Robust Dynamic Sliding-Mode Control Using Adaptive RENN for Magnetic Levitation System

In this paper, a robust dynamic sliding mode control system (RDSMC) using a recurrent Elman neural network (RENN) is proposed to control the position of a levitated object of a magnetic levitation system considering the uncertainties. First, a dynamic model of the magnetic levitation system is derived. Then, a proportional–integral–derivative (PID)-type sliding-mode control system (SMC) is adopted for tracking of the reference trajectories. Moreover, a new PID-type dynamic sliding-mode control system (DSMC) is proposed to reduce the chattering phenomenon. However, due to the hardware being limited and the uncertainty bound being unknown of the switching function for the DSMC, an RDSMC is proposed to improve the control performance and further increase the robustness of the magnetic levitation system. In the RDSMC, an RENN estimator is used to estimate an unknown nonlinear function of lumped uncertainty online and replace the switching function in the hitting control of the DSMC directly. The adaptive learning algorithms that trained the parameters of the RENN online are derived using Lyapunov stability theorem. Furthermore, a robust compensator is proposed to confront the uncertainties including approximation error, optimal parameter vectors, and higher order terms in Taylor series. Finally, some experimental results of tracking the various periodic trajectories demonstrate the validity of the proposed RDSMC for practical applications.      

Reduced-order Generalized Proportional Integral Observer Based Continuous Dynamic Sliding Mode Control for Magnetic Levitation System with Time-varying Disturbances

In order to reduce the influence of time-varying disturbances for magnetic levitation system, we propose a reduced-order generalized proportional integral observer (RGPIO) based continuous dynamic sliding mode control scheme for magnetic levitation system in this paper. Unlike the popular extended state observer (ESO), it could deal with constant or slowing varying disturbances from theoretical point of view, the reduced-order generalized proportional integral observer (RGPIO) is designed to estimate the time-varying disturbances and system states, then the dynamic sliding mode surface is developed and deduce a continuous sliding mode controller (CSMC) for magnetic levitation system. Compared with ESO based continuous sliding mode controller, the proposed method not only ensures the position tracking accuracy, but also obtain better time-varying disturbance reject ability. Simulation and experimental results are also given to verify the effectiveness.

     

二阶动态滑模控制在磁悬浮控制系统中的应用

磁悬浮是典型的非线性、不稳定系统.为了实现其控制,本文采用了一种结合二阶滑模和动态滑模两种设计思想的二阶动态滑模控制器的设计方法,首先推导了磁悬浮系统的线性化状态空间模型;然后针对被控对象设计了二阶动态滑模控制器;最后与普通滑模控制器进行对比仿真试验.仿真结果表明,所设计的二阶动态滑模控制器在使小球快速稳定到达平衡点的同时,大大削弱了普通滑模控制器中存在的严重抖振现象.     

电液伺服系统的多滑模鲁棒自适应控制

针对一类参数与外负载非匹配不确定的非线性高阶系统,提出了一种基于逐步递推方法的多滑模鲁棒自适应控制策略.应用逐步递推的多滑模控制方法简化了高阶系统的控制问题,同时在自适应控制中加入鲁棒控制的方法,以消除不确定性对控制性能的影响.首先利用逐步递推方法与状态反馈精确线性化理论,得出确定系统的多滑模控制器设计方法;然后基于Lyapunov稳定性分析方法,给出不确定系统的参数自适应律,及鲁棒自适应控制器的设计方法.本文把该控制策略应用到电液伺服系统的位置跟踪控制中,仿真结果显示,该控制方法具有较强的鲁棒性及良好的跟踪效果.     

Nonlinear robust adaptive hierarchical sliding mode control approach for quadrotors

This paper exploits a nonlinear robust adaptive hierarchical sliding mode control approach for quadrotors subject to thrust constraint and inertial parameter uncertainty to accomplish trajectory tracking missions. Because of under‐actuated nature of the quadrotor, a hierarchical control strategy is available; and position and attitude loop controllers are synthesized according to adaptive sliding mode control projects, where adaptive updates with projection algorithm are developed to ensure bounded estimations for uncertain inertial parameters. Further, during the position loop controller development, an auxiliary dynamic system is introduced, and selection criteria for controller parameters are established to maintain the thrust constraint and to ensure the non‐singular requirement of command attitude extraction. It has demonstrated that, the asymptotically stable trajectory tracking can be realized by the asymptotically stable cascaded closed‐loop system and auxiliary dynamic system. Simulations validate and highlight the proposed control approach. Copyright © 2016 John Wiley & Sons, Ltd.     

