The steady-state and convergence performances are important indicators to evaluate adaptive algorithms. The step-size affects these two important indicators directly. Many relevant scholars have also proposed some variable step-size adaptive algorithms for improving performance. However, there are still some problems in these existing variable step-size adaptive algorithms, such as the insufficient theoretical analysis, the imbalanced performance and the unachievable parameter. These problems influence the actual performance of some algorithms greatly. Therefore, we intend to further explore an inherent relationship between the key performance and the step-size in this paper. The variation of mean square deviation (MSD) is adopted as the cost function. Based on some theoretical analyses and derivations, a novel variable step-size algorithm with a dynamic limited function (DLF) was proposed. At the same time, the sufficient theoretical analysis is conducted on the weight deviation and the convergence stability. The proposed algorithm is also tested with some typical algorithms in many different environments. Both the theoretical analysis and the experimental result all have verified that the proposed algorithm equips a superior performance.

To reduce the common mode voltage (CMV), suppress the CMV spikes, and improve the steady-state performance, a simplified reactive torque model predictive control (RT-MPC) for induction motors (IMs) is proposed. The proposed prediction model can effectively reduce the complexity of the control algorithm with the direct torque control (DTC) based voltage vector (VV) preselection approach. In addition, the proposed CMV suppression strategy can restrict the CMV within ±Vdc/6, and does not require the exclusion of non-adjacent non-opposite VVs, thus resulting in the system showing good steady-state performance. The effectiveness of the proposed design has been tested and verified by the practical experiment. The proposed algorithm can reduce the execution time by an average of 26.33% compared to the major competitors.

Recursive least absolute(RLA) error algorithm is derived which is basically the sign algorithm (SA) combined with recursive estimation of the inverse covariance matrix of the reference input. The name RLA comes from the absolute error criterion. Analysis of the transient behavior and steady-state performance of the RLA algorithm is fully developed. Results of experiment show that the RLA algorithm considerably improves the convergence rate of the SA while preserving the robustness against impulse noise. Good agreement between the simulation and the theoretically calculated convergence validates the analysis.