三级倒立摆的自动摆起与稳定控制

采用非线性逆系统轨迹控制实现三级倒立摆的自动摆起,并设计了变增益LQR控制器将其稳定在竖直倒立位置.首先,三级倒立摆从静止下垂状态摆起到竖直倒立位置的过程,从数学角度看是一个两点边值问题,通过求解该两点边值问题获得摆起的标称轨迹,利用逆系统方法设计前馈控制,同时结合增益调度反馈控制使摆起过程稳定;其次,在稳定控制阶段,...     

Control strategies on stable manifolds for energy-efficient swing-ups of double pendula

Optimal control problems for mechanical systems often arise in technical applications. To find solutions with minimal control effort, the system’s natural, uncontrolled dynamics can be used. Promising candidates to be considered for energy-efficient trajectories are highly dynamic, but uncontrolled motions on (un)stable manifolds of equilibria. In this contribution, we propose a control strategy for mechanical systems which sequences uncontrolled trajectories on (un)stable manifolds with short control manoeuvres to design a feedforward control. In particular, we present optimal swing-up solutions for a double pendulum which are based on trajectories on the stable manifold of the pendulum’s up–up equilibrium. To demonstrate the advantages of our approach compared to a black-box optimisation, we perform a post-optimisation with the optimal control sequence as an initial guess. The numerical results are evaluated in a simulation environment for the double pendulum on a cart and applied to a real test rig.     

小车二级摆摆起控制器设计

研究了小车二级并行摆系统及小车二级串行摆系统的摆起控制器设计问题,并给出了这两种系统的实验结果.首先,针对上述两种系统,设计了两步控制器,即1)摆起双摆达到倒立稳摆位置的控制器,2)进行稳摆控制的控制器.其次,由于小车二级摆位移受轨道长度限制,又考虑了小车位移的控制问题.上述两种实际系统的摆起及稳摆成功,验证了所提出设计方法的有效性.     

Swing-up and stabilization of a cart–pendulum system under restricted cart track length

This paper describes the swing-up and stabilization of a cart–pendulum system with a restricted cart track length and restricted control force using generalized energy control methods. Starting from a pendant position, the pendulum is swung up to the upright unstable equilibrium configuration using energy control principles. An “energy well” is built within the cart track to prevent the cart from going outside the limited length. When sufficient energy is acquired by the pendulum, it goes into a “cruise” mode when the acquired energy is maintained. Finally, when the pendulum is close to the upright configuration, a stabilizing controller is activated around a linear zone about the upright configuration. The proposed scheme has worked well both in simulation and a practical setup and the conditions for stability have been derived using the multiple Lyapunov functions approach.     

Swing-up control strategies for a reaction wheel pendulum

Control of a reaction wheel pendulum, a prototype of an under-actuated system, is easily done using switching control strategies, which combines swing-up control and balancing control schemes. In this article, two novel swing-up control strategies for a reaction wheel pendulum have been proposed. The first swing-up control strategy treats the oscillations of the pendulum as perturbations from the bottom equilibrium point. The second swing-up control is based on interconnection and damping assignment-passivity based control (IDA-PBC). IDA-PBC preserves Euler Lagrangian structure of the system and gives more physical insight about any mechanical system. Any balancing controller can be coupled with the proposed swing-up control strategies to stabilise the pendulum at the top unstable equilibrium position. The control task of balancing the pendulum in top upright position is completed by switching from swing-up scheme to the balancing scheme at the point where the pendulum is very near to the top equilibrium point. Proposed swing-up control strategies have been implemented in real time in switching mode. The two proposed swing-up control schemes provide fast responses as compared to existing energy based schemes.     

圆轨倒立摆摆起过程神经网络闭环控制方法

在圆轨倒立摆摆起过程开环控制律优化算法的基础上,应用高精度多层人工神经网络 插值原理,研究了摆起过程的闭环控制方法.以每个时间段上的状态变量和相应的控制变量为 输入输出学习样本,建立前馈人工神经网络,构成摆起过程的反馈控制系统.通过仿真与实际控 制,表明所研究方法是可行和有效的,并为复杂非线性系统的闭环控制提供了新的思路.     