Dynamic modelling and adaptive robust tracking control of a space robot with two-link flexible manipulators under unknown disturbances

In this paper, both the closed-form dynamics and adaptive robust tracking control of a space robot with two-link flexible manipulators under unknown disturbances are developed. The dynamic model of the system is described with assumed modes approach and Lagrangian method. The flexible manipulators are represented as Euler–Bernoulli beams. Based on singular perturbation technique, the displacements/joint angles and flexible modes are modelled as slow and fast variables, respectively. A sliding mode control is designed for trajectories tracking of the slow subsystem under unknown but bounded disturbances, and an adaptive sliding mode control is derived for slow subsystem under unknown slowly time-varying disturbances. An optimal linear quadratic regulator method is proposed for the fast subsystem to damp out the vibrations of the flexible manipulators. Theoretical analysis validates the stability of the proposed composite controller. Numerical simulation results demonstrate the performance of the closed-loop flexible space robot system.     

Inverse optimal sliding mode control of spacecraft with coupled translation and attitude dynamics

This paper proposes two robust inverse optimal control schemes for spacecraft with coupled translation and attitude dynamics in the presence of external disturbances. For the first controller, an inverse optimal control law is designed based on Sontag-type formula and the control Lyapunov function. Then a robust inverse optimal position and attitude controller is designed by using a new second-order integral sliding mode control method to combine a sliding mode control with the derived inverse optimal control. The global asymptotic stability of the proposed control law is proved by using the second method of Lyapunov. For the other control law, a nonlinear H_∞ inverse optimal controller for spacecraft position and attitude tracking motion is developed to achieve the design conditions of controller gains that the control law becomes suboptimal H_∞ state feedback control. The ultimate boundedness of system state is proved by using the Lyapunov stability theory. Both developed robust inverse optimal controllers can minimise a performance index and ensure the stability of the closed-loop system and external disturbance attenuation. An example of position and attitude tracking manoeuvres is presented and simulation results are included to show the performance of the proposed controllers.     

Output‐feedback tracking in causal nonminimum‐phase nonlinear systems using higher‐order sliding modes

Asymptotic output‐feedback tracking in a class of causal nonminimum phase uncertain nonlinear systems is addressed via sliding mode techniques. Sliding mode control is proposed for robust stabilization of the output tracking error in the presence of a bounded disturbance. The output reference profile and the unknown input/disturbance are supposed to be described by unknown linear exogenous systems of a given order. Local asymptotic stability of the output tracking error dynamics along with the boundedness of the internal states are proven. The unstable internal states are estimated asymptotically via the proposed multistage observer that is based on the method of extended system center. A higher‐order sliding mode observer/differentiator is used for the exact estimation of the input–output states in a finite time. The bounded disturbance is reconstructed asymptotically. A numerical example illustrates the efficiency of the proposed output‐feedback tracking approach developed for causal nonminimum phase nonlinear systems. Copyright © 2009 John Wiley & Sons, Ltd.     

Toward Aerial Grasping and Manipulation with Multiple UAVs

In this paper, a multiple UAVs control scheme is developed considering the full nonlinear position/orientation model of a j-Quadrotor system. A novel second order sliding mode controller is presented which guarantees exponential and robust tracking of admissible time-varying pose. The harmful chattering is not involved and no dynamic model is required to implement the controller to yield fast and precise tracking. Additionally, well-posed terminal and controlled time convergence allows an enforced contact at given pre-defined stable contact points at the same time. A stiffness control is proposed for grasping objects considering virtual linkages approach. Our approach yields high performance from the control system, in contrast to other simple controllers proposed for load carrying. In this sense, our advanced nonlinear control solves the apparent limitations imposed by the available technology from the viewpoint of the precise tracking control, and control of the inherent unstable underactuated dynamics, for frictionless contact points (neither rolling nor sliding are considered). A numerical simulation study, under various conditions, shows the numerical feasibility of the proposed approach.     

