Romanovski Polynomials Method and Its Application for Non-central Potential System

Transactions of the Institute of Measurement and Control

2019

A switched reluctance motor (SRM) drive system has highly nonlinear uncertainties owing to a convex construction. It is hard for the linear control methods to achieve good performance for the SRM drive system. An adaptive nonlinear backstepping control system using the mended recurrent Romanovski polynomials neural network and mended PSO with an adaptive law and an error estimated law is proposed to estimate the lumped uncertainty and to compensate the estimated error in order to enhance the robustness of the SRM drive system. Additionally, in accordance with the Lyapunov stability theorem, the adaptive law in the mended recurrent Romanovski polynomials neural network and the error estimated law are established. Furthermore, to help improve convergence and to obtain better learning performance, the mended particle swarm optimization (PSO) algorithm is utilized for adjusting the two varied learning rates of the two parameters in the mended recurrent Romanovski polynomials neural network. Finally, some experimental results and a comparative analysis are verified that the proposed control scheme has better control performances for controlling the SRM drive system.

Section: Design Of Adaptive Nonlinear Backstepping Control Systemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Retracted: Adaptive nonlinear backstepping control using mended recurrent Romanovski polynomials neural network and mended particle swarm optimization for switched reluctance motor drive system

Transactions of the Institute of Measurement and Control

2019

“…The zero‐, the first‐, and the second‐order Romanovski polynomials are given by

R_{0}^{(α, β)} ((), x) = 1

R_{1}^{(α, β)} ((), x) = 2 italicβx + α

, and

R_{2}^{(α, β)} ((), x) = ((), 2 β + 1) ((), 2 β + 2) x^{2} + 2 α ((), 2 β + 1) x + ((), α^{2} + 2 β + 2)

, respectively. The higher‐order Romanovski polynomials may be generated by the recursive formula

R_{n + 1}^{(α, β)} ((), x) = ((), α - 2 x ((), - β + n + 1)) R_{n}^{(α, β)} ((), x) - n ((), 1 + x^{2}) ((), - 2 β + n + 1) R_{n - 1}^{(α, β)} ((), x)

v_{i}^{1}

v_{k}^{3}

, is the activation function, which is selected as a linear function.…”

Section: Design Ofadaptive Nonlinear Backstepping Control Systemmentioning

confidence: 99%

“…The functional‐type neural network, which has faster convergence and lesser computational complexity, has been proposed to bring down computational cost. On the other hand, Romanovski polynomials have been applied to solve the general solutions of noncentral potential system, to approximate the exact solutions of several physics problems ranging from quantum mechanics and quark physics to random matrix theory. Raposo et al proposed the Romanovski polynomials to apply in exact solutions of several physics problems.…”

Section: Introductionmentioning

confidence: 99%

“…Weber et al proposed the Romanovski polynomials to solve the one‐dimensional Schrödinger equation with the trigonometric Rosen‐Morse. Suparmi et al proposed the Romanovski polynomials to apply in the analytical solution of Schrodinger equation for Eckart potential plus with trigonometric Poschl‐Teller noncentral potential system. However, the Romanovski polynomials could approximate and solve the exact solutions of several physics problems.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Switched reluctance motor circuit drive system using adaptive nonlinear backstepping control with mended recurrent Romanovski polynomials neural network and mended particle swarm optimization

Int J Numerical Modelling

Chang

2019

A switched reluctance motor (SRM) circuit drive system caused many nonlinear effects due to convex construction. The linear control methods were hard to achieve good performance for the SRM circuit drive. The adaptive nonlinear backstepping control system using switching function is proposed for controlling the SRM drive system to obtain good performance. To reduce chattering of control effort, the adaptive nonlinear backstepping control system using adaptive law is proposed to estimate the required lumped uncertainty. When the inertia of the counterweight is varying, this proposed method cannot get a satisfactory performance. The adaptive nonlinear backstepping control system using mended recurrent Romanovski polynomials neural network with adaptive law and error-estimated law is proposed for controlling the SRM drive system to raise robustness of the SRM drive system. Furthermore, two variable learning rates in the mended recurrent Romanovski polynomials neural network are adopted by using mended particle swarm optimization (PSO) algorithm to speed up parameter's convergence. Finally, comparative performances through some experimental results are verified that the proposed control system has better control performances than those of the proposed methods for the SRM drive system. KEYWORDS adaptive backstepping control, particle swarm optimization, recurrent Romanovski polynomials neural network, switched reluctance motor

Retracted: SCRIM drive system using adaptive backstepping control and mended recurrent Romanovski polynomials neural network with reformed particle swarm optimization

Adaptive Control & Signal

Chang

2019

Summary Due to air‐gap field harmonic, cogging torque, stator's current time harmonic, and the influence of flux saturation, a six‐phase copper rotor induction motor (SCRIM) drive system has highly nonlinear uncertainties. Thus, the linear control method for the SCRIM drive system is difficult to achieved good performance under the nonlinear uncertainty action. To obtain better control performance, the adaptive backstepping control system using switching function is firstly proposed for controlling the SCRIM drive system to overcome the uncertainty influence. With the proposed control system, the SCRIM drive system holds in robustness to these uncertainties for the tracking of periodic reference trajectories. To enhance the robustness of the SCRIM drive system, the adaptive backstepping control system using adaptive law is proposed for estimating the required lumped uncertainty to reduce chattering phenomenon. When the inertia of the counterweight is varying, this proposed method can perform well in general situations but cannot get a satisfactory performance. The adaptive backstepping control system using mended recurrent Romanovski polynomials neural network with reformed particle swarm optimization (PSO) is thus proposed to estimate the lumped uncertainty and to compensate estimated error for obtaining better control performance. Furthermore, two variable learning rates of the weights in the mended recurrent Romanovski polynomials neural network are adopted by using reformed PSO to speed up parameter's convergence. Finally, some experimental results with comparative control performances are demonstrated, and then, the effectiveness of proposed control system with better control performance is verified for the position tracking of periodic reference inputs.