Adaptive fuzzy control with smooth inverse for nonlinear systems preceded by non-symmetric dead-zone

In this study, the adaptive output feedback control problem of a class of nonlinear systems preceded by non-symmetric dead-zone is considered. To cope with the possible control signal chattering phenomenon which is caused by non-smooth dead-zone inverse, a new smooth inverse is proposed for non-symmetric dead-zone compensation. For the systematic design procedure of the adaptive fuzzy control algorithm, we combine the backstepping technique and small-gain approach. The Takagi–Sugeno fuzzy logic systems are used to approximate unknown system nonlinearities. The closed-loop stability is studied by using small gain theorem and the closed-loop system is proved to be semi-globally uniformly ultimately bounded. Simulation results indicate that, compared to the algorithm with the non-smooth inverse, the proposed control strategy can achieve better tracking performance and the chattering phenomenon can be avoided effectively.     

Adaptive tracking of nonlinear systems with non-symmetric dead-zone input

Quite successfully adaptive control strategies have been applied to uncertain dynamical systems subject to dead-zone nonlinearities. However, adaptive tracking of systems with non-symmetric dead-zone characteristics has not been fully discussed with minimal knowledge of the dead-zone parameters. It is shown that the controlled system preceded by a non-symmetric dead-zone input can be represented as an uncertain nonlinear system subject to a linear input with time-varying input coefficient. To cope with this problem, a new adaptive compensation algorithm is employed without constructing the dead-zone inverse. The proposed adaptive scheme requires only the information of bounds of the dead-zone slopes and treats the time-varying input coefficient as a system uncertainty. The new control scheme ensures bounded-error trajectory tracking and assures the boundedness of all the signals in the adaptive closed loop. By appropriate selections of the controller parameters, we show that the smoothness of the controller does not affect the accuracy of trajectory tracking control. A numerical example is included to show the effectiveness of the theoretical results.     

Decentralized adaptive control for large-scale time-delay systems with dead-zone input

In this paper, a decentralized adaptive control scheme is proposed to address output tracking of a class of interconnected time-delay subsystems with the input of each loop preceded by an unknown dead-zone. Each local controller is designed using the backstepping technique and consists of a new robust control law and new updating laws. Unknown time-varying delays are compensated by using appropriate Lyapunov-Krasovskii functionals. Furthermore, by introducing a new smooth dead-zone inverse, the proposed backstepping design is able to eliminate the effects resulting from dead-zone nonlinearities in the input. It is shown that the proposed controller can guarantee not only stability, but also good transient performance.     

An adaptive dead-zone inverse controller for systems with sandwiched dead-zones

This paper addresses adaptive control of sandwich non-linear systems having an unknown sandwiched dead-zone between the linear dynamic blocks, as illustrated by a hydraulic valve system. An adaptive hybrid control scheme for control of such sandwiched dead-zone systems is developed. The proposed control scheme employs an inner-loop discrete-time feedback design and an outer-loop continuous-time feedback design, combined with an adaptive dead-zone inverse to cancel the dead-zone effect for improving output tracking. Stability and tracking performance of the closed-loop control system are analysed. Simulation results are used to illustrate the effectiveness of the proposed adaptive dead-zone inverse controller.     

基于模糊扰动观测器的PMSM积分滑模控制研究

为了克服传统永磁同步电机(Permanent magnet synchronous motor,PMSM)的滑模控制增益大容易产生抖振的问题,提出基于模糊观测器的PMSM积分滑模控制策略。采用新型趋近律设计积分滑模控制器取代传统的滑模控制器,提高系统的动态响应性能。结合模糊控制与自适应控制的特点,设计模糊扰动观测器,能够迅速有效地观测系统内部参数变化和外部扰动,并对积分滑模速度控制器进行前馈补偿,削弱系统抖振的同时提高了系统的鲁棒性。通过李雅普诺夫理论证明了该控制系统的稳定性。仿真及实验结果验证了该方法具有较强的鲁棒性,可以实现良好的跟踪效果并且无抖动。     

Adaptive output control of uncertain nonlinear systems with non-symmetric dead-zone input

