A composite controller for trajectory tracking applied to the Furuta pendulum

In this paper, a new composite scheme is proposed, where the total control action is composed of the sum of a feedback-linearization-based controller and an energy-based compensation. This new proposition is applied to the rotary inverted pendulum or Furuta pendulum. The Furuta pendulum is a well-known underactuated mechanical system with two degrees of freedom. The control objective in this case is the tracking of a desired periodic trajectory in the actuated joint, while the unactuated link is regulated at the upward position. The closed-loop system is analyzed showing uniformly ultimately boundedness of the error trajectories. The design procedure is shown in a constructive form, such that it may be applied to other underactuated mechanical systems, with the proper definitions of the output function and the energy function. Numerical simulations and real-time experiments show the practical viability of the controller. Finally, the proposed algorithm is compared with a tracking controller previously reported in the literature. The new algorithm shows better performance in both arm trajectory tracking and pendulum regulation.     

Robust stabilization of underactuated nonlinear systems: A fast terminal sliding mode approach

This paper presents a fast terminal sliding mode based control design strategy for a class of uncertain underactuated nonlinear systems. Strategically, this development encompasses those electro-mechanical underactuated systems which can be transformed into the so-called regular form. The novelty of the proposed technique lies in the hierarchical development of a fast terminal sliding attractor design for the considered class. Having established sliding mode along the designed manifold, the close loop dynamics become finite time stable which, consequently, result in high precision. In addition, the adverse effects of the chattering phenomenon are reduced via strong reachability condition and the robustness of the system against uncertainties is confirmed theoretically. A simulation as well as experimental study of an inverted pendulum is presented to demonstrate the applicability of the proposed technique.     

An improved backstepping design for the control of an underactuated inverted pendulum

This paper presents an improved backstepping design (IBD) for the control of a new type of underactuated inverted pendulum. The characteristics and possible applications of the inverted pendulum are presented. Nonlinear models and a linearized model are given for a straightforward explanation of its dynamic features. The conventional backstepping design (CBD) is revisited for this plant. The IBD is then used to reduce the complexity of the design and to allow the specification of transient characteristics, to improve the system’s performance. Experimental studies are conducted to investigate the effectiveness of the proposed scheme.     

Linear control of the flywheel inverted pendulum

The flywheel inverted pendulum is an underactuated mechanical system with a nonlinear model but admitting a linear approximation around the unstable equilibrium point in the upper position. Although underactuated systems usually require nonlinear controllers, the easy tuning and understanding of linear controllers make them more attractive for designers and final users. In a recent paper, a simple PID controller was proposed by the authors, leading to an internally unstable controlled plant. To achieve global stability, two options are developed here: first by introducing an internal stabilizing controller and second by replacing the PID controller by an observer-based state feedback control. Simulation and experimental results show the effectiveness of the design.     

基于微分平坦的旋转倒立摆双闭环抗扰 PID 控制

针对一类不稳定、欠驱动二自由度旋转倒立摆系统, 提出一种基于微分平坦的双闭环抗扰 PID 控制方法。 首先, 建立倒 立摆的非线性动力学模型, 利用近似线性化分析系统的不稳定零动态与非最小相位特性; 然后, 结合微分平坦理论, 设计倒立摆 平坦输出,重构系统平坦状态, 并建立平坦状态与角度输出之间的转化关系,克服倒立摆的非最小相位影响; 进一步, 针对微分 平坦系统, 设计抗扰 PID 双闭环控制结构和带宽化调节方法, 在主动抗扰机制下实现对摆杆角度与悬臂角度的精准控制; 最后, 通过仿真与实验, 验证所提方法的有效性和实用性。 所提方法为欠驱动系统提供了一种结构简单、抗扰能力强的控制方案。     

Nonlinear state feedback controller design for underactuated mechanical system: A modified block backstepping approach

This paper presents the formulation of a novel block-backstepping based control algorithm to address the stabilization problem for a generalized nonlinear underactuated mechanical system. For the convenience of compact design, first, the state model of the underactuated system has been converted into the block-strict feedback form. Next, we have incorporated backstepping control action to derive the expression of the control input for the generic nonlinear underactuated system. The proposed block backstepping technique has further been enriched by incorporating an integral action additionally for enhancing the steady state performance of the overall system. Asymptotic stability of the overall system has been analyzed using Lyapunov stability criteria. Subsequently, the stability of the zero dynamics has also been analyzed to ensure the global asymptotic stability of the entire nonlinear system at its desired equilibrium point. The proposed control algorithm has been applied for the stabilization of a benchmarked underactuated mechanical system to verify the effectiveness of the proposed control law in real-time environment.     

