Control of a Class of Underactuated Mechanical Systems Using Sliding Modes

In this paper, we present a sliding mode control algorithm to robustly stabilize a class of underactuated mechanical systems that are not linearly controllable and violate Brockett's necessary condition for smooth asymptotic stabilization of the equilibrium, with parametric uncertainties. In defining the class of systems, a few simplifying assumptions are made on the structure of the dynamics; in particular, the damping forces are assumed to be linear in velocities. We first propose a switching surface design for this class of systems, and subsequently, a switched algorithm to reach this surface in finite time using conventional and higher order sliding mode controllers. The stability of the closed-loop system is investigated with an undefined relative degree of the sliding functions. The controller gains are designed such that the controller stabilizes the actual system with parametric uncertainty. The proposed control algorithm is applied to two benchmark problems: a mobile robot and an underactuated underwater vehicle. Simulation results are presented to validate the proposed scheme.     

Sliding Mode Control for Swing‐Up and Stabilization of the Cart‐Pole Underactuated System

This paper uses sliding mode control to accomplish the objectives of swing‐up and stabilization of the cart‐pole underactuated system. The features of underactuated systems prohibit direct application of conventional sliding mode control for fully‐actuated systems. In this paper, we design a novel sliding mode control for the cart‐pole underactuated system so that the control goals can be achieved. In addition, by simply changing the parameters of the sliding surface, we use only one sliding mode control scheme to swing up and to stabilize the cart‐pole system. Using the sliding mode dynamics and the internal dynamics, we show that the proposed sliding mode control can swing up the cart‐pole system from the stable equilibrium and can stabilize the system to the unstable equilibrium. Our simulation results on a cart‐pole system demonstrate the feasibility of the proposed sliding mode control. The proposed control schemes, the stability analysis, and the numerical simulation provide a useful guideline for designing the sliding mode control for the cart‐pole underactuated system.     

Robust Backstepping Control Based on Integral Sliding Modes for Tracking of Quadrotors

Modern non-inertial robots are usually underactuated, such as fix or rotary wing Unmanned Aerial Vehicles (UAVs), underwater or nautical robots, to name a few. Those systems are subject to complex aerodynamic or hydrodynamic forces which make the dynamic model more difficult, and typically are subject to bounded smooth time-varying disturbances. In these systems, it is preferred a formal control approach whose closed-loop system can predict an acceptable performance since deviations may produce instability and may lead to catastrophic results. Backstepping provides an intuitive solution since it solves underactuation iteratively through slaving the actuated subsystem so as to provide a virtual controller in order to stabilize the underactuated subsystem. However it requires a full knowledge of the plant and derivatives of the state, which it is prone to instability for any uncertainty; and although robust sliding mode has been proposed, discontinuities may be harmful for air- or water-borne nonlinear plants. In this paper, a novel robust backstepping-based controller that induces integral sliding modes is proposed for the Newton–Euler underactuated dynamic model of a quadrotor subject to smooth bounded disturbances, including wind gust and sideslip aerodynamics, as well as dissipative drag in position and orientation dynamics. The chattering-free sliding mode compensates for persistent or intermittent, and possible unmatched state dependant disturbances with reduced information of the dynamic model. Representative simulations are presented and discussed.     

Double Closed-loop Integral Terminal Sliding Mode for a Class of Underactuated Systems Based on Sliding Mode Observer

Aiming to solve the tracking control problem of a class of second-order underactuated mechanical systems with unknown model parts, external disturbances and noise disturbances, a double closed-loop layered integral terminal sliding mode control method based on sliding mode observer is proposed. At the outset, the Lagrange model of the system is transformed into an affine model, and a sliding mode observer is designed according to the system structure. Neatly, the outer loop controller is designed using the observer’s estimated state, and the output value of the outer loop controller is filtered with a low pass filter. Then the inner loop controller is designed by using hierarchical sliding mode control method. On a premise of ensuring tracking performance, the control method can maximally improve convergence speed and reduce chattering even if there are unknown model parts, external interference and noise interference phenomena in the system. This simulation results distinctly display the effectiveness of the control tactics.     

欠驱动刚体航天器姿态机动滑模控制研究

针对欠驱动刚体航天器的姿态机动控制问题,提出一种滑模变结构姿态控制器的设计方法.首先给出3轴稳定的欠驱动航天器姿态动力学和运动学模型,分析其模型特点;然后,设计了欠驱动刚体航天器的渐近稳定滑模控制律,并证明了其李雅普诺夫意义下的全局渐近稳定性.最后的仿真结果表明,该方法能够有效实现欠驱动航天器的姿态控制,且系统具有全局稳定性和鲁棒性.     