This paper deals with the adaptive output feedback control problem of a class of uncertain nonlinear systems with an unknown non-symmetric dead-zone nonlinearity. The nonlinear system considered here is dominated by a triangular system without zero dynamics satisfying polynomial growth in the unmeasurable states. An adaptive control scheme is developed without constructing the dead-zone inverse. The proposed adaptive control scheme requires only the information of bounds of the slopes and the breakpoint of dead-zone nonlinearity. The novelty of this paper is that a universal-type adaptive output feedback controller is numerically constructed by using a sum of squares (SOS) optimization algorithm, which ensures the boundedness of all the signals in the adaptive closed-loop without knowing the growth rate of the uncertainties. An example is presented to show the effectiveness of the proposed approach.     

Sigma adaptive fuzzy sliding mode control of a class of nonlinear systems

Based on fuzzy approximators of nonlinear functions, a new adaptive fuzzy sliding mode control scheme is proposed for a class of nonlinear plants. In comparison with most existing methods, in which the parameter projection algorithm is often involved to prevent the estimated value of the input gain function from evolving into zero, the proposed control law has shown its success and simplicity in tackling the case when the value of the estimated input gain function becomes zero during online operations. A variant of adaptive law with dead-zone sigma-modification is introduced to help achieve this goal. The bounding parameters of the model approximation error and the external disturbance are all regarded as unknown constants in this paper, and adaptive laws for them are devised for tracking purposes. Based on Lyapunov's stability theory the proposed controller has been shown to render the tracking error arbitrarily close to zero. A comparably good tracking performance is obtained as illustrated by the simulation results for an inverted pendulum system.     

RCMAC-based adaptive control design for brushless DC motors

This paper proposes a recurrent cerebellar model articulation controller (RCMAC)-based adaptive control for brushless DC motors. This control system is composed of a RCMAC and a compensation controller. RCMAC is used to mimic an ideal controller, and the compensation controller is designed to compensate for the approximation error between the ideal controller and RCMAC. The Lyapunov stability theory is utilized to derive the parameter tuning algorithm, so that the uniformly ultimately bound stability of the closed-loop system can be achieved. For comparison, a fuzzy control, an adaptive fuzzy control and the developed RCMAC-based adaptive control are implemented on a field programmable gate array chip for controlling a brushless DC motor. Experimental results reveal that the proposed RCMAC-based adaptive control system can achieve the best tracking performance. Moreover, since the developed RCMAC-based adaptive control scheme uses a hyperbolic tangent function to compensate for the approximation error, there is no chattering phenomenon in the control effort. Thus, the proposed control method is more suitable for real-time practical control applications.     

Design of a fuzzy adaptive controller for MIMO nonlinear time-delay systems with unknown actuator nonlinearities and unknown control direction

This paper aims at investigating the fuzzy adaptive control design for uncertain multivariable systems with unknown actuator nonlinearities and unknown control direction that possibly exhibit time-delay. The actuator nonlinearities involve dead-zone or backlash-like hysteresis, while the control direction is closely related to the sign of the control gain matrix. Two fuzzy adaptive controllers are proposed to deal with such an issue. The design of the first controller is mainly carried out in the free time-delay case, while the second control design is performed assuming that the system exhibits time-varying delays. Of practical interest, the adaptive compensation of the effects of the actuator nonlinearities requires neither the knowledge of their parameters nor the construction of their inverse. Furthermore, the lack of knowledge of the control direction is handled by incorporating in the control law a Nussbaum-type function. The effectiveness of the proposed fuzzy adaptive controllers is illustrated through simulation results.     

Adaptive neural dynamic surface control for servo systems with unknown dead-zone

An adaptive neural controller is proposed for nonlinear systems with a nonlinear dead-zone and multiple time-delays. The often used inverse model compensation approach is avoided by representing the dead-zone as a time-varying system. The “explosion of complexity” in the backstepping synthesis is eliminated in terms of the dynamic surface control (DSC) technique. A novel high-order neural network (HONN) with only a scalar weight parameter is developed to account for unknown nonlinearities. The control singularity and some restrictive requirements on the system are circumvented. Simulations and experiments for a turntable servo system with permanent-magnet synchronous motor (PMSM) are provided to verify the reliability and effectiveness.     

