Adaptive fuzzy robust control of PMSM with smooth inverse based dead-zone compensation

It is a challenging work to design high precision/high performance motion controller for permanent magnet synchronous motor (PMSM) due to some difficulties, such as varying operating conditions, parametric uncertainties and external disturbances. In order to improve tracking control performance of PMSM, this paper proposes an adaptive fuzzy robust control (AFRC) algorithm with smooth inverse based dead-zone compensation. Instead of nonsmooth dead-zone inverse which would cause the possible control signal chattering phenomenon, a new smooth dead-zone inverse is proposed for non-symmetric dead-zone compensation in PMSM system. AFRC controller is synthesized by combining backstepping technique and small gain theorem. Discontinuous projectionbased parameter adaptive law is used to estimate unknown system parameters. The Takagi-Sugeno fuzzy logic systems are employed to approximate the unstructured dynamics. Robust control law ensures the robustness of closed loop control system. The proposed AFRC algorithm with smooth inverse based dead-zone compensation is verified on a practical PMSM control system. The comparative experimental results indicate that the smooth inverse for non-symmetric dead-zone nonlinearity can effectively avoid the chattering phenomenon which would be caused by nonsmooth dead-zone inverse, and the proposed control strategy can improve the PMSM output tracking performance.     

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.     

Adaptive variable structure control of MIMO nonlinear systems with time-varying delays and unknown dead-zones

In this paper, adaptive variable structure neural control is presented for a class of uncertain multi-input multi-output （MIMO） nonlinear systems with state time-varying delays and unknown nonlinear dead-zones. The unknown time-varying delay uncer- tainties are compensated for using appropriate Lyapunov-Krasovskii functionals in the design. The approach removes the assumption of linear function outside the deadband without necessarily constructing a dead-zone inverse as an added contribution. By utilizing the integral-type Lyapunov function and introducing an adaptive compensation term for the upper bound of the residual and optimal approximation error as well as the dead-zone disturbance, the closed-loop control system is proved to be semi-globally uniformly ultimately bounded. In addition, a modified adaptive control algorithm is given in order to avoid the high-frequency chattering phenomenon. Simulation results demonstrate the effectiveness of the approach.     

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 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.     

Robust adaptive control for uncertain nonlinear systems with unknown control directions and actuator nonlinearity

A robust adaptive control scheme is proposed for a class of uncertain nonlinear systems in strict feedback form with both unknown control directions and non-symmetric dead-zone nonlinearity based on backstepping design.The conditions that the dead-zone slopes and the boundaries are equal and symmetric are removed by simplifying nonlinear dead-zone input model,the assumption that the priori knowledge of the control directions to be known is eliminated by utilizing Nussbaum-type gain technique and neural networks(NN) approximation capability.The possible controller singularity problem and the effect of dead-zone input nonlinearity are avoided perfectly by combining integral Lyapunov design with sliding mode control strategy.All the signals in the closed-loop system are guaranteed to be semi-globally uniformly ultimately bounded and the tracking error of the system is proven to be converged to a small neighborhood of the origin.Simulation results demonstrate the effectiveness of the proposed control scheme.     

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.     

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.     

Chattering free adaptive fuzzy terminal sliding mode control for second order nonlinear system

A novel fuzzy terminal sliding mode control （FTSMC） scheme is proposed for position tracking of a class of second-order nonlinear uncertain system. In the proposed scheme, we integrate input-output linearization technique to cancel the nonlinearities. By using a function-augmented sliding hyperplane, it is guaranteed that the output tracking error converges to zero in finite time which can be set arbitrarily. The proposed scheme eliminates reaching phase problem, so that the closed-loop system always shows invariance property to parameter uncertainties. Fuzzy logic systems are used to approximate the unknown system functions and switch item. Robust adaptive law is proposed to reduce approximation errors between true nonlinear functions and fuzzy systems, thus chattering phenomenon can be eliminated. Stability of the proposed control scheme is proved and the scheme is applied to an inverted pendulum system. Simulation studies are provided to confirm performance and effectiveness of the proposed control approach.     

Chattering free adaptive fuzzy terminal sliding mode control for second order nonlinear system

A novel fuzzy terminal sliding mode control (FTSMC) scheme is proposed for position tracking of a class of second-order nonlinear uncertain system. In the proposed scheme, we integrate input-output linearization technique to cancel the nonlinearities. By using a function-augmented sliding hyperplane, it is guaranteed that the output tracking error converges to zero in finite time which can be set arbitrarily. The proposed scheme eliminates reaching phase problem, so that the closed-loop system always shows invariance property to parameter uncertainties. Fuzzy logic systems are used to approximate the unknown system functions and switch item. Robust adaptive law is proposed to reduce approximation errors between true nonlinear functions and fuzzy systems, thus chattering phenomenon can be eliminated. Stability of the proposed control scheme is proved and the scheme is applied to an inverted pendulum system. Simulation studies are provided to confirm performance and effectiveness of the proposed control approach.     

