Adaptive nonsingular fast terminal sliding-mode control for the tracking problem of uncertain dynamical systems

In this paper, robust and adaptive nonsingular fast terminal sliding-mode (NFTSM) control schemes for the trajectory tracking problem are proposed with known or unknown upper bound of the system uncertainty and external disturbances. The developed controllers take the advantage of the NFTSM theory to ensure fast convergence rate, singularity avoidance, and robustness against uncertainties and external disturbances. First, a robust NFTSM controller is proposed which guarantees that sliding surface and equilibrium point can be reached in a short finite-time from any initial state. Then, in order to cope with the unknown upper bound of the system uncertainty which may be occurring in practical applications, a new adaptive NFTSM algorithm is developed. One feature of the proposed control law is their adaptation techniques where the prior knowledge of parameters uncertainty and disturbances is not needed. However, the adaptive tuning law can estimate the upper bound of these uncertainties using only position and velocity measurements. Moreover, the proposed controller eliminates the chattering effect without losing the robustness property and the precision. Stability analysis is performed using the Lyapunov stability theory, and simulation studies are conducted to verify the effectiveness of the developed control schemes.     

基于反演设计的机械臂非奇异终端神经滑模控制

针对具有建模误差和不确定干扰的多关节机械臂的轨迹跟踪问题,设计反演非奇异终端神经滑模控制。该方案是采用能有限时间收敛的非奇异终端滑模面,根据滑模控制原理和反演方法设计反演滑模控制器;对于反演滑模控制系统中由于建模误差和不确定干扰造成的不确定因素的上界,设计径向基(Radial basis function, RBF)神经网络自适应律,在线估计不确定因素的上界;利用李亚普诺夫定理证明了系统的稳定性。仿真结果表明,该方法具有良好的轨迹跟踪性能,提高对于建模误差和不确定干扰等因素的鲁棒性,削弱了抖动。     

Neural network disturbance observer-based distributed finite-time formation tracking control for multiple unmanned helicopters

The distributed finite-time formation tracking control problem for multiple unmanned helicopters is investigated in this paper. The control object is to maintain the positions of follower helicopters in formation with external interferences. The helicopter model is divided into a second order outer-loop subsystem and a second order inner-loop subsystem based on multiple-time scale features. Using radial basis function neural network (RBFNN) technique, we first propose a novel finite-time multivariable neural network disturbance observer (FMNNDO) to estimate the external disturbance and model uncertainty, where the neural network (NN) approximation errors can be dynamically compensated by adaptive law. Next, based on FMNNDO, a distributed finite-time formation tracking controller and a finite-time attitude tracking controller are designed using the nonsingular fast terminal sliding mode (NFTSM) method. In order to estimate the second derivative of the virtual desired attitude signal, a novel finite-time sliding mode integral filter is designed. Finally, Lyapunov analysis and multiple-time scale principle ensure the realization of control goal in finite-time. The effectiveness of the proposed FMNNDO and controllers are then verified by numerical simulations.     

Finite-time fault tolerant attitude stabilization control for rigid spacecraft

A sliding mode based finite-time control scheme is presented to address the problem of attitude stabilization for rigid spacecraft in the presence of actuator fault and external disturbances. More specifically, a nonlinear observer is first proposed to reconstruct the amplitude of actuator faults and external disturbances. It is proved that precise reconstruction with zero observer error is achieved in finite time. Then, together with the system states, the reconstructed information is used to synthesize a nonsingular terminal sliding mode attitude controller. The attitude and the angular velocity are asymptotically governed to zero with finite-time convergence. A numerical example is presented to demonstrate the effectiveness of the proposed scheme.     