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.     

切换控制在倒立摆系统摆起和镇定中的应用

本文针对一级直线型倒立摆对象,基于非线性共振原理和线性二次型最优状态反馈控制,提出了一种基于状态的切换控制策略,实现了倒立摆的快速摆起和镇定。最后通过仿真实验表明,本文提出的方法对一级直线型倒立摆系统的摆起和镇定具有较好效果。     

二级倒立摆摆起控制的研究

通过对二级倒立摆系统的理论分析，研究二级摆从自然悬垂位置摆到倒立点位置的摆起控制问题，提出了基于动态设计变量优化算法的复杂非线性系统控制策略．仿真实验证明，该策略可成功地实现圆轨和直轨两种二级倒立摆的摆起控制，并且算法具有较快的收敛速度和较高的计算精度．     

A neural network-based approximation method for discrete-timenonlinear servomechanism problem

A feedback controller that solves the discrete-time nonlinear servomechanism problem relies on the solution of a set of nonlinear functional equations known as the discrete regulator equations. The exact solution of the discrete regulator equations is usually unavailable due to the nonlinearity of the system. The paper proposes to approximately solve the discrete regulator equations using a feedforward neural network. This approach leads to an effective way to practically solve the discrete nonlinear servomechanism problem. The approach has been illustrated using the well-known inverted pendulum on a cart system. The simulation shows that the control law designed by the proposed approach performs much better than the conventional linear control law.     

基于摹矩阵的倒立摆摆起的最优控制

在倒立摆小车轨道较短的条件下实现倒立摆快速稳定的摆起,是摆起控制的难点。利用摹矩阵的多阶段决策寻优方法,将倒立摆的摆起控制表示为一个求最短时间的多阶段决策问题。采用VC与Matlab混合编程,实现了用摹矩阵方法寻找单级倒立摆摆起控制的最优路径与最优决策。通过对一轨道长度受限的单级倒立摆的仿真控制和实时控制,证明了该方法的可行性。     

Interconnection and damping assignment passivity-based control of mechanical systems with underactuation degree one

Interconnection and damping assignment passivity-based control is a new controller design methodology developed for (asymptotic) stabilization of nonlinear systems that does not rely on, sometimes unnatural and technique-driven, linearization or decoupling procedures but instead endows the closed-loop system with a Hamiltonian structure with a desired energy function-that qualifies as Lyapunov function for the desired equilibrium. The assignable energy functions are characterized by a set of partial differential equations that must be solved to determine the control law. We prove in this paper that for a class of mechanical systems with underactuation degree one the partial differential equations can be explicitly solved. Furthermore, we introduce a suitable parametrization of assignable energy functions that provides the designer with a handle to address transient performance and robustness issues. Finally, we develop a speed estimator that allows the implementation of position-feedback controllers. The new result is applied to obtain an (almost) globally stabilizing scheme for the vertical takeoff and landing aircraft with strong input coupling, and a controller for the pendulum in a cart that can swing-up the pendulum from any position in the upper half plane and stop the cart at any desired location. In both cases we obtain very simple and intuitive position-feedback solutions.     

An approach to fuzzy control of nonlinear systems: stability anddesign issues

Presents a design methodology for stabilization of a class of nonlinear systems. First, the authors represent a nonlinear plant with a Takagi-Sugeno fuzzy model. Then a model-based fuzzy controller design utilizing the concept of the so-called “parallel distributed compensation” is employed. The main idea of the controller design is to derive each control rule so as to compensate each rule of a fuzzy system. The design procedure is conceptually simple and natural. Moreover, the stability analysis and control design problems can be reduced to linear matrix inequality (LMI) problems. Therefore, they can be solved efficiently in practice by convex programming techniques for LMIs. The design methodology is illustrated by application to the problem of balancing and swing-up of an inverted pendulum on a cart     

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.     

