Flatness‐Based Trajectory Tracking Control of an Underconstrained Cable Suspension Manipulator

Cable suspension manipulators support a payload platform in space by several spatially arranged cables with computercontrolled winches. The winches are mounted either fixed or on movable trolleys. Compared to conventional cranes, it is possible to control not only the translational motion of the payload but also its orientation in order to perform, for example, assembly tasks. By this, cable suspension manipulators combine the ability of cranes to support heavy payloads in a large workspace with the dexterity of robot manipulators. The present contribution treats nonlinear trajectory tracking control of cable suspension manipulators that are kinematically undetermined and statically determined. In particular, the cable suspension manipulator Cablev [4] is considered that has been developed at University of Rostock (Fig. 1). Its payload platform is supported by three cables with winches mounted on trolleys that move themselves on a gantry. Thus, the payload platform may perform sway motions with three degrees of freedom while the cable lengths are kept fixed. Applications are, for example, precise handling and assembling large and heavy components on construction sites or on shipyards. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Hoisting Manipulation for Flying Cranes

A control strategy for hoisting drives of crane systems is discussed. Based on modal coupling control, the desired hoisting velocity is manipulated by superposition of a suitably modulated motion in order to suppress the so–called spaghetti–problem of hoisting–induced pendulations. For a 3–dimensional multibody system featuring the flying–crane –concept the extension of this control strategy to more complicated systems is exemplified. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Trajectory tracking control of variable length pendulum by partial energy shaping

This paper concerns a trajectory tracking control problem for a pendulum with variable length, which is an underactuated mechanical system of two degrees-of-freedom with a single input of adjusting the length of the pendulum. We aim to study whether it is possible to design a time-invariant control law to pump appropriate energy into the variable length pendulum for achieving a desired swing motion (trajectory) with given desired energy and length of the pendulum. First, we show that it is difficult to avoid singular points in the controller designed by using the conventional energy-based control approach in which the total mechanical energy of the pendulum is controlled. Second, we present a tracking controller free of singular points by using only the kinetic energy of rotation and the potential energy of the pendulum and not using the kinetic energy of the motion along the rod. Third, we analyze globally the motion of the pendulum and clarify the stability issue of two closed-loop equilibrium points; and we also provide some conditions on control parameters for achieving the tracking objective. Finally, we show numerical simulation results to validate the presented theoretical results.     

Control of an extending nonlinear elastic cable with an active vibration control strategy

An active control strategy based on the fuzzy sliding mode control (FSMC) is developed in this research for controlling the large-amplitude vibrations of an extending nonlinear elastic cable. The geometric nonlinearity of the cable and the fixed–fixed boundary of the cable are considered. For effectively and accurately control the motion of the cable with the active control strategy developed, the governing equation of the elastic cable is established and transformed into a multi-dimensional dynamic system with the 3rd order Galerkin method. The active control strategy is developed on the basis of the dynamic system, and the control strategy is applicable to multi-dimensional dynamic systems. In the numerical simulation, large-amplitude vibrations of the cable are effectively controlled with the control strategy. The results of the research demonstrate significances for controlling the cable vibrations of an elevator in practice.     

Structural vibration control by means of nonlinear pendulum dampers

This paper discusses the application of a nonlinear Pendulum Tuned Mass Damper (PTMD) for the reduction of structural vibrations. Pendulum dynamic absorbers are used extensively to reduce the vibration level of slender elastic structures such as towers. A PTMD is a device consisting of a suspended mass, and a damper that is attached to the tower in order to reduce its dynamic response. The primary eigenfrequency of the nonlinear damper is tuned to a particular structural frequency. Energy is dissipated by the damping force acting on the structure. Here, the PTMD is applied to a tower as a continuous system consisting of distributed mass and elasticity. The optimum values of PTMD parameters are found based on minimization of the response of the tower tip–point. Time history and frequency domain responses for the tower with PTMD in linear and nonlinear condition are compared. In addition, the equations of motion of active pendulum control are intruduced. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Series solution of a class of nonlinear optimal regulators

A class of nonlinear optimal regulators is studied by means of a series expansion of the equations of motion, the optimal cost function, and the optimal control function in a Hamilton-Jacobi context. An indicial formulation of the problem based on symmetric tensor representations is given, and an algorithm for solution of the resulting equations is developed. Associated computational issues are also discussed. An example for the optimal control of a double inverted pendulum is presented to illustrate the approach.This research was partially supported by National Science Foundation Grant BCS 93-01584 and by the Frank M. Freimann Chair in Electrical Engineering at the University of Notre Dame. The authors thank the reviewers for their careful and constructive comments on the paper.     

