K . W resolver digital convener -j T S -I I l l -Figure 1. Vector control system. Figure 3. Equivalent circuit of the PMSM. To provide a smooth torque (81, PMSMs require a sinusoidal phase current, which requires an inverter switching strategy such as the delta current control [9]. I t combines an intuitively simple control strategy with a fixed maximum switching frequency [ lO][ll], in contrast to the hystersis 0-7803-0634-1/92\$03 .OO OIEEE 550 c -