Time Optimal Current or Torque Control

Emerging applications, like electrical test rigs for automotive, require extremely fast large-signal torque responses. Conventional, low-complexity PID-like controllers are inadequate for that task, especially when associated with Internal Permanent Magnet Synchronous Motor (IPMSM) drives. This kind of motor mostly features a marked saliency ratio, which entails that both the d- and q-axis current take part in the torque generation. Therefore, the control algorithm must guarantee a fast and precise control over both the current components. It is currently straightforward to obtain a good current control under quasi steady state conditions, whereas it is not take for granted under quick and large variations of the torque reference. In this last condition, the current regulators are easily saturated by the voltage saturation of the inverter, even at low speed. PID controllers are not optimized to work under voltage saturation. Several solutions to this problem have been proposed in literature, but none of them addressed the topic in order to achieve the fastest possible response from the torque/current controller.

Two new solutions have been developed and proposed: the time optimal Current control (toCc) and the time optimal Torque control (toTc). They have been obtained by applying Pontryagin’s Optimal Control theory to a model of the IPMSM. The toCc guarantees the achievement of the fastest current response, while the toTc ensures the fastest torque response, both under voltage saturation. The novel controls are designed to work in parallel with any known current/torque control strategy. An algorithm decides when to use the conventional control and when to use the optimal control, according to the working conditions of the drive. Basically, the conventional control is enabled in steady or quasi steady state conditions, while the optimal control is enabled when large and fast torque variations are demanded.


This control strategy assures the fastest current/torque response after any demanded current/torque reference variation. It can be demonstrated that such a control exhibits faster response than hysteresis control, even if the latter is often considered the fastest control scheme.

The research study includes a theoretical analysis of the problem, as well as an extended set of simulations and experimental results documented in the following papers.

  • N.Bianchi, S.Bolognani, M.Zigliotto, Time Optimal Current Control for PMSM Drives, Proceedings of IEEE International Conference on Industrial Electronics, Control and Instrumentation, IECON'02, Sevilla, Spain, 2002.
  • S.Bolognani, L.Tubiana, M.Tomasini, M.Zigliotto, DSP-based Time Optimal Current Control for High Performance IPM Motor Drives, Proceedings of IEEE Annual Applied Power Electronics Conference, PESC'04, Aachen Germany, 2004.
  • S.Bolognani, M.Ceschia, M.Tomasini, L.Tubiana, M.Zigliotto, //FPGA Implementation of a Recursive Algorithm for Time Optimal Control of AC Drives, (Invited Paper) 11th International Conference on Power Electronics and Motion Control, EPE-PEMC'04, Riga, Latvia, 2004.
  • S.Bolognani, M.Tomasini, L.Tubiana, M.Zigliotto, Design and Implementation of a Minimum-Time Torque Control for IPM Motor Drives, Conference Records of IEEE Industry Application Society, IAS 2005, Hong Kong, PRC, 2005.
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