Hybrid finite-time trajectory tracking control of a quadrotor

In this paper, accurate trajectory tracking control problem of a quadrotor with unknown dynamics and disturbances is addressed by devising a hybrid finite-time control (HFTC) approach. An adaptive integral sliding mode (AISM) control law is proposed for altitude subsystem of the quadrotor, whereby underactuated characteristics can decoupled. Backstepping technique is further deployed to control the horizontal position subsystem. To exactly attenuate external disturbances, a finite-time disturbance observer (FDO) combining with nonsingular terminal sliding mode (NTSM) control strategy is constructed for attitude subsystem, and thereby achieve finite-time stability. Using the compounded control scheme, trajectory tracking errors can be stabilized rapidly. Simulation results and comprehensive comparisons show that the proposed HFTC scheme has remarkably superior performance.     

Finite-time tracking control of nth-order chained-form non-holonomic systems in the presence of disturbances

This paper addresses the problem of finite-time tracking controller design for nth-order chained-form non-holonomic systems in the presence of unknown disturbances. To this aim, a generalized disturbance observer based controller is proposed and combined with a recursive terminal sliding mode approach which guarantees finite-time convergence of the disturbance observer dynamic. By introducing a time-varying transformation and introducing a new control law, the existence of the sliding around the recursive terminal sliding mode surfaces is guaranteed. Finally, the proposed approach is applied for a wheeled mobile robot with a fourth-order chained-form non-holonomic model. The simulation results demonstrate the desirable and robust tracking performance of the proposed approach in the presence of unknown disturbance.     

Adaptive second-order fast nonsingular terminal sliding mode control for robotic manipulators

This paper presents an adaptive chattering-free sliding mode controller for trajectory tracking of robotic manipulators in the presence of external disturbances and inertia uncertainties. To achieve fast convergence and desirable tracking precision, a second-order fast nonsingular terminal sliding mode (SOFNTSM) controller is designed to guarantee system performance and robust stability. Chattering is eliminated using continuous control law due to high-frequency switching terms contained in the first derivative of actual control signals. Meanwhile, uncertainties are compensated by introducing the adaptive technique, whose prior knowledge about upper bound is not required. Finally, simulation results validate the effectiveness of the proposed control scheme.     

Finite-time sliding mode controller for perturbed second-order systems

This paper presents a novel finite-time sliding mode controller applied to perturbed second order systems. The proposed scheme employs a disturbance observer that can identify growing in time disturbances. Then, the observer is combined with a sliding mode controller to achieve finite-time stabilization of the second-order system. The convergence of the observer as well as the finite-time stability of the closed-loop system is theoretically demonstrated. Besides, it is also shown that the finite-time convergence properties of a given controller can be enhanced when using a compensation term based on the disturbance observer. The proposed controller is compared with a twisting algorithm and a finite-time sliding mode controller with disturbance estimation. Also, a conventional proportional integral derivative (PID) controller is combined with the proposed disturbance observer in a trajectory tracking task. Numerical simulations indicate that the proposed controller attains finite-time stabilization of the second order system by requiring a less amount of power than that demanded by the other control schemes and without being affected by the peaking phenomenon. Besides, the performance of the PID technique is enhanced by applying the proposed control methodology.     

Finite-time Extended State Observer based fault tolerant output feedback control for attitude stabilization

This work addresses the challenging problem of finite-time fault tolerant attitude stabilization control for the rigid spacecraft attitude control system without the angular velocity measurements, in the presence of external disturbances and actuator failures. Consider the severe circumstances with above failures and uncertainties, a novel continuous finite-time Extended State Observer is first established to observe the attitude angular velocity and the synthetic failure simultaneously. Unlike the existing observers, the finite-time methodology and Extended State Observer are utilized, to achieve the finite-time uniformly ultimately bounded stability of the attitude angular velocity and extended state observation errors. Furthermore, a novel continuous finite-time attitude controller is developed by using the nonsingular terminal sliding mode control and super-twisting method. The main feature of this work stems from our use of multiply advanced techniques or methodologies that enables the finite-time stability of the closed-loop attitude control system and the designed control scheme is continuous with the property of chattering restraining. Finally, numerical simulation results are presented to illustrate the effectiveness and fine performances of the finite-time observer and controller for the attitude control system.     

