This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY 1 Optimal and Fault-Tolerant Torque Control of Servo Motors Subject to Voltage and Current Limits Farhad Aghili Abstract— This brief presents an optimal and ripple-free torque control of a brushless servo motor with any back-emk waveform that minimizes power dissipation subject to voltage and current limits of the motor’s drivers/amplifiers. When one or more phases reach the voltage and/or current limits, the controller optimally reshapes the stator currents of the remaining phases for continuing accurate torque production. This allows the motor to operate above the rated speed and torque that would be achieved without current reshaping. In the event that an open-circuit or short-circuit of a winding occurs, the torque controller can also isolate the faulty phase in order to generate torque as requested given the voltage and current constraints of the healthy phases. Assuming the inductance of stator coils is negligible allows the description of the phase voltage and current limit requirements by a set of inequity constraints. It follows by the derivation of a closed-form solution for the optimal phase currents at given angular position, velocity, and desired torque—rendering the control algorithm suitable for real-time implementation. Experimental results illustrate the capability of the controller to achieve precise torque production during voltage/current saturation of the motor’s drivers or a phase failure. Index Terms— Constrained optimization, current saturation, fault-tolerant, optimal control, permanent magnet machines, torque control of electric motors, torque ripple, voltage saturation. I. I NTRODUCTION B RUSHLESS dc motors are commonly used as the drives of servo systems in a wide range of industrial applica- tions from robotics and automation to aerospace and military. Accurate and ripple-free torque control of brushless motors is essential for precision control of such servo systems. In brushless motors, the electric power is distributed by an electronically controlled commutation system, instead of a mechanical commutator found in brushed dc motors. The conventional electronic commutator incorporates a feedback from the rotor angular position into a control system, which excites the stator coils of the motor in a specific order in order to rotate the magnetic field generated by the coils to be followed along by the rotor. Conventional drivers of brushless motors produce sinusoidal current waveforms for smooth motor operation. However, nonideal motors do not have a perfectly sinusoidally distributed magneto-motive force, and hence a sinusoidal commutation can result in torque ripple. Manuscript received April 27, 2011; revised February 9, 2012; accepted May 24, 2012. Manuscript received in final form May 24, 2012. Recom- mended by Associate Editor T. Parisini. The author is with Canadian Space Agency, Saint-Hubert, QC J3Y 8Y9, Canada (e-mail: farhad.aghili@asc-csa.gc.ca). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TCST.2012.2202118 It has been proved that suppressing the torque ripple of the motor drive of a servo system can significantly improve the system performance by reducing speed fluctuations [1], [2]. Commercial high-performance electric motors reduce the pul- sating torque by increasing the number of motor poles. However, such motors tend to be expensive and bulky due to construction and assembly of multiple coil windings. Control approaches for accurate torque production in electric motors and their underlying models have been studied by several researchers [1]–[14]. It was assumed in these works that the phase currents can be controlled accurately and instantaneously, and therefore the currents can be treated as the control inputs. Then, the waveforms of the motor phase currents are adequately preshaped so that the generated torque is equal to the requested torque. However, when the motor’s drivers have fixed-rate current and voltage limits, some of them may not be able to deliver the current inputs dictated by the electronic commutator that may occur when the motor operates at high torque or speed. Consequently, the performance of the torque production may significantly deteriorate as a result of phase current distortions caused by either voltage or current saturation. Flux weakening allows a machine to operate above the base speed in constant-power, high-speed region when there is a fixed inverter voltage and current [15]. Below the rated speed, all of the stator currents can be used to produce torque. Above the rated speed, a part of the stator current must be used to oppose the permanent magnet (PM) flux while the remaining portion is used to produce torque. Several authors have addressed flux weakening in PM machines [16]–[19]. However, this technique can deal with electric motors with prefect sinusoidal back-electromotive force (EMF) waveform and, in addition, phase current limits are not taken into account. This brief presents a closed-form solution for optimal excitation currents for accurate torque control of brushless motors with any waveform that minimizes power dissipation subject to currents and voltage limits of the motor’s drivers. When the motor terminal voltages and/or phase currents reach their saturation levels, the controller automatically reshapes the excitation currents in such a way that the motor generates torque as requested. This optimal management of motor’s excitation currents can significantly increase the rated speed and torque of the motor in the face of the voltage and current limits of the drivers. In addition, the torque controller can be used as a remedial strategy to compensate for a phase failure, by optimally reshaping the currents of the remaining healthy phases for accurate torque production. This brief is organized as follows. Section II presents modeling of a brush- less motor subject to current and voltage limits of its phases. 1063–6536/$31.00 © 2012 IEEE