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

Artificial Tune of Fuel Ratio: Design a Novel SISO Fuzzy Backstepping Adaptive Variable Structure Control

This paper examines single input single output (SISO) chattering free variable structure control (VSC) which controller coefficient is on-line tuned by fuzzy backstepping algorithm. VSC methodology is selected as a framework to construct the control law and address the stability and robustness of the close loop system based on Lyapunove formulation. The main goal is to guarantee acceptable fuel ratio result and adjust. The proposed approach effectively combines the design technique from variable structure controller is based on Lyapunov and fuzzy estimator to estimate the nonlinearity of undefined system dynamic in backstepping controller. The input represents the function between variable structure function, error and the rate of error. The outputs represent fuel ratio, respectively. The fuzzy backstepping methodology is on-line tune the variable structure function based on adaptive methodology. The performance of the SISO VSC which controller coefficient is on-line tuned by fuzzy backstepping algorithm (FBSAVSC) is validated through comparison with VSC and proposed method. Simulation results signify good performance of trajectory in presence of uncertainty torque load. DOI:http://dx.doi.org/10.11591/ijece.v3i2.209

Rotor field orientation speed and torque control of BDFM with adaptive second order sliding mode

This paper presents two cascaded second order sliding mode controllers (SOSMCs) for brushless doubly fed motor (BDFM) adjustable speed system, which regulate the speed and torque. And an adaptive super twisting algorithm is incorporated into the SOSMCs to adaptively regulate the law of SOSMC. The proposed controllers for BDFM eliminate the average chattering encountered by most sliding mode control (SMC) schemes, and also possess the robustness and excellent static and dynamic performances of SMC. Simulation results show that the proposed control strategy is feasible, proper and effective. © 2013 IEEE

Fuzzy sliding mode control of a multi-DOF parallel robot in rehabilitation environment

Multi-degrees of freedom (DOF) parallel robot, due to its compact structure and high operation accuracy, is a promising candidate for medical rehabilitation devices. However, its controllability relating to the nonlinear characteristics challenges its interaction with human subjects during the rehabilitation process. In this paper, we investigated the control of a parallel robot system using fuzzy sliding mode control (FSMC) for constructing a simple controller in practical rehabilitation, where a fuzzy logic system was used as the additional compensator to the sliding mode controller (SMC) for performance enhancement and chattering elimination. The system stability is guaranteed by the Lyapunov stability theorem. Experiments were conducted on a lower limb rehabilitation robot, which was built based on kinematics and dynamics analysis of the 6-DOF Stewart platform. The experimental results showed that the position tracking precision of the proposed FSMC is sufficient in practical applications, while the velocity chattering had been effectively reduced in comparison with the conventional FSMC with parameters tuned by fuzzy systems

Unknown dynamics estimator-based output-feedback control for nonlinear pure-feedback systems

Most existing adaptive control designs for nonlinear pure-feedback systems have been derived based on backstepping or dynamic surface control (DSC) methods, requiring full system states to be measurable. The neural networks (NNs) or fuzzy logic systems (FLSs) used to accommodate uncertainties also impose demanding computational cost and sluggish convergence. To address these issues, this paper proposes a new output-feedback control for uncertain pure-feedback systems without using backstepping and function approximator. A coordinate transform is first used to represent the pure-feedback system in a canonical form to evade using the backstepping or DSC scheme. Then the Levant's differentiator is used to reconstruct the unknown states of the derived canonical system. Finally, a new unknown system dynamics estimator with only one tuning parameter is developed to compensate for the lumped unknown dynamics in the feedback control. This leads to an alternative, simple approximation-free control method for pure-feedback systems, where only the system output needs to be measured. The stability of the closed-loop control system, including the unknown dynamics estimator and the feedback control is proved. Comparative simulations and experiments based on a PMSM test-rig are carried out to test and validate the effectiveness of the proposed method