具有未知非线性死区的自适应模糊控制

基于滑模控制原理，利用模糊系统的逼近能力，提出一种自适应模糊控制方法．该方法提出一种简化非线性死区输入模型，取消了非线性死区输入模型的倾斜度相等以及死区边界对称的条件，还取消了非线性死区输入模型各种参数已知的条件．该方法通过引入逼近误差的自适应补偿项来消除建模误差和参数估计误差的影响．理论分析证明了闭环系统是半全局一致终结有界，跟踪误差收敛到零．仿真结果表明了该方案的有效性．     

Adaptive fuzzy control for pure-feedback stochastic nonlinear systems with unknown dead-zone input

This paper is concerned with the problem of adaptive fuzzy output tracking control for a class of nonlinear pure-feedback stochastic systems with unknown dead-zone. Fuzzy logic systems in Mamdani type are used to approximate the unknown nonlinearities, then a novel adaptive fuzzy tracking controller is designed by using backstepping technique. The control scheme is systematically derived without requiring any information on the boundedness of dead-zone parameters (slopes and break-points) and the repeated differentiation of the virtual control signals. The proposed adaptive fuzzy controller guarantees that all the signals in the closed-loop system are bounded in probability and the system output eventually converges to a small neighbourhood of the desired reference signal in the sense of mean quartic value. Simulation results further illustrate the effectiveness of the proposed control scheme.     

Decentralized adaptive stabilization of interconnected nonlinear systems with unknown non-symmetric dead-zone inputs

The decentralized adaptive stabilization method is proposed for uncertain interconnected nonlinear systems with unknown non-symmetric dead-zone inputs. The class of systems considered in this paper consists of strict-feedback nonlinear subsystems with unknown non-symmetric dead-zone inputs which interact through their outputs. The unknown nonlinear interaction terms are assumed to be bounded by nonlinear functions with unknown parameters. For the simple controller design, the local controller for each subsystem is systematically derived based on the dynamic surface design technique, without constructing the dead-zone inverse and requiring the bound information of dead-zone parameters (slopes and break-points). All unknown parameters of interconnected nonlinear systems are compensated by the adaptive technique. From Lyapunov stability theorem, it is proved that all signals in the interconnected closed-loop system with decentralized adaptive controllers are semi-globally bounded. Simulation results for tripled inverted pendulums demonstrate the effectiveness of the proposed approach.     

Adaptive cascade control of a hydraulic actuator with an adaptive dead-zone compensation and optimization based on evolutionary algorithms

This work presents an adaptive cascade controller tuned by using evolutionary algorithms for the trajectory tracking control of a hydraulic actuator with an overlapped proportional valve. The hydraulic actuator mathematical model includes the dead-zone nonlinearity due to the use of the overlapped valve. By considering the hydraulic actuator as a mechanical subsystem driven by a hydraulic one, a cascade strategy is proposed. Such cascade strategy is based on the order reduction and allows one to propose different control laws for each subsystem. Adaptive algorithms are used to compensate the parametric uncertainties in the hydraulic and mechanical subsystems including an adaptive compensation for the valve dead-zone. In the sequence, evolutionary algorithms are used to tune the proposed controller for performance optimization. Simulation results illustrate the main characteristics of the proposed controller and the performance of the evolutionary algorithm called differential evolution in tuning of proposed controller.     

Adaptive output control of nonlinear systems with uncertain dead-zone nonlinearity

In this note, we present a new scheme to design adaptive controllers for uncertain systems preceded by unknown dead-zone nonlinearity. The control design is achieved by introducing a smooth inverse function of the dead-zone and using it in the controller design with backstepping technique. For the design and implementation of the controller, no knowledge is assumed on the unknown system parameters. It is shown that the proposed controller not only can guarantee stability, but also transient performance.     

