Stabilization of the Furuta pendulum around its homoclinic orbit

We present an energy based control approach to control the Furuta pendulum. A controller is proposed for swinging the pendulum and raise it to its uppermost unstable equilibrium position. The passivity properties of the system are used as a guideline in the control strategy. The stability analysis is carried out by using a Lyapunov technique.     

A nonlinear hybrid controller for swinging-up and stabilizing the Furuta pendulum

The conventional switching strategy for solving the inverted pendulum control problem is based on two steps: swinging-up and stabilization. In this note, first, a new strategy for swinging the Furuta pendulum up towards the desired upright position is designed using the Speed-Gradient method, which uses only directly measured coordinates. Then, a nonlinear controller, based on the Forwarding approach, stabilizes the upright position. As a new contribution the latter leads to a nonlinear stabilizer around the upright position, whose Lyapunov function yields a larger size estimation of the domain of attraction than the one obtained with the traditional linear approach. This estimation allows us to use it in a global switching strategy in the practical implementation and guarantees almost-global asymptotic stability of the equilibrium. Successful experimental results are reported with the available laboratory Furuta pendulum.     

Nonlinear controller tuning based on a sequence of identifications of linearized time-varying models

A novel algorithm for tuning controllers for nonlinear plants is presented. The algorithm iteratively minimizes a criterion of the control performance. In each iteration one experiment is performed with a reference signal slightly different from the previous reference signal. The input–output signals of the plant are used to identify a linear time-varying model of the plant which is then used to calculate an update of the controller parameters. The algorithm requires an initial feedback controller that stabilizes the closed loop for the desired reference signal and in its vicinity, and that the closed-loop outputs are similar for the previous and current reference signals. The tuning algorithm is successfully tested on a laboratory set-up of the Furuta pendulum.     

基于快速起摆的Furuta摆切换控制系统

针对由一个驱动臂和一个未驱动摆杆组成的欠驱动Furuta摆系统,设计了实现其稳定的切换控制系统.控制任务是将未驱动摆杆稳定在上方不稳定平衡点的同时,将驱动臂控制到零点,分为两部分:首先基于部分反馈线性化技术设计一个饱和的状态反馈控制器,将摆杆快速控制到上方不稳定平衡点附近;然后切换到一个线性的全状态反馈控制器,实现系统的稳定控制.仿真实验验证了控制器的有效性.     

鲁棒H-状态反馈控制

本文对结构参数不确定线性定常多变量系统的鲁棒Ｈ∞状态反馈设计问题进行了研究，给出了系统鲁棒稳定和干扰衰减的条件，及相应的鲁棒Ｈ∞状态反馈设计方法，并用这种方法设计了一个倒立摆平衡控制器。仿真结果表明，与ＬＱ设计方法相比，按本文所提出的设计方法得到的控制器具有鲁棒稳定能力强、闭环动态性能良好等优点。     

Virtual-Holonomic-Constraints-Based Design of Stable Oscillations of Furuta Pendulum: Theory and Experiments

The Furuta pendulum consists of an arm rotating in the horizontal plane and a pendulum attached to its end. Rotation of the arm is controlled by a DC motor, while the pendulum is moving freely in the plane, orthogonal to the arm. Motivated, in particular, by possible applications for walking/running/balancing robots, we consider the Furuta pendulum as a system for which synchronized periodic motions of all the generalized coordinates are to be created and stabilized. The goal is to achieve, via appropriate feedback control action, orbitally exponentially stable oscillations of the pendulum of various shapes around its upright and downward positions, accompanied with oscillations of the arm. Our approach is based on the idea of stabilization of a particular virtual holonomic constraint imposed on the configuration coordinates, which has been theoretically developed recently. Here, we elaborate on the complete design procedure. The results are illustrated not only through numerical simulations but also through successful experimental tests.     

Nearly optimal neural network stabilization of bipedal standing using genetic algorithm

In this work, stability control of bipedal standing is investigated. The biped is simplified as an inverted pendulum with a foot-link. The controller consists of a general regression neural network (GRNN) feedback control, which stabilizes the inverted pendulum in a region around the upright position, and a PID feedback control, which keeps the pendulum at the upright position. The GRNN controller is also designed to minimize an energy-related cost function while satisfying the constraints between the foot-link and the ground. The optimization has been carried out using the genetic algorithm (GA) and the GRNN is directly trained during optimization iteration process to provide the closed loop feedback optimal controller. The stability of the controlled system is analyzed using the concept of Lyapunov exponents, and a stability region is determined. Simulation results show that the controller can keep the inverted pendulum at the upright position while nearly minimizing an energy-related cost function and keeping the foot-link stationary on the ground. The work contributes to bipedal balancing control, which is important to the development of bipedal robots.     

