Nonsingular terminal sliding mode control of nonlinear second‐order systems with input saturation

This paper considers the nonsingular terminal sliding mode (TSM) controller design for a nonlinear second‐order system subject to input saturation. A new nonsingular TSM manifold is constructed by integrating the conventional nonsingular TSM manifold with a saturation function. When the bound of the uncertainty is known, based on the designed TSM manifold, a saturated controller can be designed directly for the nonlinear system. When the bound of the uncertainty is unknown, a disturbance observer is first employed to estimate the uncertainty, followed by constructing a composite controller consisting of a bounded feedback controller and a forward compensator. Theoretical analysis shows that under the proposed two control methods, the states of the closed‐loop system will both converge to zero in finite time. Simulation results demonstrate the effectiveness of the proposed methods. Copyright © 2015 John Wiley & Sons, Ltd.     

Robust Adaptive Fractional‐Order Terminal Sliding Mode Control for Lower‐Limb Exoskeleton

This paper introduces a robust adaptive fractional‐order non‐singular fast terminal sliding mode control (RFO‐TSM) for a lower‐limb exoskeleton system subject to unknown external disturbances and uncertainties. The referred RFO‐TSM is developed in consideration of the advantages of fractional‐order and non‐singular fast terminal sliding mode control (FONTSM): fractional‐order is used to obtain good tracking performance, while the non‐singular fast TSM is employed to achieve fast finite‐time convergence, non‐singularity and reducing chattering phenomenon in control input. In particular, an adaptive scheme is formulated with FONTSM to deal with uncertain dynamics of exoskeleton under unknown external disturbances, which makes the system robust. Moreover, an asymptotical stability analysis of the closed‐loop system is validated by Lyapunov proposition, which guarantees the sliding condition. Lastly, the efficacy of the proposed method is verified through numerical simulations in comparison with advanced and classical methods.     

快速非奇异终端滑模在混沌系统中的应用

为解决传统线性滑模控制中的速度较慢和终端滑模的奇异性问题,提出一种快速非奇异终端滑模的控制策略,并将其应用于Lorenz混沌系统中。控制策略为当系统状态离平衡点较远时采用线性滑模,使其快速地到达滑模面;而一旦滑模到达所设计的滑模面时控制策略变为非奇异终端滑模,使其快速地收敛于平衡点。此策略将线性滑模和终端滑模的优点相结合,从而使整个系统的状态在全程都具有较快的收敛速度,此方法改善了传统的线性滑模只能渐近地趋近于平衡点的动态缺点;同时也改善了单独采用终端滑模时,离平衡点较远的状态到达时间较长的缺点;且有效地避免了奇异现象的发生。最后通过M atlab仿真,对Lorenz混沌系统进行仿真,验证了该方法的有效性。     

Robust adaptive finite‐time parameter estimation and control for robotic systems

This paper studies adaptive parameter estimation and control for nonlinear robotic systems based on parameter estimation errors. A framework to obtain an expression of the parameter estimation error is proposed first by introducing a set of auxiliary filtered variables. Then three novel adaptive laws driven by the estimation error are presented, where exponential error convergence is proved under the conventional persistent excitation (PE) condition; the direct measurement of the time derivatives of the system states are avoided. The adaptive laws are modified via a sliding mode technique to achieve finite‐time convergence, and an online verification of the alternative PE condition is introduced. Leakage terms, functions of the estimation error, are incorporated into the adaptation laws to avoid windup of the adaptation algorithms. The adaptive algorithm applied to robotic systems permits that tracking control and exact parameter estimation are achieved simultaneously in finite time using a terminal sliding mode (TSM) control law. In this case, the PE condition can be replaced with a sufficient richness requirement of the command signals and thus is verifiable a priori. The potential singularity problem encountered in TSM controls is remedied by introducing a two‐phase control procedure. The robustness of the proposed methods against disturbances is investigated. Simulations based on the ‘Bristol‐Elumotion‐Robotic‐Torso II’ (BERT II) are provided to validate the efficacy of the introduced methods. Copyright © 2014 John Wiley & Sons, Ltd.     