Global fast dynamic terminal sliding mode control for a quadrotor UAV

A control method based on global fast dynamic terminal sliding mode control (TSMC) technique is proposed to design the flight controller for performing the finite-time position and attitude tracking control of a small quadrotor UAV. Firstly, the dynamic model of the quadrotor is divided into two subsystems, i.e., a fully actuated subsystem and an underactuated subsystem. Secondly, the dynamic flight controllers of the quadrotor are formulated based on global fast dynamic TSMC, which is able to guarantee that the position and velocity tracking errors of all system state variables converge to zero in finite-time. Moreover, the global fast dynamic TSMC is also able to eliminate the chattering phenomenon caused by the switching control action and realize the high precision performance. In addition, the stabilities of two subsystems are demonstrated by Lyapunov theory, respectively. Lastly, the simulation results are given to illustrate the effectiveness and robustness of the proposed control method in the presence of external disturbances.     

Sliding mode control with PID sliding surface and experimental application to an electromechanical plant

In this study, a sliding mode control system with a proportional+integral+derivative (PID) sliding surface is adopted to control the speed of an electromechanical plant. A robust sliding mode controller is derived so that the actual trajectory tracks the desired trajectory despite uncertainty, nonlinear dynamics, and external disturbances. The proposed sliding mode controller is chosen to ensure the stability of overall dynamics during the reaching phase and sliding phase. The stability of the system is guaranteed in the sense of the Lyapunov stability theorem. The chattering problem is overcome using a hyperbolic function for the sliding surface. Experimental results that are compared with the results of conventional PID verify that the proposed sliding mode controller can achieve favorable tracking performance, and it is robust with regard to uncertainties and disturbances.     

Optimal second order sliding mode control for nonlinear uncertain systems

In this paper, a chattering free optimal second order sliding mode control (OSOSMC) method is proposed to stabilize nonlinear systems affected by uncertainties. The nonlinear optimal control strategy is based on the control Lyapunov function (CLF). For ensuring robustness of the optimal controller in the presence of parametric uncertainty and external disturbances, a sliding mode control scheme is realized by combining an integral and a terminal sliding surface. The resulting second order sliding mode can effectively reduce chattering in the control input. Simulation results confirm the supremacy of the proposed optimal second order sliding mode control over some existing sliding mode controllers in controlling nonlinear systems affected by uncertainty.     

基于趋近律离散滑模控制的柔性梁振动抑制

研究了基于趋近律的离散滑模控制在智能柔性悬臂梁振动控制中的应用.以压电陶瓷为作动器,电阻应变片为传感器,采用有限元方法和模态截断技术建立结构动力学模型.由于柔性结构系统受到不确定外部扰动和量测噪声的影响以及参数的不确定性,滑模变结构控制可以实现滑动模态与系统的外干扰和参数摄动无关,即滑动模态的不变性.结构振动控制在系统状态由于外部干扰的影响偏离平衡状态,在控制器作用下能使系统趋于零状态.采用趋近律离散滑模控制方法设计状态调节器.由于状态量不能直接测量,故利用离散卡尔曼滤波技术构造状态估计器.采用试验模态测试方法得到结构的前4阶固有频率和阻尼比,与有限元方法的结果比较,说明该模型的正确性.使用dSPACE实时仿真系统和MATLAB/Simulink搭建控制系统,进行了振动主动控制试验.试验结果表明,所设计的控制器能有效抑制结构的振动响应.     

High precision tracking control of a servo gantry with dynamic friction compensation

This paper is concerned with the tracking control problem of a voice coil motor (VCM) actuated servo gantry system. By utilizing an adaptive control technique combined with a sliding mode approach, an adaptive sliding mode control (ASMC) law with friction compensation scheme is proposed in presence of both frictions and external disturbances. Based on the LuGre dynamic friction model, a dual-observer structure is used to estimate the unmeasurable friction state, and an adaptive control law is synthesized to effectively handle the unknown friction model parameters as well as the bound of the disturbances. Moreover, the proposed control law is also implemented on a VCM servo gantry system for motion tracking. Simulations and experimental results demonstrate good tracking performance, which outperform traditional control approaches.     

