Adaptive Backstepping Control for Fractional-Order Nonlinear Systems with External Disturbance and Uncertain Parameters Using Smooth Control

In this paper, we consider controlling a class of single-input-single-output (SISO) commensurate fractional-order nonlinear systems with parametric uncertainty and external disturbance. Based on backstepping approach, an adaptive controller is proposed with adaptive laws that are used to estimate the unknown system parameters and the bound of unknown disturbance. Instead of using discontinuous functions such as the $\mathrm{sign}$ function, an auxiliary function is employed to obtain a smooth control input that is still able to achieve perfect tracking in the presence of bounded disturbances. Indeed, global boundedness of all closed-loop signals and asymptotic perfect tracking of fractional-order system output to a given reference trajectory are proved by using fractional directed Lyapunov method. To verify the effectiveness of the proposed control method, simulation examples are presented.Comment: Accepted by the IEEE Transactions on Systems, Man and Cybernetics: Systems with Minor Revision

Fast Adaptive Robust Differentiator Based Robust-Adaptive Control of Grid-Tied Inverters with a New L Filter Design Method

In this research, a new nonlinear and adaptive state feedback controller with a fast-adaptive robust differentiator is presented for grid-tied inverters. All parameters and external disturbances are taken as uncertain in the design of the proposed controller without the disadvantages of singularity and over-parameterization. A robust differentiator based on the second order sliding mode is also developed with a fast-adaptive structure to be able to consider the time derivative of the virtual control input. Unlike the conventional backstepping, the proposed differentiator overcomes the problem of explosion of complexity. In the closed-loop control system, the three phase source currents and direct current (DC) bus voltage are assumed to be available for feedback. Using the Lyapunov stability theory, it is proven that the overall control system has the global asymptotic stability. In addition, a new simple L filter design method based on the total harmonic distortion approach is also proposed. Simulations and experimental results show that the proposed controller assurances drive the tracking errors to zero with better performance, and it is robust against all uncertainties. Moreover, the proposed L filter design method matches the total harmonic distortion (THD) aim in the design with the experimental result

A Comparative Study Between Convolution and Optimal Backstepping Controller for Single Arm Pneumatic Artificial Muscles

This study was based on the dynamic modeling and parameter characterization of the one-link robot arm driven by pneumatic artificial muscles. This work discusses an up-to-date control design based on the notion of a conventional and optimal backstepping controller for regulating a one-link robot arm with conflicting biceps and triceps positions supplied by pneumatic artificial muscles. The main problems found in systems that utilize pneumatic artificial muscle as actuators are primarily the large uncertainties, non-linearities, and time-varying features that severely impede movement performance in tracking control. In consideration of the uncertainty, high nonlinearity, and external disturbances that can exist during the motion. Lyapunov-based backstepping control technique was utilized to assure the stability of the system with improved dynamic performance. The bat algorithm optimization method is utilized in order to modify the variables used in the design of the controller to enhance the efficiency of the suggested controller. According to the conclusions, a quantitative comparison of the response in the PAM actuated the arm model in the current study and earlier investigations with the Backstepping controlled system revealed fair agreement with a variation of 37.5% from the optimal classical synergetic controller. In addition, computer simulations were utilized in order to compare the effectiveness of the proposed conventional controls and the optimal background. It has been proven that an optimal controller can control the uncertainties and maintain the controlled system’s stability

Generalized Adaptive Backstepping Synchronization for Non-Identical Parametrically Excited Systems

In this paper, we investigate the synchronization of chaotic systems consisting of non-identical parametrically excited oscillators. The backstepping design, which is a recursive procedure that combines the choice of a Lyapunov function with the design of a controller is generalized and employed so as to achieve global chaos synchronization between a parametrically excited gyroscope and each of the parametrically excited pendulum and Duffing oscillator. Numerical simulations are implemented to verify the results

Nonlinear Dynamic Surface Control of Chaos in Permanent Magnet Synchronous Motor Based on the Minimum Weights of RBF Neural Network

This paper is concerned with the problem of the nonlinear dynamic surface control (DSC) of chaos based on the minimum weights of RBF neural network for the permanent magnet synchronous motor system (PMSM) wherein the unknown parameters, disturbances, and chaos are presented. RBF neural network is used to approximate the nonlinearities and an adaptive law is employed to estimate unknown parameters. Then, a simple and effective controller is designed by introducing dynamic surface control technique on the basis of first-order filters. Asymptotically tracking stability in the sense of uniformly ultimate boundedness is achieved in a short time. Finally, the performance of the proposed controller is testified through simulation results

Control and synchronization of the generalized Lorenz system with mismatched uncertainties using backstepping technique and time‐delay estimation

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/140007/1/cta2353.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/140007/2/cta2353_am.pd