Finite time position synchronised control for parallel manipulators using fast terminal sliding mode

A new finite time position synchronised control approach for parallel manipulators is proposed using a fast terminal sliding mode (TSM). By developing a novel synchronisation and coupling position error, a non-singular fast TSM is proposed in coupling position error space. The proposed controller can guarantee position error and synchronisation error converge to zero in a finite time simultaneously without requiring the explicit using system dynamic model. The corresponding stability analysis is presented to lay a foundation for theoretical understanding to the underlying issues as well as safe operation for real systems. An illustrative example is demonstrated in support of the effectiveness of the proposed approach.     

Tuning space mapping with tuning exponent of T‐matrix

Tuning space mapping (TSM) with tuning exponent parameter of T‐matrix is proposed. A section of design interest in the electromagnetic (EM) model is replaced by “n” pieces cascaded T‐matrixes, and each T‐matrix is the EM‐simulated T‐parameter of preassigned unit cell circuit (PUCC). Finally the optimal exponent parameter of T‐matrix is transferred to original design variables. The proposed TSM not only inherits the advantages of circuit tuning element‐less (CTEL) TSM in prior art but also overcome the number range limitation that the tuning parameter must be positive for tuning in CTEL TSM. The proposed method has the minimal specification error and lowest simulation time comparing with other TSM methods. Verification examples, comparisons and discussions are also implemented. © 2015 Wiley Periodicals, Inc. Int J RF and Microwave CAE 26:232–239, 2016.     

Disturbance attenuation with fast global finite‐time convergence for generalized high‐order uncertain nonlinear systems

This paper focuses on the problem of disturbance attenuation with fast global finite‐time convergence (FTC) for a class of generalized high‐order uncertain nonlinear systems. Combining the fast finite‐time stabilization technique with a delicate manipulation of sign functions, a new control approach is proposed to attenuate the serious uncertainties substantially, including time‐varying control coefficients, nonlinear parameters, and external disturbances, while achieving the performance evaluated in terms of L₂‐L_2p gain. A notable feature of the control strategy is the fast FTC, which greatly shortens the convergent time when the initial state is far away from the origin. A numerical example is provided to demonstrate the effectiveness of the proposed method.     

非奇异快速的终端滑模控制方法及其跟车控制应用

最少传感器跟车系统中,跟踪误差收敛缓慢和对前车干扰鲁棒性差是两个主要问题.基于终端滑模(TSM)控制方法,设计一种控制量非奇异且收敛快速的跟车控制律,并实现其实车应用.回顾已有非奇异快速终端滑模控制方法的基本原理;分析最少传感器跟车系统的特点,建立包含车辆和车间纵向动力学特性的两状态模型,设计非奇异快速终端滑模控制律;证明闭环系统到达阶段和滑动阶段的快速收敛特性,以及它对前车加减速干扰的强鲁棒性.仿真分析及实车实验表明,该控制器输出的节气门开度光滑无抖振,本车平稳快速跟随前车行驶,且当前车加速度有界时,闭环系统鲁棒收敛.     

有限时间收敛的Terminal滑模控制设计

讨论了一类SISO非线性系统的滑模变结构控制有限时间收敛问题,提出一种新的Terminal滑动模态及相应控制的设计方法,可用于带有外部扰动的二阶非线性系统。研究结果表明,系统状态在滑模面上能以较快的速度达到平衡点,在滑模面上到达平衡点的时间均是有限的,并且与普通的Terminal滑模相比,在滑模面上能以更短的时间到达平衡点。仿真结果表明了所提方法的有效性。     

Two‐stage stability control for strict‐feedback systems with input delays and input nonlinear uncertainties

