On Finite‐Time Stabilization of Active Disturbance Rejection Control for Uncertain Nonlinear Systems

This paper designs the active disturbance rejection control (ADRC) to achieve finite‐time stabilization for a class of uncertain nonlinear systems. The proposed control incorporates both an extended state observer (ESO) as well as an adaptive sliding mode controller. The ESO is utilized to estimate the full system states and the total uncertainties, and the adaptive strategy is incorporated to deal with the estimation errors. It is proved that, with the application of the proposed control law, semi‐global finite‐time stabilization can be achieved. Effectiveness of the proposed method is illustrated with a numerical example.     

Finite‐Time Fault‐Tolerant Control for a Class of Non‐Affine Nonlinear System Using Sliding Mode Disturbance Observer

This study investigates a finite‐time fault‐tolerant control scheme for a class of non‐affine nonlinear system with actuator faults and unknown disturbances. A global approximation method is applied to non‐affine nonlinear system to convert it into an affine‐like expression with accuracy. An adaptive terminal sliding mode disturbance observer is proposed to estimate unknown compound disturbances in finite time, including external disturbances and system uncertainties, which enhances system robustness. Controllers based on finite‐time Lyapunov theory are designed to force tracking errors to zero in finite time. Simulation results demonstrate the effectiveness of proposed method.     

Finite‐Time Sliding Mode Trajectory Tracking Control of Uncertain Mechanical Systems

The problem of finite‐time tracking control is studied for uncertain nonlinear mechanical systems. To achieve finite‐time convergence of tracking errors, a simple linear sliding surface based on polynomial reference trajectory is proposed to enable the trajectory tracking errors to converge to zero in a finite time, which is assigned arbitrarily in advance. The sliding mode control technique is employed in the development of the finite‐time controller to guarantee the excellent robustness of the closed‐loop system. The proposed sliding mode scheme eliminates the reaching phase problem, so that the closed‐loop system always holds the invariance property to parametric uncertainties and external disturbances. Lyapunov stability analysis is performed to show the global finite‐time convergence of the tracking errors. A numerical example of a rigid spacecraft attitude tracking problem demonstrates the effectiveness of the proposed controller.     

Observer‐based finite‐time output‐feedback controller for DC‐DC buck converters with unknown load variations

The output voltage regulation problem of a DC‐DC buck converter is investigated in this paper via an observer‐based finite‐time output‐feedback control approach. Considering the effects of unknown load variations and the case without current sensor, by using the technique of adding a power integrator and the idea of nonseparation principle, a finite‐time voltage regulation control algorithm via dynamic output feedback is designed. The main feature of the designed observer and controller does not need any load's information. Theoretically, it is proven that the output voltage can reach the desired voltage in a finite time under the proposed controller. The effectiveness of the proposed control method is illustrated by numerical simulations and experimental results.     

Experimental Implementation of New Sliding Mode Control Law applied To a DC–DC Boost Converter

The real implementation of sliding mode controllers (SMCs) to a DC–DC boost converter is a challenge due to the nonminimum phase behavior of these kinds of converters and the SMCs chattering problem. In this paper, new integral sliding mode control laws with linear and proposed nonlinear sliding surfaces are developed to overcome these problems. An experimental comparative study between these SMCs and the classical SMC applied for a DC–DC boost converter is presented.     

Sum‐of‐Squares‐Based Finite‐Time Adaptive Sliding Mode Control of Uncertain Polynomial Systems With Input Nonlinearities