永磁球形电机的少保守性滑模控制

永磁球形电机轨迹跟踪控制方法常常利用高增益的控制输出来保证系统的鲁棒性及跟踪控制的快速性.但这种保守控制会带来较大的控制作用,甚至导致执行器饱和.为了减少控制的保守性,本文设计了一种带有非线性干扰观测器的模糊滑模控制器来解决球形电机的轨迹跟踪问题.利用干扰观测器对不确定性、摩擦、外界干扰、负载扰动等进行估计,并在控制输入端进行补偿实现对干扰的抑制.并利用滑模控制器抵消干扰观测器的干扰观测误差及不可观测部分的干扰,为了减少滑模的抖振,本文利用模糊逻辑对该部分进行逼近,并利用模糊的输出增益代替滑模的切换增益.此外通过Lyapunov方程证明了本文控制器的稳定性.仿真结果表明在存在模型不确定性及各种干扰的情况下,本文的轨迹跟踪控制具有良好的动静态性能和少保守性.     

Adaptive actuator compensation control with feedback linearization

An adaptive inverse controller is developed for feedback linearizable nonlinear systems with nonsmooth actuator nonlinearities. The use of an actuator nonlinearity inverse and a feedback linearizing controller leads to an error equation suitable for deriving an adaptive update law for the inverse parameters. Closed-loop signal boundedness is proved analytically, and system performance improvement is shown by simulation results. Such adaptive control schemes are also developed for multivariable nonlinear systems with actuator nonlinearities. For nonlinear systems that do not possess a relative degree, dynamic extension is employed to realize adaptive inverse compensation designs for actuator nonlinearities. These adaptive designs ensure closed-loop stability in the presence of uncertain actuator nonlinearities     

Adaptive Inverse Control of Excitation System with Actuator Uncertainty

In this paper, we present a new approach of designing adaptive inverse controller for synchronous generator excitation system containing nonsmooth nonlinearities in actuator device. The proposed controller considers not only the dynamics of generator but also nonlinearities in actuator. To address such a challenge, support vector machines (SVM) is adopted to identify the plant and to construct the inverse controller. SVM networks, used to compensate nonlinearities in synchronous generator as well as in actuator, are adjusted online by an adaptive law via back propagation (BP) algorithm. To guarantee convergence and for fast learning, adaptive learning rate and convergence theorem are developed. Simulation results are given, showing satisfactory control performance and illustrate the potential of the proposed adaptive inverse controller as useful for practical purpose.     

永磁同步电机调速系统的多维泰勒网逆控制

针对永磁同步电机(PMSM)的高性能控制问题,在充分考虑时变特性、不确定性以及测量噪声等随机因素的基础上,通过PMSM的逆系统将被控对象补偿成为具有线性传递关系的系统,提出一种基于改进自适应逆控制的控制方案.采用矢量控制的双闭环控制结构,将多维泰勒网逆控制方法引入速度环.首先,对PMSM数学模型的可逆性进行证明以解决非线性系统逆建模的存在性问题;然后,建立新颖的动态网络化控制器-----多维泰勒网(MTN),其具有结构简单、计算复杂度低的优点;最后,为了实现高精度的速度控制,将3个MTN分别作为实现系统建模的自适应模型辨识器、逆建模的自适应逆控制器和噪声干扰消除的非线性自适应滤波器,并将PMSM的动态响应控制和消除干扰的控制分为相对独立的过程进行,同时实现最优控制.仿真结果表明,所提出控制方案能够实现PMSM伺服系统精确的速度控制,具有良好的跟踪性能和较强的抗干扰能力.     

Adaptive sliding inverse control of a class of non-linear systems preceded by unknown non-symmetrical dead-zone

This paper deals with the adaptive control of a class of continuous-time non-linear dynamic systems preceded by unknown non-symmetrical, non-equal slope dead-zones. By exploring the properties of the dead-zone model intuitively and mathematically, a dead-zone inverse is constructed. Based on this inverse construction, an adaptive sliding controller is designed. Lyapunov stability analysis shows that the proposed adaptive control law ensures global stability of the adaptive system and achieves desired tracking precision. Simulation results attained for an uncertain non-linear system are presented to illustrate and further validate the effectiveness of the proposed approach.