Torque ripple minimization in SRM drive using second-order-generalized-integrator-based FLL equivalent PR current controller

Abstract

A second-order-generalized-integrator (SOGI)-based frequency-locked-loop (FLL) equivalent proportional-resonant (PR) current controller is introduced in this paper to minimize torque ripple in switched reluctance motor (SRM) drive system. The typical cascaded closed-loop speed control of SRM comprises a speed controller giving desired torque, a static look-up table mapping the desired torque to desired/reference phase currents of SRM, and a current controller to track the reference phase currents. It is often seen that conventional current controllers like hysteresis controllers, proportional-integral (PI) controllers, and even intelligent controllers such as fuzzy logic controllers and model predictive direct torque controllers (MPDTC) are not very effective in minimizing the torque pulsations for a wide range of operating scenarios. The proposed SOGI-FLL-PR-based current control strategy is aimed at improving torque control under a wide range of operations of SRM. The performance of the proposed current controller has been compared to that of traditional current controllers like the hysteresis controller, the proportional-integral controller, the fuzzy logic current controller (FLCC), and MPDTC; and has shown to be superior in both simulation and experimental studies. Our study details a systematic approach to the dynamic modeling of SRMs, control strategy formulation, dynamic analysis, and experimental verification.

Appendix

1.1 Model predictive direct torque control (MPDTC) method

SRM ought to investigate model predictive direct torque control (MPDTC) to lessen torque ripple in the low-speed range given that the switching frequency will be high at higher speed and result in a larger torque ripple. In this study, MPDTC [27] replaces conventional direct torque control (DTC) with double hysteresis control to eliminate torque pulsation and boost SRM performance. To reduce torque ripple, traditional MPDTC cost functions include total torque. To minimize torque ripple, this torque control strategy distributes the total electromagnetic torque to each phase using a cubic torque sharing function. Figure 34 shows the MATLAB/Simulink architecture used to create the MPDTC control system for the SRM drive experimental verification platform.

1.2 Voltage vector selection

Phases A, B, and C are the voltage vector's operational states. Figure 35 shows the eight sectors V0-V7 that make up the space voltage vectors area, with the basic space voltage vectors represented by N1–N8. The suitable space voltage vectors can control the flux linkage and torque. Additionally, Table 8 has a listing of the voltage vectors in space that are shown in Fig. 35.

1.3 Torque predictive model for SRM

The standard equation for the phase voltage is as follows:

$$ v_{q} = Ri_{q} + \frac{{{\text{d}}\lambda_{q} \left( {i_{q} ,\theta_{q} } \right)}}{{{\text{d}}t}};\quad q = 1,\,2,\,3,\, \ldots $$

(28)

where $v_{q}$, $R$, $i_{q}$, and $\theta_{q}$ are denoted as phase voltage, phase resistance, phase current, and phase rotor position, respectively. $\lambda_{q}$ is the phase flux, which depends on the phase current and the rotor position.

The dynamic model (28) could be modified in the following ways to facilitate the development of a torque predictive model:

$$ \frac{{{\text{d}}i_{q} }}{{{\text{d}}t}} = \frac{1}{{{\text{d}}\lambda_{q} /{\text{d}}i_{q} }}\left( {v_{q} - Ri_{q} - \frac{{{\text{d}}\lambda_{q} }}{{{\text{d}}\theta_{q} }}\omega } \right) $$

(29)

$$ \frac{{{\text{d}}\theta_{q} }}{{{\text{d}}t}} = \omega $$

(30)

where $\omega$ is the rotor speed. The digital device operates in discrete time. As a result, the continuous-time model must be transformed into a discrete-time model.

$$ \begin{gathered} i_{k + 1} = i_{k} + \frac{{T_{s} }}{{{\text{d}}\lambda /{\text{d}}i_{k} }}\left[ {v_{k + 1} - Ri_{k} - \frac{{{\text{d}}\lambda }}{{{\text{d}}\theta_{k} }}\omega_{k} } \right] \hfill \\ \theta_{k + 1} = \theta_{k} + \omega_{k} T_{s} \hfill \\ T_{e,k + 1} = \sum T_{{{\text{ph}},k + 1}} \hfill \\ \end{gathered} $$

(31)

We can determine the phase torque at the (k + 1) instant by predicting the phase current and rotor position at the kth step. Once the cost function is defined, it may be used to pick the best vector for controlling the voltage.

$$ {\text{Min}}\,J\left( {u_{k} } \right) = \left( {T_{e,k + 1} - T_{d} } \right)^{2} ;\;u_{k} \in \left\{ {N1,\,N2,\, \ldots \,,\,N8} \right\} $$

(32)

1.4 Hysteresis current control

The full negative DC link voltage ($- V_{{{\text{dc}}}}$), chosen based on motor voltage rating, is applied by the hysteresis current controller across a phase winding during turn-off. The hysteresis current controller generates switching signals, which are fed to the asymmetric bridge converter to switch the DC link voltage for regulating the phase currents. To maintain the phase current at the computed $i_{{{\text{ref}}{.}}}$, a hysteresis band is defined by $i_{{{\text{upper}}}}$ and $i_{{{\text{lower}}}}$. These values are calculated based on $i_{{{\text{ref}}{.}}}$ and a tolerance band $\alpha$, as shown in (Eq. 33). Generally, $\alpha$ is given as a percentage of the current reference, $i_{{{\text{ref}}{.}}}$.

$$ \begin{gathered} i_{{{\text{upper}}}} = i_{{{\text{ref}}}} (1 + \alpha ) \hfill \\ i_{{{\text{lower}}}} = i_{{{\text{ref}}}} (1 - \alpha ) \hfill \\ \end{gathered} $$

(33)

Hysteresis control of phase current is implemented using soft (unipolar) switching strategy [15], at time step k, as shown in Eq. 34.

$$ V_{{{\text{ph}}}} \left( k \right) = \left\{ \begin{gathered} 0\parallel {\text{ref}}{\text{.current}} \le 0 \cap i_{{{\text{ph}}}} \le 0 \hfill \\ - V_{{{\text{dc}}}} \parallel ... \cap i_{{{\text{ph}}}} > 0 \hfill \\ 0\parallel {\text{ref}}{\text{.current}} > 0 \cap i_{{{\text{ph}}}} \ge i_{{{\text{upper}}}} \hfill \\ + V_{{{\text{dc}}}} \parallel ... \cap i_{{{\text{ph}}}} < i_{{{\text{lower}}}} \hfill \\ V_{{{\text{ph}}}} (k - 1)\parallel ... \cap i_{{{\text{upper}}}} > i_{{{\text{ph}}}} \ge i_{{{\text{lower}}}} \hfill \\ 0\parallel ... \cap {\text{otherwise}} \hfill \\ \end{gathered} \right. $$

(34)

where the sign “$\parallel$”denotes provided and the symbol “$\cap$” represents logical.