Backstepping Control System Research Articles

CMAC-based adaptive backstepping synchronization of uncertain chaotic systems

This study proposes an adaptive backstepping control system for synchronizing uncertain chaotic system by using cerebellar model articulation controller (CMAC). CMAC is a nonlinear network with simple computation, good generalization capability and fast learning property. The proposed CMAC-based adaptive backstepping control (CABC) system uses backstepping method and adaptive cerebellar model articulation controller (ACMAC) for synchronizing uncertain chaotic system. Finally, simulation results for the Genesio system are presented to illustrate the effectiveness of the proposed control system.

Robust Levitation Control for Linear Maglev Rail System Using Fuzzy Neural Network

The levitation control in a linear magnetic-levitation (Maglev) rail system is a subject of considerable scientific interest because of highly nonlinear and unstable behaviors. This study mainly designs a robust fuzzy-neural-network control (RFNNC) scheme for the levitated positioning of the linear Maglev rail system with nonnegative inputs. In the model-free RFNNC system, an online learning ability is designed to cope with the problem of chattering phenomena caused by the sign action in backstepping control (BSC) design and to ensure the stability of the controlled system without the requirement of auxiliary compensated controllers despite the existence of uncertainties. Moreover, the nonnegative outputs of the RFNNC system can be directly supplied to electromagnets in the Maglev system without complicated control transformations for relaxing strict constrains in conventional model-based control methodologies. The effectiveness of the proposed control schemes for the levitation control of a Maglev system is verified by numerical simulations and experimental results, and the superiority of the RFNNC system is indicated in comparison with the BSC system.

FPGA-based adaptive backstepping control system using RBFN for linear induction motor drive

A field-programmable gate array (FPGA)-based adaptive backstepping control system with radial basis function network (RBFN) observer is proposed to control the mover position of a linear induction motor (LIM). First, the indirect field-oriented mechanism is adopted for controlling the LIM. Next, a backstepping control law is designed step by step for the tracking control of periodic reference trajectories, in which the uncertainties are lumped by a conservative constant. However, the lumped uncertainty is unknown and difficult to obtain in advance in practical applications. Therefore an RBFN is derived to observe the lumped uncertainty in real-time, and an adaptive backstepping control system with RBFN observer is resulted. Then, an FPGA chip is adopted to implement the indirect field-oriented mechanism and the developed control algorithms for possible low-cost, high-performance industrial applications. The effectiveness of the proposed control scheme is verified by some simulated and experimental results. By using the adaptive backstepping control system with RBFN observer, the FPGA-based LIM drive possesses the advantages of good transient control performance and robustness to uncertainties in the tracking of periodic reference trajectories.

Robust Adaptive Backstepping Motion Control of Linear Ultrasonic Motors Using Fuzzy Neural Network

A robust adaptive fuzzy neural network (RAFNN) backstepping control system is proposed to control the position of an X-Y-Theta motion control stage using linear ultrasonic motors (LUSMs) to track various contours in this study. First, an X-Y-Theta motion control stage is introduced. Then, the single-axis dynamics of LUSM mechanism with the introduction of a lumped uncertainty, which includes cross-coupled interference and friction force, is derived. Moreover, a conventional backstepping approach is proposed to compensate the uncertainties occurred in the motion control system. Furthermore, to improve the control performance in the tracking of the reference contours, an RAFNN backstepping control system is proposed to remove the chattering phenomena caused by the sign function in the backstepping control law. In the proposed RAFNN backstepping control system, a Sugeno-type adaptive fuzzy neural network (SAFNN) is employed to estimate the lumped uncertainty directly and a compensator is utilized to confront the reconstructed error of the SAFNN. In addition, the motions at the X axis, Y axis, and Theta axis are controlled separately. The experimental results show that the contour tracking performance is significantly improved and the robustness to parameter variations, external disturbances, cross-coupled interference, and friction force can be obtained, as well using the proposed RAFNN backstepping control system.

チューニング関数を用いる適応バックステッピング制御系にパラメータ射影アルゴリズムを併用する一構成法

Various methods for improving the robustness of adaptive backstepping control systems have been proposed. One of such methods uses an adaptive law with the parameter projection algorithm which realizes a projection action by changing the integral kernel of the adaptive law to another function. It is known that a stable adaptive backstepping control system is achieved based on the overparameterization scheme or high gain non-linear damping scheme when the change type projection algorithm is used for parameter projection. However, in the former scheme, the adaptive controller may be complex for a high order and high relative degree plant. A peculiar problem to high gain feedback such as actuator saturation and difficulty of numeric realization may be caused in the latter scheme. This paper shows that the change type projection algorithm cannot be applied to the tuning functions scheme. On the basis of the fact, this paper proposes a new design method for tuning functions scheme with non-change type projection algorithm. Also, it is shown that the proposed method can solve the problems of the conventional method.

Development of Lyapunov-Based Genetic Algorithm Control for Linear Piezoelectric Ceramic Motor Drive

In general, the role of genetic algorithm (GA) is operated offline as a minor compensator or tuner in the control engineering because the systematic design and the latent stability problem of a GA-based control scheme are required to be solved. This paper originally designs a Lyapunov-based GA control (LGAC) scheme, and it applies for a practical control engineering example of the online motion control of a linear piezoelectric ceramic motor driven by a hybrid resonant inverter. In this control scheme, a GA control system via backstepping design technique is utilized to be the major controller, and adaptation laws derived from Lyapunov stability analyses are manipulated to adjust appropriate evolutionary steps. As a result, the system stability can be guaranteed directly without strict constraint conditions and detailed system knowledge. The effectiveness of the proposed drive and control system is verified by experimental results in the presence of uncertainties. From the measured results, the LGAC system performs superior high-precision motion control under wide operation range than conventional backstepping control system.