This paper proposes a novel adaptive sliding mode control (ASMC) for a class of polynomial systems comprising uncertain terms and input nonlinearities. In this approach, a new polynomial sliding surface is proposed and designed based on the sum‐of‐squares (SOS) decomposition. In the proposed method, an adaptive control law is derived such that the finite‐time reachability of the state trajectories in the presence of input nonlinearity and uncertainties is guaranteed. To do this, it is assumed that the uncertain terms are bounded and the input nonlinearities belong to sectors with positive slope parameters. However, the bound of the uncertain terms is unknown and adaptation law is proposed to effectively estimate the uncertainty bounds. Furthermore, based on a novel polynomial Lyapunov function, the finite‐time convergence of the sliding surface to a pre‐chosen small neighborhood of the origin is guaranteed. To eliminate the time derivatives of the polynomial terms in the stability analysis conditions, the SOS variables of the Lyapunov matrix are optimally selected. In order to show the merits and the robust performance of the proposed controller, chaotic Chen system is provided. Numerical simulation results demonstrate chattering reduction in the proposed approach and the high accuracy in estimating the unknown parameters.     

一种BUCK电路自适应的滑模控制算法

针对常见的BUCK电路滑模控制方案中存在的负载突变产生的干扰问题,设计一种新的自适应滑模控制器.通过观测BUCK电路中负载电阻的变化,自适应的修改控制参数以获得良好的动态性能和稳定性.通过实验仿真证明该方法在负载电阻变化时,能有效减小系统状态误差和提高系统稳定性.     

Finite‐time tracking control for a class of nonlinear systems with multiple mismatched disturbances

This article investigates the finite‐time output tracking problem for a class of nonlinear systems with multiple mismatched disturbances. To efficiently estimate the disturbances and their derivatives, a continuous finite‐time disturbance observer (CFTDO) design method is developed. Based on the modified adding a power integrator method and CFTDO technique, a composite tracking controller is constructed such that the system output can track the desired reference signal in finite time. Simulation results demonstrate the effectiveness of the proposed control approach.     

基于滑模干扰观测器的直流电机系统复合控制

随着直流电机设备在农林业、制造工业和航空航天领域应用得越来越广泛,实际工程对其性能的要求也越来越高。针对直流电机系统控制中面临的建模误差、参数摄动以及摩擦力矩干扰问题,提出一种滑模干扰观测器(SMDOB,sliding mode disturbance observer),其输出可作为控制系统中干扰补偿的设计依据。基于所设计的内环SMDOB,并利用不变性原理,提出一种外环复合控制方案,从而实现直流电机系统的位置跟踪能力。仿真结果表明,相比传统的控制方案,该控制方案下电机系统的跟踪性能更好,对建模误差、参数摄动以及摩擦力矩干扰的鲁棒性更高。而且,该控制方案的结构较为简单,易于工程实现。     

一类非线性系统的多面滑模控制

提出一种基于模糊ＣＭＡＣ神经网络的多面滑模变结构控制算法,其特点是无须已知不确定性函数及其各阶导数的上界,与经典设计广阔霜比,所提出的方案允许非参数化不确定性,仿真实例显示了该方法的有效性。     

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.     

Design of Second Order Sliding Mode and Sliding Mode Algorithms: A Practical Insight to DC-DC Buck Converter

This paper presents a simple and systematic approach to design second order sliding mode controller for buck converters. The second order sliding mode control (SOSMC) based on twisting algorithm has been implemented to control buck switch mode converter. The idea behind this strategy is to suppress chattering and maintain robustness and finite time convergence properties of the output voltage error to the equilibrium point under the load variations and parametric uncertainties. In addition, the influence of the twisting algorithm on the performance of closed-loop system is investigated and compared with other algorithms of first order sliding mode control such as adaptive sliding mode control (ASMC), nonsingular terminal sliding mode control (NTSMC).In comparative evaluation, the transient response of the output voltage with the step change in the load and the start-up response of the output voltage with the step change in the input voltage of buck converter were compared. Experimental results were obtained from a hardware setup constructed in laboratory. Finally, for all of the surveyed control methods, the theoretical considerations, numerical simulations, and experimental measurements from a laboratory prototype are compared for different operating points. It is shown that the proposed twisting method presents an improvement in steady state error and settling time of output voltage during load changes.      