Robust Sliding Control of Robotic Manipulators Based on a Heuristic Modification of the Sliding Gain

A task space robust trajectory tracking control is developed for robotic manipulators. A second order linear model, which defines the desired impedance for the robot, is used to generate the reference position, velocity and acceleration trajectories under the influence of an external force. The control objective is to make the robotic manipulator’s end effector track the reference trajectories in the task space. A sliding mode based robust control is used to deal with system uncertainties and external perturbations. Thus, a sliding manifold is defined by a linear combination of the tracking errors of the system in the task space built from the difference between the real and the desired position, velocity and acceleration trajectories in comparison with previous works where the sliding manifold was defined by the desired impedance and the external force. Moreover, the ideal relay has been substituted by a relay with a dead-zone in order to fit in with the actual way in which a real computational device implements the typical sign function in sliding mode control. Furthermore, a higher level supervision algorithm is proposed in order to reduce the amplitude of the high frequency components of the output associated to an overestimation of the system uncertainty bounds. Then, the robust control law is applied to the case of a robot with parametric uncertainty and unmodeled dynamics. The closed-loop system is proved to be robustly stable with all signals bounded for all time while the control objective is fulfilled in practice. Finally, a simulation example which shows the usefulness of the proposed scheme is presented.     

Robust Tracking Control Of The Variable Stiffness Actuator Based On The Lever Mechanism

This paper is concerned with the design of a robust adaptive tracking control scheme for a class of variable stiffness actuators (VSAs) based on the lever mechanisms. For these VSAs based on the lever mechanisms, the AwAS‐II developed at Italian Institute of Technology (IIT) is chosen as the study object, and it is an enhanced version of the original realization AwAS (actuator with adjustable stiffness). Firstly, for the dynamic model of the AwAS‐II system in the presence of parametric uncertainties, unknown bounded friction torques, unknown bounded external disturbance and input saturation constraints, by using the coordinate transformations and the static state feedback linearization, the state space model of the AwAS‐II system with composite disturbances and input saturation constraints is transformed into an uncertain multiple‐input multiple‐output (MIMO) linear system with lumped disturbances and input saturation constraints. Subsequently, a combination of the feedback linearization, disturbance observer, sliding mode control and adaptive input saturation compensation law is adopted for the design of the robust tracking controller that simultaneously regulates the position and stiffness of the AwAS‐II system. Under the proposed controller, the semi‐global uniformly ultimately bounded stability of the closed‐loop system has been proved via Lyapunov stability analysis. Simulation results illustrate the effectiveness and the robustness of the proposed robust adaptive tracking control scheme.     

Robust adaptive fixed‐time tracking control of 6‐DOF spacecraft fly‐around mission for noncooperative target

The fixed‐time relative position tracking and attitude synchronization control problem of a spacecraft fly‐around mission for a noncooperative target in the presence of parameter uncertainties and external disturbances is investigated. Firstly, a novel and coupled relative position and attitude motion model for a noncooperative fly‐around mission is established. Subsequently, a novel nonsingular fast terminal sliding mode (NFTSM) surface is developed, and the explicit estimation of the convergence time independent of initial states is provided. Fair and systematic comparisons among several typical terminal sliding modes show that the designed NFTSM has faster convergence performance than the fast terminal sliding mode. Then, a robust integrated adaptive fixed‐time NFTSM control law with no precise knowledge of the mass and inertia matrix and disturbances by combining the nonsingular terminal sliding mode technique with an adaptive methodology is proposed, which can eliminate the chattering phenomenon and guarantee that the relative position and attitude tracking errors can converge into the small regions containing the origin in fixed time. Finally, numerical simulations are performed to demonstrate the effectiveness of the proposed control schemes.     

动态滑模控制及其在移动机器人输出跟踪中的应用

针对轮式移动机器人的输出跟踪问题,提出一种动态滑模控制方法,首先给出机器人的动力学简化模型,然后将其分解成两个低阶子系统,并给出其输出跟踪的动态滑模控制器设计方法,仿真试验表明该方法能明显地削弱滑模控制系统的抖振。     

Sliding Mode Disturbance Observer‐based Motion Control for a Piezoelectric Actuator‐based Surgical Device

This paper presents a sliding mode disturbance observer‐based motion tracking control methodology. In particular, the methodology is applied to control a semi‐automated hand‐held ear surgical device for the treatment of otitis media with effusion. The proposed control methodology is utilised to deal with the undesirable effects in the motion system, such as non‐linear dynamics, parametric uncertainties and external disturbances. It employs a proportional‐derivative control scheme together with a sliding mode disturbance observer for rejecting the undesirable effects. The stability of the proposed control methodology is proven theoretically and its effectiveness is evaluated experimentally. In addition, promising motion tracking experimental results are shown, and it can be observed that the proposed approach offers more robust performance for controlling the hand‐held surgical device and other similar instruments.     