水平欠驱动机械臂的反步自适应滑模控制

针对二自由度水平欠驱动机械臂系统,提出了基于分层滑模控制思想的反步自适应滑模控制方法．该方法能够在不对系统状态模型进行复杂坐标变换,并且没有约束方程限制的前提下实现对欠驱动系统的反馈滑模控制．仿真结果表明了该方法的有效性,而且优化后的控制器具有较好的适应性和控制效果．     

基于离散滑模预测的欠驱动AUV三维航迹跟踪控制

针对欠驱动自主水下航行器（AUV）的模型不确定和外界海流干扰问题,为了实现欠驱动AUV的三维航迹跟踪控制,采用虚拟向导法建立空间运动误差离散化模型.基于递归滑模思想设计离散滑模预测控制器,利用滚动优化和反馈校正方法补偿了不确定项对滑模预测模型的影响.最后针对某欠驱动AUV进行了空间曲线跟踪控制仿真实验.结果表明,所设计的控制器可以较好地克服时变非线性水动力阻尼对系统的影响,并对外界海流干扰有较好的抑制作用,保证了欠驱动AUV三维航迹跟踪系统的鲁棒性,实现了三维航迹的精确跟踪.     

欠驱动RTAC的滑模自抗扰镇定控制

针对欠驱动RTAC (rotational/translational actuator)的镇定问题,提出了一种滑模自抗扰控制方法,通过对总扰动的观测和补偿降低了未知扰动对RTAC的影响.为克服RTAC的欠驱动特性,所提方法通过将可驱动的摆球角度和无驱动的小车位置两个状态相结合,构建出虚拟被控量作为系统输出,从而使RTAC的动力学模型转换为非欠驱动模型.基于重建的模型设计线性扩张状态观测器(linear extended state observer, LESO)和滑模控制器,并采用Lyapunov方法证明RTAC的闭环稳定性,实现了RTAC的镇定控制,有效抑制了小车的振荡.最后,通过数值仿真和硬件实验验证了所提控制方法的有效性,与已有方法的对比分析证明该方法具有良好的控制性能.     

Control algorithms for stabilizing underactuated robots

Three control algorithms are developed to stabilize an underactuated two-link robot at its unstable inverted position. The well-known linear quadratic regulator is described first. Next, a stabilization control law using partial feedback linearization is developed where the reference trajectories for the linearized degrees of freedom are designed by analyzing the zero dynamics. The linear quadratic regulator and partial feedback linearization control algorithms both assume an exact dynamic model. To deal with modeling inaccuracies, a robust controller using sliding mode concepts is supplied. Numerical simulations are presented. © 1998 John Wiley & Sons, Inc.     

Adaptive Proportional-Derivative Sliding Mode Control Law With Improved Transient Performance for Underactuated Overhead Crane Systems

In this paper, an adaptive proportional-derivative sliding mode control (APD-SMC) law, is proposed for 2D underactuated overhead crane systems. The proposed controller has the advantages of simple structure, easy to implement of PD control, strong robustness of SMC with respect to external disturbances and uncertain system parameters, and adaptation for unknown system dynamics associated with the feedforward parts. In the proposed APD-SMC law, the PD control part is used to stabilize the controlled system, the SMC part is used to compensate the external disturbances and system uncertainties, and the adaptive control part is utilized to estimate the unknown system parameters. The coupling behavior between the trolley movement and the payload swing is enhanced and, therefore, the transient performance of the proposed controller is improved. The Lyapunov techniques and the LaSalle's invariance theorem are employed in to support the theoretical derivations. Experimental results are provided to validate the superior performance of the proposed control law.      

Globally Stabilizing a Class of Underactuated Mechanical Systems on the Basis of Finite-Time Stabilizing Observer

Globally exponentially stabilizing a class of underactuated mechanical systems (UMS) with nonaffine nonlinear dynamics is investigated in this paper. The considered UMS has a nonaffine nonlinear subsystem that can be globally asymptotically stabilized by saturated feedbacks, but the saturated feedback cannot be analytically expressed in closed-form. This obstacle limits the real-time applications of most controllers presented in literatures. In this paper, a hybrid feedback strategy is presented to globally exponentially stabilize the UMS with nonaffine and strict-feedback canonical forms. The hybrid feedback strategy is characterized by the composition of partial states feedback and partial virtual outputs feedback based on a higher-order finite-time stabilizing observer. The presented hybrid feedback controller can be synthesized by applying Lyapunov stability theory. Some numerical simulations associated with two underactuated nonlinear systems, the Acrobot system and the Inertia-Wheel-Pendulum (IWP) system, are employed to demonstrate the effectiveness of the proposed controller. The presented control strategy can be applied in real time, thus providing a new feasible dynamic model other than the differential flatness systems for synthesizing the mechanical systems of general underactuated legged robots.     

FTESO‐Based Finite Time Control for Underactuated System Within a Bounded Input

Finite time control problem is investigated for a class of underactuated systems with uncertainties and external disturbances. For the sake of expanding control region furthest within a bound input, finite time extended state observer (FTESO) and a novel adaptive terminal sliding mode (ATSM) controller are applied to improve the stability performance of system. Compared to the general extended state observer (ESO), FTESO makes use of fractional powers to reduce the estimation errors to zero in finite time. The coordinate transformation is made for more degrees of design freedom. Rigorous analysis of finite time convergence results has been performed through Lyapunov theory and sufficient conditions are provided for the observer/controller‐design. Finally, simulation results on the Rotating Inverted Pendulum are given to demonstrate the effectiveness of the proposed controller and observer.     