三级倒立摆系统全程滑模变结构控制

提出了一种基于全程滑模的变结构控制方法对具有单控制输入的三级倒立摆系统进行平衡控制的综合设计和成功的实验研究.该方法使得倒立摆系统从初始时刻开始就运行在滑模面上,从而使系统具有较强的鲁棒性.实验结果证明了该控制方法的有效性和可行性.     

Optimal Motion Planning for Differentially Flat Underactuated Mechanical Systems

Underactuated mechanical system has less independent inputs than the degrees of freedom(DOF) of the mechanism. The energy efficiency of this class of mechanical systems is an essential problem in practice. On the basis of the sufficient and necessary condition that concludes a single input nonlinear system is differentially flat, it is shown that the flat output of the single input tmderactuated mechanical system can be obtained by finding a smooth output function such that the relative degree of the system equals to the dimension of the state space. If the fiat output of the underactuated system can be solved explicitly, and by constructing a smooth curve with satisfying given boundary conditions in flat output space, an energy efficiency optimization method is proposed for the motion planning of the differentially fiat underactuated mechanical systems. The inertia wheel pendulum is used to verify the proposed optimization method, and some numerical simulations show that the presented optimal motion planning method can efficaciously reduce the energy cost for given control tasks.     

基于LQR的直线一级倒立摆最优控制系统研究

从理论和实践上对直线一级倒立摆作了深入的研究.用牛顿-欧拉方法建立了倒立摆的数学模型,在此基础上采用线性二次型最优控制方法设计了倒立摆的控制器.通过固高公司GLIP2003倒立摆系统验证了设计结果,并达到较好的控制效果.     

基于ADAMS和MATLAB的双回路PID控制倒立摆联合仿真

倒立摆系统是典型的快速、多变量、非线性、绝对不稳定系统,是检验各种控制理论的理想模型。研究了倒立摆系统的构成并建立了数学模型,针对摆杆角度和小车位移两个输出量采用双回路PID控制并设计了PID控制器,在ADAMS软件中建立了倒立摆系统的机械模型,在MATLAB软件中建立了控制模型,通过接口实现了双回路PID控制倒立摆的联合仿真。文中方法直接从ADAMS中产生机械系统仿真模型,避免了推导、列写较复杂的方程描述机械系统,大大简化了建模过程,而且能够更直观地观察仿真结果。     

基于SIRM的倒立摆模糊控制器

探讨了倒立摆控制中的一些方法和应用，指出了通常模糊控制规则过于复杂的问题，设计了基于SIRM(单输入规则模块)的模糊控制器，既解决了模糊控制规则复杂的问题，又实现了倒立摆的快速稳定。最后，通过仿真验证了控制系统的效果。     

Online payload estimation for the control of underactuated mechanical systems

This paper presents a payload estimation scheme for underactuated robotic manipulators with passive joints that are not driven by actuators. In the proposed scheme, only the payload, which can be quite uncertain when a robot performs various tasks, is estimated, because the manipulator’s electrical and other mechanical parameters are generally known in advance. In comparison to other adaptive schemes for underactuated robotic manipulators, the proposed scheme produces satisfactory transient performance and also reduces the computational burden in real-time implementation. The proposed estimation law is also based on the theory of Variable Structure Systems. In contrast to existing adaptation laws that have an integral form, the proposed law estimates uncertain payload using lowpass filtering of a switching signal that is always bounded, which avoids the parameter-drifting problem that is often encountered when using the previous integral laws. Real-time experiments are conducted using an inverted pendulum and the experimental results demonstrate the feasibility and effectiveness of the proposed scheme.     

Stabilization and tracking control of X-Z inverted pendulum with sliding-mode control

X-Z inverted pendulum is a new kind of inverted pendulum which can move with the combination of the vertical and horizontal forces. Through a new transformation, the X-Z inverted pendulum is decomposed into three simple models. Based on the simple models, sliding-mode control is applied to stabilization and tracking control of the inverted pendulum. The performance of the sliding mode control is compared with that of the PID control. Simulation results show that the design scheme of sliding-mode control is effective for the stabilization and tracking control of the X-Z inverted pendulum.     