惯性轮倒立摆的鲁棒镇定

用一个时滞状态反馈控制律镇定惯性轮倒立摆,不仅保证闭环系统全局渐近稳定,还允许闭环系统承受一定的时滞.将惯性轮倒立摆转化为存在高阶非线性的4维积分器链,然后设计一个明确规定了饱和度和时滞参数的饱和控制律.用简单方式证明了闭环的全局渐近稳定性.仿真表明设计是有效的.     

An Output Feedback Position/Speed Regulator for a Torque—driven Inertia Wheel Pendulum

This paper presents a position/speed regulator for a torque–driven inertia wheel pendulum where only position measurements are available for feedback. Our contribution is to introduce a controller that does not need joint velocity measurements, and instead it uses the output of a linear filtering of weighted joint position errors to add damping. The proposed controller allows bringing the nonactuated pendulum rod towards its upright position, while the wheel spins asymptotically to a desired constant speed. A complete stability analysis based on Barbashin–Krasovskii’s theorem is presented together with an estimate of domain of attraction. Simulation results upon a torque–driven inertia wheel pendulum model illustrate the performance of the proposed controller.

     

Generating self-excited oscillations for underactuated mechanical systems via two-relay controller

A tool for the design of a periodic motion in an underactuated mechanical system via generating a self-excited oscillation of a desired amplitude and frequency by means of the variable structure control is proposed. First, an approximate approach based on the describing function method is given, which requires that the mechanical plant should be a linear low-pass filter–the hypothesis that usually holds when the oscillations are relatively fast. The method based on the locus of a perturbed relay systems provides an exact model of the oscillations when the plant is linear. Finally, the Poincaré map's design provides the value of the controller parameters ensuring the locally orbitally stable periodic motions for an arbitrary mechanical plant. The proposed approach is shown by the controller design and experiments on the Furuta pendulum.     

A novel criterion for nonlinear time-delay systems using LMI fuzzy Lyapunov method

This study presents a kind of fuzzy robustness design for nonlinear time-delay systems based on the fuzzy Lyapunov method, which is defined in terms of fuzzy blending quadratic Lyapunov functions. The basic idea of the proposed approach is to construct a fuzzy controller for nonlinear dynamic systems with disturbances in which the delay-independent robust stability criterion is derived in terms of the fuzzy Lyapunov method. Based on the robustness design and parallel distributed compensation (PDC) scheme, the problems of modeling errors between nonlinear dynamic systems and Takagi–Sugeno (T–S) fuzzy models are solved. Furthermore, the presented delay-independent condition is transformed into linear matrix inequalities (LMIs) so that the fuzzy state feedback gain and common solutions are numerically feasible with swarm intelligence algorithms. The proposed method is illustrated on a nonlinear inverted pendulum system and the simulation results show that the robustness controller cannot only stabilize the nonlinear inverted pendulum system, but has the robustness against external disturbance.     

Parametric Stabilization of Quantized Interconnected Systems with Application to Coupled Inverted Pendulums

This paper studies the analysis of parametric stability and decentralized state feedback control of a kind of quantized interconnected systems. The output of each controller is quantized logarithmically before it is input to the subsystem, and the quantized density would affect the stability of the systems. First, a decentralized state feedback controller is designed for interconnected systems without quantization and the corresponding stable region is obtained. Second, for a given controller, the lower bound of the quantization density is evaluated from parameters of local controllers. Finally, the proposed method is applied to coupled inverted pendulums systems which can be viewed as quantized interconnected systems. The simulation results show that by using the proposed quantized controllers, the interconnected inverted pendulum systems are parametrically stabilized.     

