Torque Ripple Suppression Control for Permanent Magnet Motors Giuseppe Fedele and Andrea Ferrise Department of Informatics, Modeling, Electronics and Systems Engineering University of Calabria, Italy Email: (gfedele,aferrise)@dimes.unical.it Abstract— Permanent magnet motors are largely employed due to their high performances in terms of efficiency, power factor and power density. However, non-uniformity into the generated torque may heavily limit their use. In this paper a novel approach is proposed to cancel torque ripple when motor parameters are unknown. The cancellation scheme is based on the frequencies estimation of periodic disturbances acting on the generated motor torque. The estimation process makes use of an adaptive frequency-locked loop system driven by speed measurements. A fractional-order controller is designed to guarantee the stability of the closed-loop system. Index Terms—ripple suppression, fractional-order controller, generalized integrators, permanent magnet motor. I. I NTRODUCTION Permanent magnet motors (PMMs) are generally em- ployed in elevated performance variable frequency drives [1], [2]. Such motors can be supplied from a three-phase or single-phase voltage system [3] and they are becom- ing dominant in the industrial applications market [4]. As remarked in [2], the efficiency of PMMs enables totally enclosed design with surface cooling with high flux densities in the air-gap facilitating the construction of motors of unsurpassed power density. However, the presence of non- uniformity in the developed torques may heavily affect the motor performances. Such a non-uniformity may occur due to the following cases [2], [5]: • in trapezoidal emf machines, the torque changes peri- odically in synchronism with the revolving rotor since the non-ideal trapezoidal emf waveforms; • in sinusoidal emf machines, non-sinusoidal flux link- ages and current distortions may cause harmonic torque components; • critical torque harmonics range typically varies from 100Hz to 2kHz depending on flux linkage mechanical effects, speed increasing and time current harmonics effects that are not completely filtered. In fact, every speed fluctuations due to low frequency torque ripple are automatically compensated by the drive control sys- tem and harmonics of higher frequency are sufficiently attenuated by the rotor inertia. As remarked in [4], the principal source affecting torque ripple is represented by cogging torque that is due to the iteration between the permanent magnets and the stator slots. More formally, it can be represented by T cog = - 1 2 φ 2 g dR l dθ , where φ g is the air-gap flux, R l is the air-gap reluctance, and θ is the position of the rotor. As highlighted in [4], since air-gap reluctance varies periodically, the resultant cogging torque is also periodic and it is possible to consider the torque as a Fourier series of harmonic terms, i.e T cog = ∑ ∞ k=1 T mk sin(kmθ), where m is the least common multiple of the number of stator slots and the number of poles and T mk are the Fourier coefficients of the series. The problem of suppressing the torque ripple in PMMs has been widely investigated and several approaches have been proposed (see [6] and the references therein, [7], [8], [9], [10], [11]). The principal techniques can be cast into two main groups. The methods belonging to the first class attempt to correct the ripple effects in the motor design such that the PMMs more closely approach its ideal char- acteristics for achieving smooth torque production. Even if such methods perform well in ripple minimization, machine design techniques additionally complicate the production process and increase the final machine cost [2], [6]. The methods belonging to the latter family try to minimize the torque ripple using an additional control effort to correct for non-ideal characteristics of the machine (see [12], [13] for example). In the case of time-varying motor parameters, on-line estimation techniques have been widely investigated [14]. The majority of such methods (recursive least square, model reference adaptive system approaches and so on) estimate all the necessary information about torque wave- form starting from the electrical subsystem (i.e. current / voltage measurements). This estimation is then used into the feedback loop to control the provided torque. Various observer-based approaches have been also reported in [15], [16], [17] in order to compensate multiple additive position periodic torque disturbances similar to pure cogging and ”quasi-cogging” due to magnetic unbalance pull. The approach discussed in this paper permits to reduce the effects of a multi-sinusoidal disturbance acting on an unknown PMM. The information required to cancel torque ripple consist in the frequency at which the ripple occurs. According to the only speed measurements, the method is able to estimate the frequency of the torque ripple and, simultaneously, cancel its effects by the input channel. No assumptions on the motor parameters are made. Unlike the methods in [15], [16], [17], where information about the model is required to properly implement the discussed observers, this paper deals with the case of completely unknown plant structure. The only hypothesis is that the frequency response of the plant, at the estimated frequencies, belongs to a generic half-plane, passing through the origin of