线性采样系统二次型最优控制器的MATLAB实现

当被控对象具有较大滞后特性时通常运用采样控制方式进行控制,而线性二次型最优控制又以其综合性、灵活性和实用性受到重视和发展.MATLAB软件的Simulink模块可以快速方便地对控制系统进行建模和仿真.文中通过实例给出了完整的线性采样系统二次型最优控制器的设计过程,简述了连续系统离散化以及线性二次型最优控制器的基本原理、设计方法,并提出了一个Sirmulink环境下的仿真模型,通过得到的闭环系统的阶跃响应分析了参数变化对最优控制系统的影响.整个设计表明了运用Simulink对采样系统进行设计和分析是完全可行的.     

CPT纯平荫罩振动系统最优控制器的研究

本文运用线形二次型(LQ)最优控制方法，利用MATLAB语言对CPT平面荫罩振动系统进行了最优控制器的设计，并对控制器参数进行了优化分析。通过仿真计算表明控制系统的有效性。该方法具有计算简单，便于调整等优点。     

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。     

永磁同步电动机的鲁棒MR-ILQ最优电流控制

提出了永磁同步电动机鲁棒参考模型逆线性二次型最优电流控制系统的结构和数学模型,设计了最优电流控制系统的伺服控制器,分析了系统的鲁棒稳定性和鲁棒跟踪性能．以内埋式永磁同步电动机为例,对系统进行了仿真研究．仿真结果表明,系统对参数变化和负载扰动具有很强的鲁棒性,可以实现高精度的电流控制和动态解耦。     

δ算子下的网络控制系统最优控制方法

研究网络控制系统的随机最优控制问题,提出了针对随机时延的网络控制系统最优控制律和二次型性能指标极小的控制律设计方案．在δ算子域内应用动态规划理论．设计网络控制系统的最优状态反馈和输出反馈控制律,得到的线性二次型高斯控制器可对系统中的随机长时延进行动态补偿．最后通过实例仿真验证了上述最优控制方案的可行性和有效性．     

二次型最优有限拍内模控制及加权阵的选择

针对生产中常见的时滞系统采用二自由度内模控制结构,为了减小跟踪误差、减少能量,最优指标下设计的有限拍控制系统进行综合.应用matlab仿真软件实现三种最优指标下的无纹波跟踪设计,并对三种设计方法进行比较,得出验证结果.然后继续对有限拍内模控制二次型最优控制系统中加权阵,并在simulink环境下针对一时滞非最小相位系统进行仿真,仿真结果表明具有二次型最优指标的设计控制性能好,且控制器设计简单,调节参数少,具有良好的应用前景.     

基于LQR最优调节器的三自由度直升机控制系统

三自由度直升机实验平台包含了一个典型的高阶次、不稳定、多变量、非线性和强藕合控制系统本文研究分析了三自由厦直升机控制系统的数学模型，介绍了线性二次型最优调节器（LQR）的基本原理，并针对直升机控制系统的平衡控制问题，设计了线性二次型最优调节器（LQR），以实现对三自由度直升机的最优控制，MATLAB仿真实验结果表明了该方法有较好的控制效果。     

精馏塔的H∞优化控制仿真

该文基于H∞控制理论对精馏塔设计了优化控制器,并进行了闭环仿真实验。仿真结果表明：当系统存在干扰时,H∞控制器比线性二次型最优调节器（LQR）使精馏塔实际达到的优化性能指标和综合控制指标都要好。     

基于线性二次型的单神经元PID最优控制器设计及仿真

讨论了线性二次型最优控制理论在神经网络PID控制系统中的应用.将二次型性能指标引入单神经元PID控制器中,设计出单神经元自适应PID最优控制器,从而实现了PID参数在线自适应寻优.给出了完整的设计过程和学习算法,分析了其稳定性.最后,运用MATLAB仿真实现证明了该方法的可行性、有效性,并得到了较为理想的控制效果.     

基于ALQ方法的飞行姿态控制系统设计

研究飞机稳定性控制优化问题,由于飞行高度和环境的变化,系统控制器性能不能满足系统的要求。为了克服常规最优控制中模型参数和外界干扰对控制器性能的影响,提出了一种应用自适应线性二次型(Adaptive Linear Quadratic,ALQ)方法的飞机纵向控制律设计技术,首先通过自适应机制实时辨识控制系统参数,辨识的参数应用于最优线性二次型的建模设计控制中,通过在线自适应的调整控制律参数,达到了理想的控制效果,仿真验证表明在存在外部扰动和建模误差时,改进算法比传统的LQ方法具有更好的鲁棒性和稳定性,可为优化设计提供参考。     

Finite horizon quadratic optimal control and a separation principle for Markovian jump linear systems

In this note, we consider the finite-horizon quadratic optimal control problem of discrete-time Markovian jump linear systems driven by a wide sense white noise sequence. We assume that the output variable and the jump parameters are available to the controller. It is desired to design a dynamic Markovian jump controller such that the closed-loop system minimizes the quadratic functional cost of the system over a finite horizon period of time. As in the case with no jumps, we show that an optimal controller can be obtained from two coupled Riccati difference equations, one associated to the optimal control problem when the state variable is available, and the other one associated to the optimal filtering problem. This is a principle of separation for the finite horizon quadratic optimal control problem for discrete-time Markovian jump linear systems. When there is only one mode of operation our results coincide with the traditional separation principle for the linear quadratic Gaussian control of discrete-time linear systems.     