In this paper, a two‐stage control procedure is proposed for stabilization of a class of strict‐feedback systems with unknown constant time delays and nonlinear uncertainties in the input. A nominal controller is first designed to compensate input time delays without considering input nonlinear uncertainties. Extended from backstepping algorithm, input delay compensation is realized by means of predicted states that are computed through integration of cascaded system dynamics, making the nominal closed‐loop system asymptotically stable. Based on the nominal controller presented for the input delay system, a multi‐timescale system is subsequently developed to estimate the unknown input nonlinearity and make the estimate approach the nominal control input as fast as possible. It is proved that the proposed control scheme can make states of the strict‐feedback systems converge to zero and all the signals of the closed‐loop systems are guaranteed to be bounded in the presence of input time delays and nonlinear uncertainties. Simulation verification is carried out to illuminate the effectiveness of the proposed control approach.     

基于非奇异终端滑模的一类回滞系统跟踪控制与仿真

该文研究一类重要的类反斜线回滞系统的鲁棒控制问题。首先通过对类反斜线回滞特性的分析,把回滞系统看作输人具有确定上限的不确定干扰的一般非线性系统;然后利用非奇异终端滑模控制方法设计控制律,使得系统在有限时间内跟踪期望轨迹,并保证系统的跟踪精度,从而削弱甚至消除回滞带来的影响。在数值仿真实验中,解决了非线性系统仿真时状态初始值赋值的问题,仿真结果表明了该方法的有效性。     

Infinite horizon optimal control for nonlinear interconnected large‐scale dynamical systems with an application to optimal attitude control

This paper presents a novel extended modal series method for solving the infinite horizon optimal control problem of nonlinear interconnected large‐scale dynamic systems. In this method, the infinite horizon nonlinear large‐scale two‐point boundary value problem (TPBVP), derived from Pontryagin's maximum principle, is transformed into a sequence of linear time‐invariant TPBVPs. Solving the latter problems in a recursive manner provides the optimal control law and the optimal trajectory in the form of a uniformly convergent series. Moreover, in special cases, the proposed procedure facilitates the application of parallel processing, which improves its computational efficiency. In this study, an iterative algorithm is also presented, which has a low computational complexity and a fast convergence rate. Just a few iterations are required to obtain a suboptimal trajectory‐control pair. Finally, effectiveness of the proposed approach is verified by solving the optimal attitude control problem. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Explicit nonlinear predictive control for a magnetic levitation system

The paper presents a methodology for the construction of an explicit nonlinear control law via approximation of the nonlinear constrained finite‐time optimal control (CFTOC). This is achieved through an approximate mapping of a general nonlinear system in a set of linear piecewise affine (PWA) systems. The key advantages of this methodology are two‐fold. First, the construction of an analytic solution of the CFTOC problem leads to an efficient explicit implementation. Second, by taking advantage of model predictive control's systematic fashion to handle constraints, an improved performance can be obtained for the closed‐loop system. The proposed theory is applied in real‐time for a system with fast dynamics: a magnetic levitation benchmark. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Robust Finite‐Time Stability Control of a Class of High‐Order Uncertain Nonlinear Systems

In this study, a novel robust finite‐time stability controller is proposed for a class of high‐order uncertain nonlinear systems. It uses the dynamic surface control (DSC) approach to simplify the traditional backstepping design for high‐order nonlinear systems, thus avoiding the “explosion of terms”. The finite‐time stability of the closed‐loop system is guaranteed to have high performance, such as fast transient and strong robustness to dynamic uncertainties, and the tracking error is made arbitrarily small. Simulation results of two examples indicate that the proposed controller is effective.     

Robust stabilization of a class of uncertain system via block decomposition and VSC

In this paper, a block decomposition procedure for sliding mode control of a class of nonlinear systems with matched and unmatched uncertainties, is proposed. Based on the nonlinear block control principle, a sliding manifold design problem is divided into a number of sub‐problems of lower dimension which can be solved independently. As a result, the nominal parts of the sliding mode dynamics is linearized. A discontinuous feedback is then used to compensate the matched uncertainty. Finally, a step‐by‐step Lyapunov technique and a high gain approach is applied to obtain hierarchical fast motions on the sliding manifolds and to achieve the robustness property of the closed‐loop system motion with respect to unmatched uncertainty. Copyright © 2002 John Wiley & Sons, Ltd.     