Sliding mode controllers for a tempered glass furnace

This paper investigates the design of two sliding mode controllers (SMCs) applied to a tempered glass furnace system. The main objective of the proposed controllers is to regulate the glass plate temperature, the upper-wall temperature and the lower-wall temperature in the furnace to a common desired temperature. The first controller is a conventional sliding mode controller. The key step in the design of this controller is the introduction of a nonlinear transformation that maps the dynamic model of the tempered glass furnace into the generalized controller canonical form; this step facilitates the design of the sliding mode controller. The second controller is based on a state-dependent coefficient (SDC) factorization of the tempered glass furnace dynamic model. Using an SDC factorization, a simplified sliding mode controller is designed. The simulation results indicate that the two proposed control schemes work very well. Moreover, the robustness of the control schemes to changes in the system׳s parameters as well as to disturbances is investigated. In addition, a comparison of the proposed control schemes with a fuzzy PID controller is performed; the results show that the proposed SDC-based sliding mode controller gave better results.     

Extended observer based on adaptive second order sliding mode control for a fixed wing UAV

This paper addresses the design of attitude and airspeed controllers for a fixed wing unmanned aerial vehicle. An adaptive second order sliding mode control is proposed for improving performance under different operating conditions and is robust in presence of external disturbances. Moreover, this control does not require the knowledge of disturbance bounds and avoids overestimation of the control gains. Furthermore, in order to implement this controller, an extended observer is designed to estimate unmeasurable states as well as external disturbances. Additionally, sufficient conditions are given to guarantee the closed-loop stability of the observer based control. Finally, using a full 6 degree of freedom model, simulation results are obtained where the performance of the proposed method is compared against active disturbance rejection based on sliding mode control.     

机械臂反演非奇异终端的神经滑模控制

为了解决具有外部干扰以及建模误差的多关节机械臂的轨迹跟踪问题,提出了一种机械臂反演非奇异终端的神经滑模控制方法。采用非奇异终端的滑模面,基于反演方法以及滑模控制的原理,设计了反演滑模控制器。针对由于外部干扰以及建模误差引起的反演滑模控制系统中不确定的因素上界,设计了径向基(radial basis function,简称RBF)神经网络的自适应律,对不确定因素上界进行了在线估计,并对控制系统的稳定性使用了Lyapunov定理进行证明。仿真分析结果表明,所提出的方法不仅可以减少系统中存在的抖振现象,而且具有较好的轨迹跟踪性能和较强的鲁棒性。     

Tracking control of nonholonomic mobile agents with external disturbances and input delay

This paper investigates the tracking control problem of chained-form nonholonomic multiagent systems (MASs). In contrast to the existing works in which some algorithms have been designed for ideal conditions, the destructive factors including external disturbances and input delay are considered in the dynamics of the agents in this work. Two distributed controllers are proposed such that the states of the controlled agents can track the states of the target in the presence of external disturbances and input delay. For this purpose, a distributed controller is firstly suggested based on a switching method to solve the tracking control problem for nonholonomic MASs with external disturbances. Then, the proposed control law is extended based on a state predictor for the tracking control of agents in the presence of input delay. The stability analysis of the two distributed controllers is also provided. Simulation results show the promising performance of the proposed algorithms.     

交流伺服系统自适应模糊滑模控制

介绍了交流伺服系统的自适应模糊滑模控制方案.通过自适应模糊控制解决了扰动补偿问题.正是因为结合了模糊控制的逼近特性和滑模控制的鲁棒性,才使得系统对外部扰动具有很好的稳定性和鲁棒性,同时消除了抖动现象.仿真实验表明这一控制方案具有很好的控制效果.