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．     

Design and analysis of a hybrid control scheme for sandwichnonsmooth nonlinear systems

This paper addresses an open control problem: the control of sandwich non-smooth nonlinear systems. Of interest are sandwiched non-smooth nonlinearities between linear dynamic blocks, as illustrated by a hydraulic valve system with a sandwiched dead-zone. A hybrid control scheme for the control of such sandwich systems is developed and presented in detail. The proposed control scheme employs an inner-loop discrete-time feedback design and an outer-loop continuous-time feedback design, combined with a nonlinearity inverse, to cancel the nonlinearity effect, for improving output tracking. The stability and tracking performance of the closed-loop control system are analyzed. Simulations are used to illustrate the effectiveness of the proposed hybrid control design     

Adaptive discrete-time sliding-mode control of nonlinear systems described by Wiener models

In this paper, we propose an adaptive control scheme that can be applied to nonlinear systems with unknown parameters. The considered class of nonlinear systems is described by the block-oriented models, specifically, the Wiener models. These models consist of dynamic linear blocks in series with static nonlinear blocks. The proposed adaptive control method is based on the inverse of the nonlinear function block and on the discrete-time sliding-mode controller. The parameters adaptation are performed using a new recursive parametric estimation algorithm. This algorithm is developed using the adjustable model method and the least squares technique. A recursive least squares (RLS) algorithm is used to estimate the inverse nonlinear function. A time-varying gain is proposed, in the discrete-time sliding mode controller, to reduce the chattering problem. The stability of the closed-loop nonlinear system, with the proposed adaptive control scheme, has been proved. An application to a pH neutralisation process has been carried out and the simulation results clearly show the effectiveness of the proposed adaptive control scheme.     

Intelligence computation based on adaptive tracking design for a class of non-linear discrete-time systems

In this article, a direct adaptive neural networks control algorithm is presented for a class of SISO discrete-time systems with non-symmetric dead-zone. The property of the dead-zone is discretized. Mean value theorem is used to transform the systems into a special form. The unknown functions in the input–output model are approximated using the radial basis function neural networks. Compared with the results for the discrete non-symmetric dead-zone, this article presents a new algorithm to reduce the computational burden. Lyapunov analysis method is utilized to prove that all the signals in the closed-loop systems are semi-global uniformly ultimately bounded. The tracking error is proved to converge to a small set around the zero. A simulation example provided to illustrate the effectiveness of the control schemes.     

Sliding mode control of wind-induced vibrations using fuzzy sliding surface and gain adaptation

Although fuzzy/adaptive sliding mode control can reduce the chattering problem in structural vibration control applications, they require the equivalent control and the upper bounds of the system uncertainties. In this paper, we used fuzzy logic to approximate the standard sliding surface and designed a dead-zone adaptive law for tuning the switching gain of the sliding mode control. The stability of the proposed controller is established using Lyapunov stability theory. A six-storey building prototype equipped with an active mass damper has been used to demonstrate the effectiveness of the proposed controller towards the wind-induced vibrations.     

Adaptive feedback control for nonlinear triangular systems subject to uncertain asymmetric dead-zone input

In this paper, an adaptive control strategy is proposed to investigate the issue of uncertain dead-zone input for nonlinear triangular systems with unknown nonlinearities. The considered system has no precise priori knowledge about the dead-zone feature and growth rate of nonlinearity. Firstly, a dynamic gain is introduced to deal with the unknown growth rate, and the dead-zone characteristic is processed by the adaptive estimation approach without constructing the dead-zone inverse. Then, by virtue of hyperbolic functions and sign functions, a new adaptive state feedback controller is proposed to guarantee the global boundedness of all signals in the closed-loop system. Moreover, the uncertain dead-zone input problem for nonlinear upper-triangular systems is solved by the similar control strategy. Finally, two simulation examples are given to verify the effectiveness of the control scheme.     

基于幂次趋近率的机械手滑模控制系统

为实现对机械手的快速高精度跟踪,采用滑模变结构控制算法对机械手进行控制。针对机械手在趋近滑模面的过程中所存在的抖震问题,在基于模糊补偿的鲁棒自适应控制的基础上,设计了一种基于趋近率的自适应模糊滑模机械手控制系统,使得系统能更快的趋近滑模面,削弱系统抖震现象。基于Matlab/Simulink仿真平台上搭建了机械手控制系统,仿真结果表明,加入趋近率能加快系统趋近滑模面,提高了系统的稳定性和跟踪性能。     

带有摄动死区输入的未知非线性系统自适应模糊控制

用自适应模糊控制来实现对带有摄动死区输入的一类未知非线性系统的控制. 文中给出了一种新的死区执行器模型, 该模型含有时变并且摄动的执行增益. 通过将死区非线性分解为一个线性类似项, 一个非线性项和一个扰动类似项降低了扰动类似项的上界, 从而可以用更小的控制力度来实现系统的鲁棒性. 利用反步后推技术与非线性参数化的模糊逼近器结合导出控制器, 该设计取消了模糊基函数须事先已知的限制. 本文不仅从理论上证明了所给控制器能够保证闭环系统的稳定性和预期的跟踪性能, 还用仿真实验验证了控制器的有效性.     

Intelligent fuzzy controller for chaos synchronization of uncertain fractional-order chaotic systems with input nonlinearities

In this research work, a novel fuzzy adaptive control is proposed to achieve a projective synchronization for a class of fractional-order chaotic systems with input nonlinearities (dead-zone together with sector nonlinearities). These master-slave systems under consideration are supposed to be with distinct models, different fractional-orders, unknown models, and dynamic external disturbances. The proposed control law consists of two main terms, namely: a fuzzy adaptive control term for appropriately approximating the uncertainties and a fractional-order variable-structure control term for robustly dealing with these inherent input nonlinearities. A Lyapunov approach is used to derive the updated laws and to prove the stability of the closed-loop control system. At last, a set of computer simulation results is carried out to illustrate and further validate the theoretical findings.     

关于多变量非线性系统的自适应模糊控制

结合模糊逻辑系统、自适应控制和H∞控制,对一类非线性多变量未知系统提出了 新的控制策略,给出了控制算法的稳定性分析.仿真结果证明了所提控制算法的有效性.