Fast terminal sliding‐mode finite‐time tracking control with differential evolution optimization algorithm using integral chain differentiator in uncertain nonlinear systems

This paper presents a fast terminal sliding‐mode tracking control for a class of uncertain nonlinear systems with unknown parameters and system states combined with time‐varying disturbances. Fast terminal sliding‐mode finite‐time tracking systems based on differential evolution algorithms incorporate an integral chain differentiator (ICD) to feedback systems for the estimation of the unknown system states. The differential evolution optimization algorithm using ICD is also applied to a tracking controller, which provides unknown parametric estimation in the limitation of unknown system states for trajectory tracking. The ICD in the tracking systems strengthens the tracking controller robustness for the disturbances by filtering noises. As a powerful finite‐time control effort, the fast terminal sliding‐mode tracking control guarantees that all tracking errors rapidly converge to the origin. The effectiveness of the proposed approach is verified via simulations, and the results exhibit high‐precision output tracking performance in uncertain nonlinear systems.     

A nonlinear state‐feedback state‐feedforward tracking control strategy for a boiler‐turbine unit

A boiler‐turbine unit is a primary module for coal‐fired power plants, and an effective automatic control system is needed for the boiler‐turbine unit to track the load changes with the drum water level kept within an acceptable range. The aim of this paper is to develop a nonlinear tracking controller for the Bell‐Åström boiler‐turbine unit. A Takagi‐Sugeno fuzzy control system is introduced for the nonlinear modeling of the Bell‐Åström boiler‐turbine unit. Based on the Takagi‐Sugeno fuzzy models, a nonlinear tracking controller is developed, and the proposed control law is comprised of a state‐feedforward term and a state‐feedback term. The stability of the closed‐loop control system is analyzed on the basis of Lyapunov stability theory via the linear matrix inequality approach and Schur complement. Moreover, model uncertainties are also considered, and it is proved that with the proposed control law the tracking error converges to zero. To assess the performance of the proposed nonlinear state‐feedback state‐feedforward control strategy, a nonlinear model predictive control strategy and a linear strategy are presented as comparisons. The effectiveness and the advantages of the proposed nonlinear state‐feedback state‐feedforward control strategy are demonstrated by simulations.     

Dynamic inversion control for a class of pure‐feedback systems

A dynamic inversion control method is proposed for a class of pure‐feedback nonlinear systems. By combing the back‐steeping control method with the singular perturbation theory, the virtual and the final actual control inputs are derived from the solutions of a series of fast dynamical equations. Stability analysis shows that the system output tracks the desired trajectory with bounded errors, which can be made arbitrarily small by choosing appropriate design parameters. Tracking performance is illustrated by simulation results. © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Approximate finite‐time control for a class of uncertain nonlinear systems with dynamic compensation

In this work, a new robust nonlinear feedback control method with dynamic active compensation is proposed; the active control method has been applied to an integral series of finite‐time single‐input single‐output nonlinear system with uncertainty. In further tracking the closed‐loop stability and nonlinear uncertainty, an extended state observer has been employed to solve the immeasurability and nonlinear uncertainty within a nonlinear system. A singular perturbation theory has been used to solve for the finite‐time stability of the closed‐loop system; furthermore, numerical simulations showed that the robust nonlinear feedback controller tracked the uncertainty in a nonlinear Duffing‐type oscillator and has proven the effectiveness of the approximate finite‐time control strategy proposed. By using an approximate finite‐time control approach with active compensation, the uncertainty in a nonlinear system could be accurately estimated and controlled. Copyright © 2017 John Wiley & Sons, Ltd.