Vibrational control of underactuated mechanical systems control design through averaging analysis

An open loop vibrational control for an underactuated mechanical system with amplitude and frequency modulation is investigated. Since there is no direct external input to an unactuated joint, the dynamic coupling between the actuated and unactuated joint is utilized for controlling the unactuated joint. Feedback linearization has been performed to fully incorporate the known nonlinearities of the underactuated system considered. The actuated joints are firstly positioned to their desired locations, and then periodic oscillatory inputs are applied to the actuated joints to move the remaining unactuated joints to their target positions. The amplitudes and frequencies of the vibrations introduced are determined through averaging analysis. A systematic way of obtaining an averaged system for the underactuated system via a coordinate transformation is developed. A manipulator in the zero gravity space can be vibrationally controlled in the event of actuator failure. A control design example of the 2R planar manipulator with a free joint with no brake is provided.     

A state observer for the Virgo inverted pendulum

We report an application of Kalman filtering to the inverted pendulum (IP) of the Virgo gravitational wave interferometer. Using subspace method system identification techniques, we calculated a linear mechanical model of Virgo IP from experimental transfer functions. We then developed a Kalman filter, based on the obtained state space representation, that estimates from open loop time domain data, the state variables of the system. This allows the observation (and eventually control) of every resonance mode of the IP mechanical structure independently.     

基于MATLAB的倒立摆LQR控制方法的研究

在忽略掉倒立摆系统本身自然不稳定因素以及摩擦阻力的影响后,倒立摆系统就成了一个典型的运动刚体系统,利用在惯性坐标系内的经典力学理论建立系统的动力学方程,采用力学分析方法建立直线型一级倒立摆的数学模型。结果证明,基于牛顿力学定律的数学建模方法,应用二次型最优控制理论对一级倒立摆实现控制,并能满足控制系统的稳定性和鲁棒性,用MATLAB进行仿真,并对仿真试验结果进行了分析研究。     

Dynamics synthesis and control for a hopping robot with articulated leg

To investigate the design and the applications of elastic underactuated mechanisms for improving the energy efficiency of dynamic mechanical systems, the dynamics and control of a one-legged hopping robot with articulated leg is studied in this paper. To ensure the controllability of the elastic underactuated mechanism, a dynamics synthesis method is proposed for designing the underactuated mechanism so that the dynamics of the system can be transformed into the strict feedback normal form. To improve the energy efficiency of the one-legged locomotion system, an optimal motion planning method is presented to optimize the trajectories of the robot joints. A nonlinear controller is proposed to stabilize the hopping robot to its balance configuration in stance phase, and a switched linear controller is proposed to stabilize the continuous hopping movement. The stability of the presented controllers is analyzed in theory and verified by some numerical simulations.     

基于视觉伺服的倒立摆实验平台的研究

基于视觉伺服的倒立摆系统可为机器视觉和智能控制领域的研究提供一个很好的实验平台。对该实验平台的视觉采集系统、运动控制系统和系统软件结构进行了详细的介绍，对各组成部分的功能和设计原理进行了具体的说明。     

倒立摆系统的分段变结构自举控制

首先给出了倒立摆系统的精确数学模型,然后通过分段变结构控制使摆杆摆起并达到最终平衡状态.在第1阶段,采用继电控制使摆杆平稳快速摆起;当摆杆摆动到平衡位置附近时切换到第2阶段,即采用李雅普诺夫直接法设计的变结构控制器,并通过饱和函数削弱变结构控制系统的抖振,实现对倒立摆的稳定控制.最后通过计算机仿真表明,变结构控制策略和控制算法良好地实现了一级倒立摆系统的自举控制,同时也证明了变结构控制方法在非线性系统控制方面的应用价值.     

Inverted pendulum control with allowance for energy dissipation

The behavior of an inverted pendulum hinged on the wheel axis is studied. An algorithm is proposed for solving both the problem of pendulum stabilization in a given position relative to the vertical and the problem of controlling the velocity of the platform on which the pendulum is located under conditions of energy dissipation. Recommendations on choosing control system parameters are given, and the time of transitional processes is estimated.