Intelligent Integral Backstepping Sliding‐mode Control Using Recurrent Neural Network For Piezo‐flexural Nanopositioning Stage

In this study, an intelligent integral backstepping sliding‐mode control (IIBSMC) system using a recurrent neural network (RNN) is proposed for the three‐dimensional motion control of a piezo‐flexural nanopositioning stage (PFNS). First, the dynamic model of the PFNS is derived. Then, an integral backstepping sliding‐mode control (IBSMC) system is proposed for the tracking of the reference contours. The steady‐state response of the control system can be improved effectively due to the addition of the integrator in the IBSMC. Moreover, to relax the requirements of the bound and discard the switching function in the IBSMC, an IIBSMC system using an RNN estimator is proposed to improve the control performance and the robustness of the PFNS. The RNN estimator is proposed to estimate the lumped uncertainty, including the system parameters and external disturbance, online. Furthermore, the online tuning law for the training of the parameters of the RNN is derived using the Lyapunov stability theorem. In addition, a robust compensator is proposed to confront the minimum reconstructed error occurring in the IIBSMC system. Finally, some experimental results for the tracking of various contours are given to demonstrate the validity of the proposed IIBSMC system. From the performance measurements of the proportional‐integral control, sliding mode control, IBSMC, and IIBSMC systems, the proposed IIBSMC system has the lowest maximum, average, and standard deviation of the position tracking errors for three‐dimensional motion control of the PFNS.     

永磁直线同步电机的自适应Backstepping滑模控制研究

针对永磁直线同步电机(PMLSM)控制系统的不确定性因素,提出了自适应 Backstepping滑模控制器,实现运动跟踪。建立 PMLSM 系统模型,采用 Backstepping 设计,在滑模控制的基础上,基于 Lyapunov 函数设计自适应率,改善控制性能。仿真结果表明,系统具有稳定快速的跟踪性能,考虑实际系统中参数不确定性因素,控制器仍具有较强鲁棒性。     

A cascade control approach to active suspension using pneumatic actuators

Operators of forest machinery suffer from intensive whole body vibrations, which are big threats to their health. Therefore, it is important to investigate effective seat undercarriages and control methods for vibration reduction. This paper addresses the control problem of a novel seat undercarriage with pneumatic actuators customized for forest machinery. A two‐layer cascade control structure is developed, where the top layer consists of a group of proportional controllers to regulate the position of pneumatic actuators and the bottom layer is a sliding mode controller for force and stiffness tracking. The advantage of the sliding mode control is to achieve robust control performance with coarse system models. The paper demonstrates that the proposed control structure is better than a traditional PID controller. The robust stability of the sliding mode controller is proved by the Lyapunov's method. Experiments show its capability of reducing at least 20% amplitude of seat vibrations from 0.5 to 1 Hz.     

Robust control of multi‐axis magnetic bearing systems

This paper proposes robust control schemes for multi‐axis magnetic bearing systems under current control and voltage control. The control schemes are based on a model which characterizes not only the electromagnetic interaction but also secondary effects such as flux leakage, fringing fluxes, and finite core permeance in the magnetic bearing. In the current control case, a sliding‐mode‐based robust controller, whose control parameters have to be deliberately chosen to account for the uni‐directionality of magnetic forces, is proposed to provide robust performance against uncertain dynamics. In the voltage control case, a control scheme that combines the sliding methodology and the backstepping technique is used to provide robust performance under the influence of the electrical dynamics. It is demonstrated through simulations and experiments that, because the nonlinearity and the uncertainty inherently residing in the system behaviour are directly tackled, the proposed controllers achieve superior tracking performances compared to control lers based on linearization. Copyright © 2001 John Wiley & Sons, Ltd.     

Adaptive sliding mode control for discrete-time multi-input multi-output systems

In this paper, robust adaptive sliding mode tracking control for discrete-time multi-input multi-output systems with unknown parameters and disturbance is considered. The robust tracking controller is comprised of adaptive control and sliding mode control design. Bounded motion of the system around the sliding surface and stability of the global system in the sense that all signals remain bounded are guaranteed. If the disturbance and the reference signal are slowly varying with respect to the sampling frequency, the proposed sliding mode controller can reject the disturbance and output tracking can be approximately achieved. Simulation results are presented to illustrate the proposed approach.     

H∞ Control and Sliding Mode Control of Magnetic Levitation System

In this paper, H∞ disturbance attenuation control and sliding mode disturbance estimation and compensation control of a magnetic levitation system are studied. A magnetic levitation apparatus is established, and its model is measured. Then the system model is feedback linearized. A H∞ controller is then designed. For comparison, a sliding mode controller and a PID controller also were designed. Some experiments were performed to compare the performance of the H∞ controller, the sliding mode controller and the PID controller.