Intelligent Adaptive Backstepping Control System for Magnetic Levitation Apparatus

We propose an intelligent adaptive backstepping control system using a recurrent neural network (RNN) to control the mover position of a magnetic levitation apparatus to compensate for uncertainties, including friction force. First, we derive a dynamic model of the magnetic levitation apparatus. Then, we suggest an adaptive backstepping approach to compensate disturbances, including the friction force, occurring in the motion control system. To further increase the robustness of the magnetic levitation apparatus, we propose an RNN estimator for the required lumped uncertainty in the adaptive backstepping control system. We further propose an online parameter training methodology, derived by the gradient descent method, to increase the learning capability of the RNN. The effectiveness of the proposed control scheme has been verified by experiment. With the proposed adaptive backstepping control system using RNN, the mover position of the magnetic levitation apparatus possesses the advantages of good transient control performance and robustness to uncertainties for the tracking of periodic trajectories

Wavelet Adaptive Backstepping Control for a Class of Nonlinear Systems

This paper proposes a wavelet adaptive backstepping control (WABC) system for a class of second-order nonlinear systems. The WABC comprises a neural backstepping controller and a robust controller. The neural backstepping controller containing a wavelet neural network (WNN) identifier is the principal controller, and the robust controller is designed to achieve L2 tracking performance with desired attenuation level. Since the WNN uses wavelet functions, its learning capability is superior to the conventional neural network for system identification. Moreover, the adaptation laws of the control system are derived in the sense of Lyapunov function and Barbalat's lemma, thus the system can be guaranteed to be asymptotically stable. The proposed WABC is applied to two nonlinear systems, a chaotic system and a wing-rock motion system to illustrate its effectiveness. Simulation results verify that the proposed WABC can achieve favorable tracking performance by incorporating of WNN identification, adaptive backstepping control, and L2 robust control techniques.

Intelligent backstepping sliding-mode control using RBFN for two-axis motion control system

An intelligent backstepping sliding-mode control system using radial basis function network (RBFN) for a two-axis motion control system using permanent magnet linear synchronous motors (PMLSMs) is proposed. First, single-axis motion dynamics with the introduction of a lumped uncertainty, including cross-coupled interference between the two-axis mechanism, is derived. Then, to improve the control performance in reference contour tracking, a backstepping sliding-mode approach is proposed to compensate for uncertainties occurring in the motion control system. The bound of the lumped uncertainty is necessary in the design of the backstepping sliding-mode control system and is difficult to obtain in advance in practical applications. Therefore, an RBFN uncertainty observer is proposed to estimate the required lumped uncertainty in the backstepping sliding-mode control system. An adaptive learning algorithm, which can learn the parameters of the RBFN online, is derived using Lyapunov stability theorem. The proposed control algorithms are implemented in a TMS320C32 DSP-based control computer, and the motions in the x-axis and y-axis are controlled separately. The simulated and experimental results of circle and four leaves reference contours show that the motion tracking performance is significantly improved and the robustness to parameter variations, external disturbances, cross-coupled interference and frictional forces can also be obtained using the proposed controller.

Adaptive backstepping control using recurrent neural network for linear induction motor drive

An adaptive backstepping control system using a recurrent neural network (RNN) is proposed to control the mover position of a linear induction motor (LIM) drive to compensate the uncertainties including the friction force in this paper. First, the dynamic model of an indirect field-oriented LIM drive is derived. Then, a backstepping approach is proposed to compensate the uncertainties including the friction force occurred in the motion control system. With the proposed backstepping control system, the mover position of the LIM drive possesses the advantages of good transient control performance and robustness to uncertainties for the tracking of periodic reference trajectories. Moreover, to further increase the robustness of the LIM drive, an RNN uncertainty observer is proposed to estimate the required lumped uncertainty in the backstepping control system. In addition, an online parameter training methodology, which is derived using the gradient-descent method, is proposed to increase the learning capability of the RNN. The effectiveness of the proposed control scheme is verified by both the simulated and experimental results.

Intelligent backstepping control for linear induction motor drive

The design and properties of an intelligent backstepping control system for a linear induction motor (LIM) drive to track periodic reference trajectories are studied. First, the dynamic model of a field-oriented control LIM drive is derived. Then a feedback linearisation controller is designed in the sense of the backstepping control technique. To relax the requirement for the bound of lumped uncertainty in the feedback linearisation control law, a recurrent fuzzy neural network (RFNN) uncertainty observer is proposed to estimate the lumped uncertainty in real time. In addition, an online parameter training methodology, derived using the Lyapunov stability theorem and the gradient descent method, is proposed to increase the learning capability of the RFNN. With the proposed intelligent backstepping control system, the mover position of the LIM drive possesses the advantages of good transient control performance and robustness to uncertainties for the tracking of periodic reference trajectories. The effectiveness of the proposed control scheme is verified by both simulated and experimental results.