DRNN在倒立摆摆起控制中的研究

针对小车一级倒立摆的起摆控制,以DRNN神经网络作为辨识器,在线自适应调整PD控制器的两项参数。在起摆范围相同的情况下,DRNN神经网络控制的倒立摆系统其模型参数变化范围为-50%～30%,传统PD控制倒立摆系统其参数变化范围为-40%～20%。结果表明,基于DRNN神经网络的PD控制器比传统的PD控制器具有较强的抗干扰能力和自适应能力,系统鲁棒性增强,效果明显优于传统的PD控制器。     

Reinforcement learning state estimator

In this study, we propose a novel use of reinforcement learning for estimating hidden variables and parameters of nonlinear dynamical systems. A critical issue in hidden-state estimation is that we cannot directly observe estimation errors. However, by defining errors of observable variables as a delayed penalty, we can apply a reinforcement learning frame-work to state estimation problems. Specifically, we derive a method to construct a nonlinear state estimator by finding an appropriate feedback input gain using the policy gradient method. We tested the proposed method on single pendulum dynamics and show that the joint angle variable could be successfully estimated by observing only the angular velocity, and vice versa. In addition, we show that we could acquire a state estimator for the pendulum swing-up task in which a swing-up controller is also acquired by reinforcement learning simultaneously. Furthermore, we demonstrate that it is possible to estimate the dynamics of the pendulum itself while the hidden variables are estimated in the pendulum swing-up task. Application of the proposed method to a two-linked biped model is also presented.     

Inverse optimal control for strict‐feedforward nonlinear systems with input delays

We consider inverse optimal control for strict‐feedforward systems with input delays. A basic predictor control is designed for compensation for this class of nonlinear systems. Furthermore, the proposed predictor control is inverse optimal with respect to a meaningful differential game problem. For a class of linearizable strict‐feedforward system, an explicit formula for compensation for input delay, which is also inverse optimal with respect to a meaningful differential game problem, is also acquired. A cart with an inverted pendulum system is given to illustrate the validity of the proposed method.     

Method of inequalities-based multiobjective genetic algorithm for optimizing a cart-double-pendulum system

This article presents a multiobjective approach to the design of the controller for the swing-up and handstand control of a general cart-double-pendulum system （CDPS）. The designed controller, which is based on the human-simulated intelligent control （HSIC） method, builds up different control modes to monitor and control the CDPS during four kinetic phases consisting of an initial oscillation phase, a swing-up phase, a posture adjustment phase, and a balance control phase. For the approach, the original method of inequalities-based （MoI） multiobjective genetic algorithm （MMGA） is extended and applied to the case study which uses a set of performance indices that includes the cart displacement over the rail boundary, the number of swings, the settling time, the overshoot of the total energy, and the control effort. The simulation results show good responses of the CDPS with the controllers obtained by the proposed approach.     

A swing-up of the acrobot based on a simple pendulum strategy

We propose a control law to swing-up the acrobot from an initial domain to a neighbourhood of the vertically upward equilibrium position. The methodology involves reducing the system to a one degree-of-freedom system, much like a simple pendulum, evolving on a critical value of the energy level set. The system is guaranteed to converge to a neighbourhood of the upward equilibrium position about which a linear feedback controller is switched on to stabilize the system.     

A new controller for the inverted pendulum on a cart

This paper presents a complete solution to the problem of swinging‐up and stabilization of the inverted pendulum on a cart, with a single control law. The resulting law has two parts: first, an energy‐shaping law is able to swing and maintain the pendulum up. Then, the second part introduces additional control to stop the cart and it is based on forwarding control with bounded input. The resulting control law is the sum of both parts and does not commute between different laws although there exist switches inside the controller. Copyright © 2008 John Wiley & Sons, Ltd.