Takagi-Sugeno模糊控制器仿真与稳定性分析

模糊集理论首先由美国学者Zadeh教授提出,在控制工程、家用电器等方面有诸多应用。本文对T-S模糊模型,针对连续系统介绍了一种基于状态反馈模糊控制器的设计方法。同时给出T-S模糊控制器应用于单倒立摆系统的一个实例,并用文中的稳定性分析方法分析它的系统稳定性。并用Matlab软件对基于该模糊系统模型的模糊控制器作仿真分析,从系统响应曲线上可以说明该系统的稳定性。     

基于性能协调的平面二级倒立摆控制

针对平面二级倒立摆系统具有的多变量、非线性、强耦合、稳定控制实时性和快速性要求高的特点,设计了利用协调因子优化控制效果的改进型LQR控制器.运用分析动力学方法对倒立摆建立数学模型,以LQR理论设计了平面倒立摆的最优控制器,在此基础上加入性能协调因子,它能根据状态变量的变化实时调整控制作用的大小,进而对LQR输出的预控制...     

基于模糊加权的倒立摆混合控制

针对小车倒立摆系统,提出了一种线性状态反馈控制和滑模控制模糊加权的控制方法.滑模控制器的作用是将摆角控制在零的一个邻域内,在此邻域内首先采用近似的线性化模型来描述倒立摆系统,然后采用基于极点配置的方法设计系统的线性状态反馈控制器以使系统的状态稳定在给定值,两个控制器的输出通过加权求和作为倒立摆的控制作用.仿真结果证实了该方法的有效性.     

基于T-S模糊模型的滑模跟踪控制

基于T-S模糊模型设计跟踪控制器,它包括两个部分:权重最大子系统局部反馈控制和采用滑模控制设计的全局监督控制,能保证系统稳定.倒立摆跟踪控制结果证明了算法的有效性.     

A new swing-up law for the Furuta pendulum

In this paper the swing-up problem for the Furuta pendulum is solved applying Fradkov's speed-gradient (SG) method to a dimension 4 model of the system. The new law is compared with the conventional Åström-Furuta strategy, based on a dimension 2 model. A comparative analysis, including simulations and experiments, whereby the advantages and effectiveness of the new law for swinging the pendulum up are shown, is included.     

网络诱导延迟的量子化和增广对象向量方法

对于网络控制系统中一般的动态输出反馈控制问题,应用延迟量子化和增广对象向量方法建立离散时间Markov跳变系统模型,并给出稳定化控制器的设计算法和倒立摆上的仿真计算.由于应用延迟量子化方法,所建立的模型和给出的设计方法也能用于求解具有常分布律的随机延迟的动态输出反馈控制问题.     

VS‐CONTROL WITH TIME‐VARYING SLIDING SECTOR — DESIGN AND APPLICATION TO PENDULUM —

In general, a Variable Structure (VS) system is designed with a sliding mode. Recently a sliding sector, designed by an algebraic Riccati equation, has been proposed to replace the sliding mode for chattering‐free VS controllers. In this paper we extend the design algorithm for the sliding sector to a time‐varying sliding sector. The time‐varying sliding sector is defined by functions dependent on both state and time, hence time‐varying uncertainty can be considered. The VS controller is designed to stabilize an uncertain system, quadratically. The design procedure for real systems is introduced via an implementation to the control of “Furuta pendulum”. To enhance the stability it is necessary to compensate the time‐varying nonlinear static friction of the actuator adequately, hence this problem is a good example to demonstrate the performance of the proposed VS control method. In the experiment, it will be shown that the VS control with the time‐varying sliding sector is superior to an orthodox chattering‐free VS control.     

直线一级倒立摆分数阶控制器设计及仿真

针对直线一级倒立摆的稳定控制问题,设计了分数阶比例积分(FOPI和FO[PI])控制器。首先,根据Newton力学方法建立了倒立摆系统的数学模型。然后,采用基于向量的增益鲁棒性分数阶控制器参数求解简化算法,设计了分数阶比例积分控制器。最后,在MATLAB环境下进行了分数阶比例积分控制器参数整定方法的有效性验证,并且对倒立摆系统分别采用分数阶比例积分控制器和整数阶PID(IOPID)控制器进行了稳定控制仿真实验,并将得到的摆杆角度响应曲线进行了对比分析。结果表明:分数阶比例积分控制器对系统的稳定控制效果优于IOPID控制器,且在分数阶比例积分控制器中,FO[PI]控制器对系统稳定控制最好,响应时间较快、振荡幅值较小且具有鲁棒性。