Chattering Free Sliding Mode Control for Uncertain Discrete Time‐Delay Singular Systems

The problem of chattering free sliding mode control for a class of uncertain discrete singular systems with state delay is investigated in this paper. As a component of the solution, a new least squares support vector machine (LS‐SVM) reaching law is proposed. In terms of linear matrix inequalities, a delay‐dependent condition for sliding mode dynamics to be regular, causal, and asymptotically stable is established, and the chattering problem that appears in traditional variable structure systems is eliminated. Numerical examples are provided to demonstrate the applicability of the proposed methods.     

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.     

Adaptive Observer‐Based Global Sliding Mode Control for Uncertain Discrete‐Time Nonlinear Systems with Time‐Delays and Input Nonlinearity

A new discrete‐time adaptive global sliding mode control (SMC) scheme combined with a state observer is proposed for the robust stabilization of uncertain nonlinear systems with mismatched time delays and input nonlinearity. A state observer is developed to estimate the unmeasured system states. By using Lyapunov stability theorem and linear matrix inequality (LMI), the condition for the existence of quasi‐sliding mode is derived and the stability of the overall closed‐loop system is guaranteed. Finally, simulation results are presented to demonstrate the validity of the proposed scheme.     

Finite‐Time H∞ State Estimation for Discrete‐Time Switched Control Systems Under Asynchronous Switching

The Luenberger observer technique has long been used for reliable state estimation of feedback control systems. In this paper it is employed for asynchronously switched control systems. The theory of finite‐time stability (FTS) and finite‐time boundedness (FTB) is incorporated, which is a relatively new concept offering open and challenging problems, especially in the field of robust state estimation for switched control systems. Many real‐world systems are supposed to run for a fixed interval of time and hence the design of finite‐time state observers has more significance from the point of view of many engineering applications. This investigation considers asynchronous switching between observer and physical systems, which accounts for inherent delays in practical applications caused by measurement and sensing mechanisms, and crafts a more practical and accurate design method. Furthermore, performance index which is a vital technique for robust system design against external disturbances is integrated in the design procedure.     

A Discrete‐Time Global Quasi‐Sliding Mode Control Scheme with Bounded External Disturbance Rejection

A global quasi‐sliding mode control (GQSMC) scheme is introduced to ensure zigzag motion with a smaller bound than that offered by Gao's method and to provide disturbance rejection throughout the entire response in discrete time. The design of an augmented forcing function is followed by three conditions in discrete time extended from global sliding mode control (GSMC) in continuous time. Furthermore, we adopt a switching gain, which is auto‐tuned as a function of sliding surface s(k), such that chattering phenomena can be considerably alleviated during the steady‐state, significantly reducing switching control applied to the plant. The proposed GQSMC scheme can provide more advantages such as an even distribution of the control input throughout the entire response and an improvement in the accuracy and speed of the desired performance, guaranteeing a quasi‐sliding mode throughout the entire response. In addition, we also consider the input disturbance rejection according to the norm‐bounded exogenous signal. Results from both the simulation and the experiments are reported. The results further verify that we can use the global sliding surface to curtail reaching the phase stage.     

基于LS-SVM的不确定非线性系统滑模控制

针对滑模控制中不确定上界值的问题,提出了一种基于LSSVM自适应上界学习的滑模控制方法.首先将系统分为确定部分和不确定部分,对确定部分采用状态反馈法进行控制,对不确定系统部分采用最小二乘支持向量机( LSSVM)来完成.该控制器不仅可以保证非线性不确定系统渐近稳定,降低一般滑模控制理论分析的条件,还有效地抑制了抖振.仿...     

一类非线性不确定非匹配时滞系统的鲁棒滑模控制

针对一类带有不匹配非线性不确定的线性时滞系统,基于稳定性理论,提出一种新的依赖于时滞的滑动模控制策略。该控制策略保证闭环系统滑动阶段的存在性,并在此基础上证明滑动模态运动的稳定性。最后通过仿真例子看出,抖振现象被大大减弱,这进一步说明该控制策略的可行性和有效性。