Stable and optimal fuzzy control of linear systems

A number of stable and optimal fuzzy controllers are developed for linear systems. Based on some classical results in control theory, we design the structure and parameters of fuzzy controllers such that the closed-loop fuzzy control systems are stable, provided that the process under control is linear and satisfies certain conditions. It turns out that if stability is the only requirement, there is much freedom in choosing the fuzzy controller parameters. Therefore, a performance criterion is set to optimalize the parameters. Using the Pontryagin minimum principle, we design an optimal fuzzy controller for linear systems with quadratic cost function. Finally, the optimal fuzzy controller is applied to a ball-and-beam system     

Model-based PI–fuzzy control of four-wheeled omni-directional mobile robots

The purpose of this study is to suggest and examine a PI–fuzzy path planner and associated low-level control system for a linear discrete dynamic model of omni-directional mobile robots to obtain optimal inputs for drivers. Velocity and acceleration filtering is also implemented in the path planner to satisfy planning prerequisites and prevent slippage. Regulated drivers’ rotational velocities and torques greatly affect the ability of these robots to perform trajectory planner tasks. These regulated values are examined in this research by setting up an optimal controller. Introducing optimal controllers such as linear quadratic tracking for multi-input–multi-output control systems in acceleration and deceleration is one of the essential subjects for motion control of omni-directional mobile robots. The main topics presented and discussed in this article are improvements in the presented discrete-time linear quadratic tracking approach such as the low-level controller and combined PI–fuzzy path planner with appropriate speed monitoring algorithm such as the high-level one in conditions both with and without external disturbance. The low-level tracking controller presented in this article provides an optimal solution to minimize the differences between the reference trajectory and the system output. The efficiency of this approach is also compared with that of previous PID controllers which employ kinematic modeling. Utilizing the new approach in trajectory-planning controller design results in more precise and appropriate outputs for the motion of four-wheeled omni-directional mobile robots, and the modeling and experimental results confirm this issue.     

Mixed LQG and H∞ coherent feedback control for linear quantum systems

The purpose of this paper is to study the mixed linear quadratic Gaussian (LQG) and H_∞ optimal control problem for linear quantum stochastic systems, where the controller itself is also a quantum system, often referred to as ‘coherent feedback controller’. A lower bound of the LQG control is proved. Then two different methods, rank-constrained linear matrix inequality method and genetic algorithm are for controller design. A passive system (cavity) and a non-passive one (degenerate parametric amplifier) demonstrate the effectiveness of these two proposed algorithms.     

线性连续时滞系统最优预见重复控制

针对一类线性连续时滞系统,提出一种最优预见重复控制设计方法.首先,通过一种等价变换,将被控时滞系统转化为无时滞系统.然后,利用L阶差分算子提升技巧,获得包含状态变量导数和跟踪误差的增广连续系统.在此基础上,通过定义一种新的性能指标,将预见重复控制设计问题转化为连续非自治系统的线性二次调节问题.进一步,基于最优控制理论,得到包含状态反馈、误差积分、重复控制、时滞补偿和预见补偿的最优预见重复控制器.该控制器包含了已有文献的多种控制器形式.最后,通过一个数值仿真实例,说明所提方法的有效性.     

结构不确定离散系统的最优非脆弱保成本控制

讨论了一类不确定线性离散系统的最优非脆弱保成本控制问题.考虑的系统和状态反馈控制器均具有时变的结构化的不确定性.基于线性矩阵不等式的方法,给出了存在和设计非脆弱保成本控制律的一个充分条件,以及在使二次成本函数上界最小意义下,最优非脆弱保成本控制律的凸优化设计方法.并用数值例子说明该方法降低了成本函数上界的保守性.     

动态区间系统的最优保性能控制--LMI方法

针对动态区间系统和一个给定的二次型性能指标,研究了其保性能控制问题,基于线性矩阵不等式(LMI)提出了最优保性能控制器设计方法,并将相关结果推广到参数不确定系统.利用功能强大的LMI工具,求解非常方便.所给实例表明,该方法用于设计动态区间系统与秩-1型参数不确定系统的最优保性能控制器,非常有效.     

Controller design for time lag systems via a quadratic criterion

Theoretical results on the optimal control of linear time lag systems with respect to a quadratic criterion are shown to provide a practical feedback controller design procedure. A computational procedure is given for obtaining a stable linear feedback controller. A comprehensive illustration is given of the application of the quadratic criterion results to the design of a feedback controller for a chemical process having transport lag.