时滞影响下受控斜拉索的参数振动稳定性

研究了轴向激励作用下受控斜拉索系统主参数共振的时滞效应,考虑了拉索垂度和几何非线性的影响,基于Hamilton变分原理建立了受控斜拉索系统轴向激励下的非线性参数振动方程,利用Galerkin方法得到时滞动力系统,运用多尺度法对受控系统的主参数共振进行了分析,得到了不同时滞值、控制增益时参数振动稳定域和受控拉索的时程曲线.研究表明,时滞影响下斜拉索振动控制系统的效果变差,参数共振的稳定域发生偏移,对受控斜拉索系统的控制效果随着时滞的增大而变差,从而对控制系统的参数设计起到指导作用.     

Model Based Trajectory Control of an Overhead Travelling Crane

Until now, most papers concerning control of overhead travelling cranes have only focussed on position control of the translational degrees of freedom, see for example [1], [3], [4], and [5]. With more advanced robotic applications envisaged, however, there is a demand for both trajectory control in six degrees of freedom and active damping of the weakly damped load oscillations due to the rope suspension [2]. Hence, a model based trajectory control is presented for an overhead travelling crane that has been upgraded with an orientation unit providing three additional axes. Starting from a central multibody model, decentralised design models are derived for each crane axis. By this, couplings between the axes are identified and appear as disturbance inputs in these decentralised design models. Each decentralised axis controller consists of linear state feedback, feedforward control, and observer based disturbance compensation and is derived in symbolic form. This allows for an adaptation of the complete control structure employing the gain scheduling technique with respect to varying system parameters like rope length and load mass. Couplings between the crane axes are compensated by feedforward control, whereas the e.ects of nonlinear friction forces are counteracted by combination of feedforward control and disturbance estimation. Experimental results, taken at a 5 t ‐ bridge crane, show the bene.ts of the proposed control scheme as regards control performance and steady‐state accuracy.     

Synchronization dynamics of two different dynamical systems

In this paper, synchronization dynamics of two different dynamical systems is investigated through the theory of discontinuous dynamical systems. The necessary and sufficient conditions for the synchronization, de-synchronization and instantaneous synchronization (penetration or grazing) are presented. Using such a synchronization theory, the synchronization of a controlled pendulum with the Duffing oscillator is systematically discussed as a sampled problem, and the corresponding analytical conditions for the synchronization are presented. The synchronization parameter study is carried out for a better understanding of synchronization characteristics of the controlled pendulum and the Duffing oscillator. Finally, the partial and full synchronizations of the controlled pendulum with periodic and chaotic motions are presented to illustrate the analytical conditions. The synchronization of the Duffing oscillator and pendulum are investigated in order to show the usefulness and efficiency of the methodology in this paper. The synchronization invariant domain is obtained. The technique presented in this paper should have a wide spectrum of applications in engineering. For example, this technique can be applied to the maneuvering target tracking, and the others.     

基于转换控制定律的倒立摆控制器设计(英文)

本文研究倒立摆的控制器设计.运用控制转换定律和Lyapunov第二方法,有效解决了由钟的分离角和控制系统中小车的置换引起的强非线性和强耦合性难题.并证明该控制器对由摆的长度和质量以及小车的质量等参数决定的非线性摩擦系数的变化具有强鲁棒性.最后,仿真实验结果证明了该控制器设计的可行性.     

The chaotic synchronization of a controlled pendulum with a periodically forced,damped Duffing oscillator

In this paper, the chaotic synchronization of the Duffing oscillator and controlled pendulum is investigated. From the analytical conditions developed in [1], the partial and full synchronizations of the controlled pendulum with chaotic motions in the Duffing oscillator are discussed. Compared with the periodic synchronization, in the chaotic synchronization, switching points for appearance and vanishing of the partial synchronization are chaotic. The control parameter map for the synchronization is developed from the analytical conditions, and the partial and full synchronizations are illustrated to show the analytical conditions. This synchronization is different from the controlled Duffing oscillator synchronizing with chaotic motion in the periodically excited pendulum. For a better understanding of synchronization characteristics between two different dynamical systems, effects with other parameters will be discussed later.     

