Permanent magnet synchronous machines (PMSM) are a popular choice for high performance variable frequency drives. Their advantages include a high torque-to-inertia ratio, power density, and efficiency. Although the advantages are numerous, a design challenge often faced when utilizing PMSMs is that they produce significant torque harmonics. The torque harmonics (often referred to as torque ripple) create acoustic noise and vibration that is undesirable in appliances.

Traditionally, in mass-produced drives where torque ripple is a concern, mitigation is achieved by modifying the machine design (i.e. magnet/tooth/slot geometry). Such modifications are useful; however, their effectiveness is limited in that ripple reduction comes at a price of reduced torque density, often requires significant design effort and additional manufacturing steps, and its success is determined by the precision of the manufacturing process. As an alternative to machine design, a number of strategies have been proposed to manipulate stator excitation to control torque harmonics. The advantages of the control-based mitigation methods are that they reduce manufacturing effort, they provide a means for a manufacturer to market a low-noise drive system as a user-selected option, and a system designer has more flexibility in terms of balancing mitigation against competing specifications including efficiency, torque density, etc.

Fig. 2

Although control-based methods have numerous advantages, their use has been restricted to custom (low-volume) applications. This in large part due to a lack of robustness in the controllers as well as the cost of additional hardware required to implement control methods. Specifically, in most of the proposed control-based techniques, knowledge of the back-emf and cogging torque harmonics are used to derive stator excitation that minimizes torque ripple (or minimizes subject to constraints such as maximizing efficiency, a fixed dc-link voltage, etc.). Rarely does a manufacturer have the resources to determine back-emf and cogging torque harmonics for each machine produced. Indeed, even if this was possible, it would be necessary to compute the values over a wide range of operating conditions, as temperature and saturation both play a role in harmonic amplitudes. To further increase cost most proposed control schemes require the use of a high-precision position encoder to actively control torque ripple harmonics.

A promising solution

Fig. 3

Recently, a series of studies have shown a possible path toward cost-effective control-based torque-ripple mitigation in mass-produced drives [1], [2], [3]. Specifically, to eliminate the need to obtain knowledge of machine parameters, a piezoelectric polyvinylidene fluoride (PVDF) polymer film is used in [1] to detect torque-ripple-induced vibration. A diagram of the sensor configured as a washer on a machine mount is shown in Fig. 1.

The vibration feedback provided by the washer is used to establish stator current harmonics that mitigate the torque ripple. More precisely, the output of the sensor is a time-domain signal that contains an entire spectrum of components (not all due to torque ripple). In order to determine an appropriate feedback (i.e. stator current waveform), the output voltage of the sensor is first multiplied (within a processor) by the sine and cosine functions of the desired torque ripple component. The product is then input into a “leaky” integrator to extract the desired amplitude. Specifically,

are voltages that are representative of the Fourier coefficients of the vibration spectrum that are caused by torque ripple. In (1) v_sensor is the output voltage of the sensor (after some conditioning), y is the component of the torque ripple (i.e. a 6th, 12th, 18th), θ_r is the position of the rotor, and ε is ‘leaky’ constant. The subscripts ‘q’ and ‘d’ are used to represent the Fourier series as a function of cosines (q) and sines (d).

Using the sensor feedback, a torque ripple mitigation strategy is derived in [2] that determines commanded stator current harmonics. For implementation, a cost function is defined in terms of the machine torque ripple harmonics. The stator current harmonics that minimize the cost function are found using a gradient algorithm. The final controller is of the form

where T*_eq and T*_ed are vectors that contain the measured torque ripple harmonic coefficients (the superscript * is used to denote measured quantity), I_qh is a vector representing the q-axis current harmonics (not including the fundamental), I_d is a vector that represents the d-axis current harmonics, K_e1 and K_e2 contain rough estimates of the coefficients of back-emf, Q is a diagonal matrix that contains components to weight overall cost in favor of one harmonic over another, and the scalar α is a control parameter used to adjust the time constant of the controller. The fundamental q-axis current harmonic (I_q1) is used to adjust the commanded average torque. The control algorithm for the q-axis components is shown in block diagram form in Fig. 2. In the figure /T_e represents average torque. A similar diagram can be established for the d-axis. Although not shown in Fig. 2, a Hall-effect-based position observer is used to provide the rotor position information. Details of the observer are provided in [3].

The measurement and control strategies described have been successfully tested on multiple machines. To provide an illustrative example, the results of applying the technique to a 3-phase machine are shown. The machine is constructed using concentrated stator windings, 12 rotor poles, and 36 stator slots. The parameters of the machine are listed in Table 1.

To implement the control, a TMS 320LF2407 DSP is used as the controller. The algorithm of (3) and (4) was programmed using fixed-point arithmetic in a C language format. The mitigation control was implemented to monitor two torsional harmonics and manipulate three current harmonics. Specifically the controller was such that I_q1 was used to track an average commanded torque, while mitigation of the 6th and 12th torque ripple induced harmonics was accomplished using

and the d-axis current harmonics were set to zero to maintain a zero d-axis torque ripple.

Fig. 4

Results of the current and torque harmonics before and after the mitigation control are shown in Fig. 3 and Fig. 4. Prior to mitigation, the current harmonics were adjusted to yield maximum torque/stator ampere. Since the machine has a nonsinusoidal back-emf, the current contains low-frequency harmonics to achieve maximum torque/ampere.

Viewing the stator current response after ripple mitigation control is executed, it is seen that a significant 5th and some 11th harmonic is present in the stator current waveform and the 6th and 12th harmonic of torque ripple is greatly reduced. The large harmonics in the current are due to the relatively large values of cogging torque that are found in the machine studied. For further insight into the controller effectiveness, a frequency domain plot of the torque ripple was obtained for both the simulation and hardware tests and is shown in Fig. 5.

The frequency domain plot shows the substantial reduction in ripple — the magnitude of 6th torque ripple harmonic and the 12th harmonic are close to the noise floor after the control is applied. It is noted that for the machine considered, the stator current harmonics are substantial, leading to a decrease in efficiency. In testing across multiple operating points, efficiencies were reduced an average of 3 percent. This points to a design tradeoff, i.e. selecting noise mitigation versus efficiency. Analytical methods derived in [2] show how such a design tradeoff can be effectively studied by adding an additional weight in the development of the cost function.

Conclusions

Fig. 5

The techniques of [1]-[3] represent an advance toward applying low-cost control- based mitigation methods in mass-produced drives where appreciable variation in machine parameters is expected. As the cost of computing power continues to decrease, such techniques may represent a competitive alternative (or a complementary approach) to machine design-based methods. A patent on the techniques is pending.