桥式吊车系统基于遗传算法的LQR控制

针对欠驱动系统——桥式吊车系统提出了基于遗传算法的LQR控制方法。首先，通过牛顿力学建立数学模型，再通过遗传算法选取的Q和R矩阵，结合线性二次型最优控制方法实现吊车系统的最优控制。仿真试验的结果表明了该方法是有效的。     

基于LQR控制的混合轴承动态特性分析

针对主动混合滑动轴承,给出了基于线性二次最优调节器(LQR)的控制策略,分析了轴承的动态特性。采用扰动压力法求解轴承的8个动力特性系数和灵敏系数;给出了不同权重矩阵下轴承动态特性系数的计算结果,并进行了分析讨论。结果表明,LQR控制简单易行,灵活性强,可以有效改善轴承系统的动态特性,降低交叉刚度,提高直接刚度和阻尼,从而改善系统的稳定性。     

连续时间无穷维正则状态信号系统的最优控制

本文研究连续时间线性无穷维正则状态信号(s/s)系统的最优问题–—线性二次调节器(LQR)最优控制问题和卡 尔曼滤波问题. 正则s/s系统的最优问题可解与正则s/s系统的某个正则i/s/o表示的最优问题可解是等价的. 在正则s/s系 统有一个预解集非空的正则i/s/o表示的前提下, 建立了系统本身的未来最优花费与系统表示的未来最优花费之间的联 系, 并给出了相应的例子.     

地月空间航天器绕飞接近跟踪控制

在圆形限制性三体问题的框架下研究了地月空间航天器绕飞接近跟踪控制方法.首先,以圆形限制性三体问题为基础建立了地月空间航天器相对运动模型,并通过无量纲化和线性化方法对模型进行了简化.接着,将地月空间航天器绕飞接近跟踪控制问题转化为模型参考输出跟踪问题,并结合模型参考输出跟踪理论和线性二次型最优控制理论设计绕飞接近跟踪控制器.最后,通过数学仿真验证控制器的有效性和可行性,仿真结果表明该方法能够实现地月空间航天器绕飞接近跟踪控制,对位置和速度的初始状态误差能够快速收敛.     

基于超稳定理论的小型无人机自适应控制策略研究

介绍一种基于Popov超稳定理论的无人机自适应控制策略,用于增强飞行控制系统的抗干扰性和对于时变参数的适应性.该控制方案首先根据LQR(linear quadratic regulator)原理对某无人机的纵向模型进行闭环反馈补偿,使被控模型满足Popov超稳定理论所要求的完全跟踪条件.然后,利用超稳定理论设计了模型参考自适应控制器,实现全部纵向飞行状态的无静差跟踪控制.最后,在系统存在参数摄动和外界干扰的情况下,对所提出的控制系统进行仿真研究.仿真结果表明,该控制方案能有效抑制受控对象自身参数摄动和外部干扰对于飞行状态的影响,具有较好的适应能力.     

磁导航AGV纠偏控制模型的研究与设计

针对轮式移动机器人循迹偏差问题,以差速驱动型AGV为研究对象,基于LQR(LinearQuadratic Regulator)线性二次型最优控制算法设计磁导航AGV纠偏控制器,控制AGV速度实现循迹跟踪。通过对磁导航AGV偏差建模,将决定AGV运行的驱动电机线性化,建立其状态空间模型,判别系统能控、能观性;同时用Matlab进行仿真设计,实验得到最佳Q、R完成最优控制器设计;通过Simulink设计基于LQR最优控制算法的AGV纠偏控制系统模型,并与传统PID控制算法进行对比分析表明,论文设计的基于LQR算法纠偏控制模型具有更好的收敛性和实时响应性。     

LQR控制和时滞反馈控制在汽车整车减振中的应用

本文建立了具有动力吸振器的汽车整车模型,分别研究了LQR控制和时滞反馈控制在降低汽车整车垂向振动方面的应用。对于LQR控制,选取了包含车身位移、速度和控制力在内的性能指标,借助matlab求解得到反馈增益矩阵;对于时滞反馈控制,首先采用特征值法分析了系统的稳定性,其次从理论上研究了时滞和反馈增益系数对吸振器减振效果的影响,并进行了数值验证。结果表明,与被动式吸振器相比,在LQR控制下吸振器使车身加速度幅值降低了51.38%,在时滞反馈控制下,当g=0.25 kg,τ=0.006 s时吸振器使车身加速度幅值降低了65.13%。     

Introduction of Feedback Linearization to Robust LQR and LQI Control – Analysis of Results from an Unmanned Bicycle Robot with Reaction Wheel

In this paper, the Jacobian‐linearization‐ and feedback‐linearization‐based techniques of obtaining linearized model approaches are combined with a family of robust LQR control laws to identify the pairing which results in superior control performance of the bicycle robot, despite uncertainty and constraints, what is the main contribution of the paper. The control performance is analyzed using various indices, related, e.g. to energy consumption of the considered laws, with the experiments conducted on a real bicycle robot. As a result, the easily‐implementable controller is obtained, which requires only to perform a set of off‐line computations with a single additional parameter δ in comparison with a standard linear‐quadratic controller, to obtain a state‐feedback vector, which, when implemented to the control system, ensures proper regulation of the output signal of the plant, despite uncertainty or possible actuator failures, obtaining energy‐efficient control law.     

Optimal control of LQR for discrete time-varying systems with input delays

In this work, we consider the optimal control problem of linear quadratic regulation for discrete time-variant systems with single input and multiple input delays. An innovative and simple method to derive the optimal controller is given. The studied problem is first equivalently converted into a problem subject to a constraint condition. Last, with the established duality, the problem is transformed into a static mathematical optimisation problem without input delays. The optimal control input solution to minimise performance index function is derived by solving this optimisation problem with two methods. A numerical simulation example is carried out and its results show that our two approaches are both feasible and very effective.     

Nonlinear Analysis and Attitude Control of a Gyrostat Satellite with Chaotic Dynamics Using Discrete‐Time LQR‐OGY

Quasi‐periodic and chaotic behavior, along with the control of chaos for a Gyrostat satellite (GS), is investigated in this work. The quaternion‐based dynamical model of the GS is first derived, and then the influences of the reaction wheels in the GS structure, under the gravity gradient perturbation that causes a route to chaos through quasi‐periodicity mechanism, is investigated. For the suppression of chaos in the system, a chaos control system with the quaternion feedback is designed for the GS based on the extension of the Ott‐Grebogi‐Yorke (OGY) method using the linearization of the Poincaré map. In the extended OGY controller, the Poincaré map is estimated using the Least Square Support Vector Machine (LSSVM) technique. After linearization of the Poincaré map, the Discrete‐time Linear Quadratic Regulator (DLQR) is applied on the linearized Poincaré map, making the DLQR‐OGY controller for chaos. The DLQR‐OGY control system stabilizes the orbits to the fixed points providing a small control input signal, which leads to a decrease in the control effort and energy consumption in the GS system.