Nonlinear vibrations of a ropeway system with moving passenger cabins

The dynamic continuous model of a carrying rope for circulating bicable aerial ropeway is formulated. To describe nonlinear in-plane vibrations excited by moving masses of passenger cabins a closed form model with Green-Lagrange deformation is developed. The equations of motion of the system are derived on the basis of Lagrange equations with Ritz approximation of cable displacements applied. Numerical example of linear and nonlinear cable vibrations is presented. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Control of the spatial motion of a multilink inverted pendulum using a torque applied to the first link

An approach to constructing a control for non-linear mechanical systems in which the number of degrees of freedom exceeds the dimension of the generalized control forces is developed. An n-link pendulum with two-degree-of-freedom joints, controlled by a torque applied to the first link, is considered as an example. Such a pendulum has 2ⁿ different equilibrium positions. A feedback control with an absolute value constraint, which transfers the pendulum from the neighbourhood of an arbitrary equilibrium position to this equilibrium position in a finite time, is constructed. For this purpose, the equations of motion of the pendulum are linearized in the neighbourhood of the equilibrium position under consideration, complete controllability of the linear model is established, and a control is constructed for it using the linear matrix inequality technique. The applicability of the control law obtained to the solution of the problem of controlling a non-linear multilink pendulum is verified. ©2014     

粘弹性板混沌振动的输出变量反馈线性化控制

研究了粘弹性板混沌振动的控制问题·　应用非线性系统精确线性化控制理论导出了一类非仿射控制系统的非线性反馈控制律·　建立了描述材料非线性的粘弹性板运动的数学模型并利用Ｃａｌｅｒｋｉｎ 方法进行简化·　采用相空间曲线和频率谱密度函数说明了在特定参数条件下系统将出现混沌振动,并以位移为输出变量将混沌振动控制为给定的周期运动·     

小垂度粘弹性索非线性响应及振动主动控制

研究具有初始应力的小垂度粘弹性索的非线性动态响应及振动主动控制。在假定索材料的本构关系为一般微分本构类型的基础上,建立小垂度粘弹性索的运动微分方程;应用Galerkin方法将其转化为可用Runge-Kutta数值积分方法求解的一系列三阶非线性常微分方程。在仅考虑面内的横向振动及忽略非线性的情况下得到了连续状态空间中的状态方程,将状态方程离散为差分方程形式,并用矩阵指数来逐步近似状态转移矩阵;基于二次性能指标的最小化得到了最优的控制力与状态向量。最后通过数值仿真研究说明了粘性参数对索动态响应的影响。     

KAM dynamics and stabilization of a particle sliding over a periodically driven curve

The dynamics of a bead sliding without friction along a periodically pulsating wire is under consideration. If the arc length of the wire is taken as the relevant coordinate, the motion of the bead is described by a periodic newtonian equation. Sufficient conditions are derived assuring that a given equilibrium is of twist type, a property that implies its nonlinear stability as well as a KAM scenario around it. Special attention is paid to the stabilization of unstable equilibria, in parallel with the stabilization of the inverted pendulum.     

Hybrid control for tracking of invariant manifolds

This paper presents a hybrid control method that controls to unstable equilibria of nonlinear systems by taking advantage of systems’ free dynamics. The approach uses a stable manifold tracking objective in a computationally efficient, optimization-based switching control design. Resulting nonlinear controllers are closed-loop and can be computed in real-time. Our method is validated for the cart–pendulum and the pendubot inversion problems. Results show the proposed approach conserves control effort compared to tracking the desired equilibrium directly. Moreover, the method avoids parameter tuning and reduces sensitivity to initial conditions. The resulting feedback map for the cart–pendulum has a switching structure similar to existing energy based swing-up strategies. We use the Lyapunov function from these prior works to numerically verify local stability for our feedback map. However, unlike the energy based swing-up strategies, our approach does not rely on pre-derived, system-specific switching controllers. We use hybrid optimization to automate switching control synthesis on-line for nonlinear systems.     

Dynamics-Based Motion Planning for a Pendulum-Actuated Spherical Rolling Robot

This paper deals with the dynamics and motion planning for a spherical rolling robot with a pendulum actuated by two motors. First, kinematic and dynamic models for the rolling robot are introduced. In general, not all feasible kinematic trajectories of the rolling carrier are dynamically realizable. A notable exception is when the contact trajectories on the sphere and on the plane are geodesic lines. Based on this consideration, a motion planning strategy for complete reconfiguration of the rolling robot is proposed. The strategy consists of two trivial movements and a nontrivial maneuver that is based on tracing multiple spherical triangles. To compute the sizes and the number of triangles, a reachability diagram is constructed. To define the control torques realizing the rest-to-rest motion along the geodesic lines, a geometric phase-based approach has been employed and tested under simulation. Compared with the minimum effort optimal control, the proposed technique is less computationally expensive while providing similar system performance, and thus it is more suitable for real-time applications.