Discrete sliding mode control to stabilize running of a biped robot with compliant kneed legs

This paper investigates performance of two event-based controllers applied to an underactuated biped robot to stabilize its running gait in presence of uncertainties. Mechanism of the biped robot includes four links leg, one point mass at the hip, point feet, and three motors parallel to rotational springs. So it has one degree of underactuation during stance phase and three degrees of underactuation during flight phase. A discrete sliding mode controller (DSMC) in comparison with a discrete linear-quadratic regulator (DLQR) is examined in order to stabilize the fixed point of the corresponding Poincare map. Using numerical simulations, it is concluded that DSMC has a better performance regarding basin of attraction and convergence speed compared to DLQR, especially in presence of disturbances.     

Two relay controller for real time trajectory generation and its application to inverted orbital stabilization of inertia wheel pendulum via quasi‐continuous HOSM

A quasi‐continuous high‐order sliding mode (QC‐HOSM) control is developed to solve the tracking control problem for an inertia wheel pendulum. A first step towards the solution of the tracking control problem in underactuated systems is to find the set of reference trajectories. A reference model based on the two relay controller idea is then developed for generating a set of desired periodic trajectories for the pendulum centered at its upright position. The two relay controller produces oscillations at the scalar output of the reference underactuated system where the desired amplitude and frequency are reached by choosing its gains. The HOSM will be capable of making the pendulum move, tracking the prescribed reference signals determined by the trajectory generator. Performance issues of the controller constructed are illustrated in an experimental study. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Control for Underactuated Systems Using Sliding Mode Observer

In this work, first we estimate all the system’s state vector, with guarantied precision, for a category of second order underactuated mechanical systems (UMS), exploiting the triangular observer (TO) model that suits to the structure of these systems. Then we propose a sliding mode controller (SMC). The latter uses the estimated states given by the observer. The underactuated system is decomposed into two subsystems, where the sliding surface is constructed in two levels for each subsystem. The proposed controller guaranties the tracking performances, with minimization of chattering phenomenon, due to the constructed observer, even for system with uncertainties. Simulation results show the effectiveness of this strategy of control.

     

欠驱动航天器相对运动的姿轨耦合控制

针对欠驱动的非对称航天器设计六自由度相对运动的姿轨耦合控制器.首先,给出用对偶四元数描述的六自由度相对运动模型;然后,基于矩阵广义逆和空控制向量提出广义的滑模控制器,以实现相对姿态欠驱动控制的渐近稳定;最后,考虑姿轨耦合特性,利用高斯伪谱法和非线性规划得到相对轨道运动能量最省的轨迹,进而利用滑模变结构控制实现对该轨迹的跟踪.仿真结果表明,所提出的方法是有效和可行的,而且较其他方法消耗的能量更少.     

Design of uncertain multi-input systems with state delay and input deadzone nonlinearity via sliding mode control

The problem of robust stabilization of a class of uncertain multi-input time-delayed systems with deadzone nonlinearity in the actuator is considered. To achieve a stable uncertain multi-input system, sliding mode control (SMC) is adopted in the controller design. The proposed controller guarantees the global reaching condition of the sliding mode in the uncertain multi-input system. In the sliding mode, the investigated time-delayed systems with deadzone nonlinearity still possess the insensitivity to the uncertainties and/or disturbances, which can be seen in the systems with linear inputs. In addition, the proposed controller can work effectively for systems no matter whether sector nonlinearity and/or deadzone exists in the actuator or not. However, such property cannot be obtained by the controller design through traditional SMC for the systems without input nonlinearity. Besides, the traditional SMC controller might produce limit cycles once the system contains deadzone in the input. Furthermore, the presented controller ensures the system trajectories globally exponentially converged in the sliding mode. Finally, two examples are illustrated to demonstrate the effectiveness of the proposed sliding mode controller.     

二维完整配置下刚性航天器姿态角速度的渐近镇定

讨论了以非完整配置的单向推力器系统为执行机构时,刚性航天器姿态角速度的镇 定问题.针对一类特殊的有扰量非完整配置的情况--共面扰量二维完整配置,基于滑动控 制律实现了姿态角速度的镇定.仿真结果证实了所述方法的有效性.     

一种新的自适应模糊滑模控制器设计方法

对一类非线性系统提出一种新的自适应模糊滑模控制器设计方法。将自适应模糊控制与滑模控制有效地结合在一起,先用滑模控制使跟踪误差进入边界层内,然后启动自适应模糊控制器。该控制器可消除滑模控制器中出现的抖振,并可在存在模糊逻辑系统逼近误差情况下使系统跟踪误差小于预先给定的任意常数。仿真算例验证了所提出方法的有效性。