三级倒立摆的LQR方法优化参数控制

倒立摆是智能控制的理想对象。使用拉格朗日方程建立三级倒立摆系统的非线性数学模型,在平衡点处对其线性化,利用LQR（Linear Quadratic Regulator）最优控制理论,导出控制规律。通过对三级倒立摆一系列稳定摆动和加扰实验仿真曲线的分析,明确了加权矩阵Q中各权系数对系统稳定性控制的重要性,由此来优化权系数的选择。实验表明,系统显示出较好的鲁棒性和动态性能。     

三级倒立摆的自适应神经模糊控制

在三级倒立摆(TIP)系统中, 应用神经网络与模糊控制相结合的自适应神经模糊推理系统(adaptive neuralfuzzy inference system), 根据样本数据调整隶属函数和控制规则参数, 使得训练后ANFIS控制器很好地模拟期望的输入输出数据. 仿真结果表明所设计的ANFIS控制器对三级倒立摆系统的稳定控制是可行的. 与LQR控制相比, 基于ANFIS控制的倒立摆系统具有良好的动态性能和抗干扰性能.     

基于参数自适应模糊PI的三级倒立摆控制

三级倒立摆作为高阶次、多变量、非线性、强耦合的不稳定系统,不易对其进行有效控制.在基本模糊控制器基础上,设计了一种参数自适应模糊PI控制器.即通过LQR(Linear Quadratic Regulator)最优控制理论方法,确定出融合函数,降低了模糊控制器的输入维数,减少了控制器规则数.经过参数修正模糊控制器,实现参数自适应调整,提高了系统控制性能.通过SIMULINK仿真及对比,结果显示,系统能在较短时间内达到稳定,控制效果、稳定性及鲁棒性均较好,能满足系统要求.     

平面一级倒立摆的稳定控制

平面倒立摆系统是进行控制理论研究的理想实验平台.在对平面一级倒立摆进行运动学和动力学分析的基础上,采用拉格朗日方程建立了它的动力学模型.分别设计了LQR控制器和模糊控制器,应用所设计的控制器对倒立摆系统进行了实时控制实验.验证了两种控制方法的优缺点.     

三级倒立摆的加权变量模糊神经网络控制

为了提高三级倒立摆系统控制的响应速度和稳定性,在设计Mamdani型摸糊推理规则控制器控制倒立摆系统稳定的基础上,设计了一种更有效率的基于Sugeno型模糊推理规则的模糊神经网络控制器。该控制器使用BP神经网络和最小二乘法的混合算法进行参数训练,能够准确归纳输入输出量的模糊隶属度函数和模糊逻辑规则。通过与Mamdani型控制器的仿真对比,表明该Sugeno型模糊神经网络控制器对三级倒立摆系统的控制具有良好的稳定性和快速性,以及较高的控制精度。     

拟人智能控制三级倒立摆

文章主要阐述一种拟人智能控制三级倒立摆的方法。其控制策略可以不依靠精确的数学模型,而借助人的控制经验、直觉和计算机技术,将定性分析与定量估算有机地结合,从而形成一种有效的控制规律。实验结果表明,该方法对被控对象的状态和参数变化具有较强的稳定鲁律性和品质鲁律性,表明了拟人智能控制方法的可行性和有效性,是一种比较实用的控制方法。     

倒立摆系统的自摆起和稳定控制

为了实现一级倒立摆系统自摆起和稳定控制，该文采用了最优控制与PID控制相结合的控制方法。首先，采用Bang—Bang控制理论设计开环时间最优控制器，实现倒立摆的平稳快速摆起，同时设计经典PID控制器控制小车位置；然后采取线性二次型最优控制理论设计LQR控制器，将倒立摆稳定在平衡位置。计算机仿真和倒立摆系统实时仿真表明，文中提出的控制策略和控制算法得到了很好的验证，取得了满意的效果。     

基于LQR三级倒立摆变论域自适应模糊控制

针对传统模糊控制的不足,以三级倒立摆为例,应用变论域自适应模糊控制理论,给出了三级倒立摆的数学模型,并验证了其可控性。考虑到三级倒立摆为多变量系统,为了解决模糊控制器规则组合爆炸问题,利用LQR理论先设计出状态反馈器,再进行降维处理。最后利用变论域自适应模糊控制理论给出伸缩因子,从而得到变论域自适应模糊控制器。仿真结果表明,该方法控制精度高,具有良好的稳定性和鲁棒性,可实现倒立摆系统的随动控制。     

倒立摆系统可线性化建模条件及稳定控制的研究

对单级倒立摆系统进行线性化建模,在初始摆角为5°的条件下采用了LQR和PD两种控制算法进行了稳定控制,都取得了良好的控制效果.在初始摆角从0°到-20°变化时,以步长为-4°进行了递推运算,分别得到了两组仿真曲线图,实验证明,两种控制算法的可线性化建模条件为|θ(0)|≤8°否则系统将呈现明显的非线性特性,线性化模型将很不准确,最后从实现稳定控制和可线性化建模条件两方面出发得出,PD控制优于LQR控制.     

基于拉格朗日建模的单级倒立摆起摆与稳定控制

基于拉格朗日方法建立直线一级倒立摆系统的数学模型.采用能量反馈进行倒立摆的起摆控制,在平衡点附近切换并采用现代控制理论中的状态空间极点配置以实现稳定控制.仿真和实验结果表明该方法对单级直线倒立摆系统的起摆与稳定控制具有很好的效果.     

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．     

一种改进的三级倒立摆变论域模糊控制器设计

在传统变论域模糊控制系统中, 论域随着输入的变化实时改变, 论域的反复调整降低了控制的实时性, 同时伸缩因子的函数结构和参数也不易确定. 基于上述问题本文设计了基于改进型变论域算法的三级倒立摆模糊控制器: 首先提出了相对变论域控制思想, 然后采用模糊逻辑推理器构造了伸缩因子, 实时调整输入变量, 从而相对性地改变论域大小, 避免了传统伸缩因子的函数结构和参数不易确定的问题, 并根据系统闭环响应曲线设计了控制 器输出调整因子. 最后采用极点配置方法对状态变量进行综合, 避免了规则爆炸问题. 三级倒立摆的仿真结果表明了该方法具有较好的控制效果.     

LMI-based LSVF control of a class of nonlinear systems with parametric uncertainty: an application to an inverted pendulum system

This work centres around the stabilisation of a nonlinear system containing parametric uncertainty using a new Control Lyapunov Function (using Lie derivatives) which comes up with a linear matrix inequality-based design. The paper has three major contributions. The first one is an extension of a theorem proposed to find the convex-concave bounds of nonlinear function towards robustness. With some restrictions in the structure of the uncertainty, the theory developed here may be applied to find out the bounds of any nonlinear function with uncertainty. The next one is the main contribution of this paper in which the form of the control law obtained is linear and has several advantages from a practical point of view over almost all other nonlinear control techniques. The third one is the expansion of the proposed control scheme towards underactuated systems. To show the effectiveness of the proposed theory the controller design is attempted for both the traditional cart inverted pendulum and the more complex mobile wheeled inverted pendulum model.     

拟人智能控制及鲁棒LQ控制在倒立摆基准问题中的应用

分别应用拟人智能控制策略解决倒立摆标称系统的控制和鲁棒LQ方法解决其鲁棒控制问题.拟人智能控制模仿人解决问题的归约思路,从物理角度出发分析被控系统并设计定性控制律.利用遗传算法良好的全局搜索收敛特点,对定性控制律中的参数进行优化搜索.当模型只存在结构化型不确定性且不确定性有界时,可通过求解一个Riccati方程来设计鲁棒LQ控制器.仿真结果表明给定的控制指标均得到满足,且控制律算法简单,实现比较方便.     

Swing-up of the double pendulum on a cart by feedforward and feedback control with experimental validation

The swing-up maneuver of the double pendulum on a cart serves to demonstrate a new approach of inversion-based feedforward control design introduced recently. The concept treats the transition task as a nonlinear two-point boundary value problem of the internal dynamics by providing free parameters in the desired output trajectory for the cart position. A feedback control is designed with linear methods to stabilize the swing-up maneuver. The emphasis of the paper is on the experimental realization of the double pendulum swing-up, which reveals the accuracy of the feedforward/feedback control scheme.     

移动可伸缩三维倒立摆模型的双足机器人步态控制策略

双足机器人的步态控制策略是保证双足稳定行走的重要条件之一.结合人在行走时ZMP平稳移动的特性,建立了一种移动可伸缩三维倒立摆模型;在约束平面内分析ZMP与COG的运动关系,将ZMP和COG分别定为快变因子和慢变因子,提出了移动可伸缩三维倒立摆模型的双足机器人步态控制策略;最后通过Matlab/ADAMS进行了步态控制仿真研究.仿真结果表明双足机器人可以稳定地行走,验证了该步态控制策略的可行性.     

Zero dynamics stabilisation and adaptive trajectory tracking for WIP vehicles through feedback linearisation and LQR technique

This paper presents a composite control strategy integrating adaptive sliding-mode control and the linear quadratic regulator (LQR) technology for a wheeled inverted pendulum (WIP) vehicle system. The system can be partitioned into an actuated rotational subsystem and an underactuated longitudinal subsystem based on the different control input in the mathematical model. In particular, the instability analysis of zero dynamic for the underactuated longitudinal subsystem is investigated in detail using the feedback linearisation technology. Then, an adaptive sliding-mode control is designed for the trajectory tracking, where an adaptive algorithm is developed to handle with the parameter uncertainties. In addition, the LQR technique is employed to guarantee zero dynamics stability so as to achieve simultaneously the vehicle body stabilisation at the upright position. Simulation results show the good performance and strong robustness of the proposed control schemes.     

Optimal Control of Nonlinear Inverted Pendulum System Using PID Controller and LQR: Performance Analysis Without and With Disturbance Input

Linear quadratic regulator(LQR) and proportional-integral-derivative(PID) control methods, which are generally used for control of linear dynamical systems, are used in this paper to control the nonlinear dynamical system. LQR is one of the optimal control techniques, which takes into account the states of the dynamical system and control input to make the optimal control decisions.The nonlinear system states are fed to LQR which is designed using a linear state-space model. This is simple as well as robust. The inverted pendulum, a highly nonlinear unstable system, is used as a benchmark for implementing the control methods. Here the control objective is to control the system such that the cart reaches a desired position and the inverted pendulum stabilizes in the upright position. In this paper, the modeling and simulation for optimal control design of nonlinear inverted pendulum-cart dynamic system using PID controller and LQR have been presented for both cases of without and with disturbance input. The Matlab-Simulink models have been developed for simulation and performance analysis of the control schemes. The simulation results justify the comparative advantage of LQR control method.     

Robust Control Design of Wheeled Inverted Pendulum Assistant Robot

This paper examines the design concept and mobile control strategy of the human assistant robot I-PENTAR (inverted pendulum type assistant robot). The motion equation is derived considering the non-holonomic constraint of the twowheeled mobile robot. Different optimal control approaches are applied to a linearized model of I-PENTAR. These include linear quadratic regulator (LQR), linear quadratic Gaussian control (LQG), H₂ control and H_∞ control. Simulation is performed for all the approaches yielding good performance results.