一种基于LMI的非线性模型预测控制终端域优化方法

对于具有约束的非线性系统, 提出了一种模型预测控制 (Model predictive control, MPC) 的终端域优化方法. 基于线性矩阵不等式(Linear matrix inequality, LMI) 优化和非线性系统的范数有界线性微分包含 (Linear differential inclusion, LDI), 给出了求解非线性 MPC 终端代价函数和局部稳定控制器的一种方法, 在此基础上可方便地得到非线性模型预测控制终端域. 一个具体的数值算例验证了算法的有效性.     

小型无人直升机的模型预测控制算法研究

针对无人直升机在阵风干扰环境中的姿态控制精度低的问题.本文将非线性刚体动力学模型在悬停点应用小扰动理论得到了线性化数学模型.考虑系统输入输出和控制量约束,采用模型预测控制将控制器的设计问题转化为每个采样时刻求解一个带不等式和等式约束的凸二次规划问题.通过设计终端状态约束解决了有限时域模型预测控制(model predictive control, MPC)算法的稳定性问题,并通过引入松弛变量使得约束优化问题更容易求解.随机和常值阵风干扰下无人机悬停仿真验证了本文MPC预测控制器具有幅度不超过0.25 m/s的良好干扰抑制能力,性能明显优于线性二次型调节器(linear-quadratic regulator, LQR).     

基于LQG性能基准的预测控制经济性能评估算法

针对已有经济性能评估算法大多采用最小方差控制(Minimum Variance Control,MVC)性能基准,存在对预测控制系统(Model Predictive Control,MPC)性能评估结果可靠性不高的问题,提出了基于线性二次高斯控制(Linear Quadratic G-aussian,LQG)性能基准的经济性能评估算法。通过数值计算方法确定LQG性能基准曲线,避免了复杂交互矩阵的计算。算法以基于模型的稳态经济优化技术为基础,将LQG基准和预测控制系统的经济性能估计相结合,并通过建立一系列稳态优化问题来描述控制系统在不同控制策略下的经济性能。与已有评估算法相比,本算法提供了一种更简单有效的评估方法,能够完成对包括预测控制在内的先进控制系统经济性能的评估.算法通过仿真算例说明了该算法的有效性。     

基于线性二次型高斯基准的多变量预测控制技术经济性能评估

由于受控过程参数的漂移及缺乏维护,令采用的控制器性能逐渐降低,需要做经济性能评估,以确保其最佳运行状态.因为目前最小方差评估算法没有考虑控制器的约束条件,对此我们采用线性二次型高斯(linearquadratic Gaussian,LQG)基准的模型预测控制(model predictive control,MPC)双层优化控制结构,将控制和输出的加权值引入上层经济性能指标,通过求解LQG问题获取控制与输出方差关系的离散点集,进一步拟合Pareto最优曲面方程,建立优化命题并求解最优经济指标及设定值.对延迟焦化加热炉的多变量MPC控制进行了性能评估及分析,证明该方法可以改进控制器设计,提高经济效益.     

基于多面体终端域的Hammerstein-Wiener非线性预测控制

许多实际系统都可以表示成一种中间为线性动态子系统、输入输出端为非线性静态子系统的Hammerstein-Wiener型非线性模型. 针对输入和输出受约束的Hammerstein-Wiener型非线性系统, 提出一种基于多面体终端域的预测控制综合算法. 离线设计时, 通过构造一系列多面体不变集, 扩大了终端域; 在多面体不变集内, 设计非线性控制律, 减少了常规线性控制律设计的保守性. 在线计算时, 通过求解有限个线性矩阵不等式(Linear matrix inequalities, LMIs)优化问题, 不仅可以满足实时性要求, 而且能够改善控制性能. 仿真结果表明了采用多面体不变集的优越性.     

基于能量反馈协调控制的电动汽车底盘减振方法

针对电动汽车底盘振动控制及其能量反馈的设计要求,建立其1/4馈能式主动悬架模型,从能量角度使用基于线性二次最优调节器(Linear Quadratic Regulator, LQR)的控制方法,使悬架在控制力作动下达到车身振动能量尽量小并获得一定的振动反馈能量.在理论分析基础上,使用与Simulink建立联合仿真系统,分析LQR控制器协调底盘在复杂工况下的振动控制及其能量反馈的综合效果.分析表明,所用LQR协调控制方法能有效协调减振及其能量反馈.     

具有多图拓扑结构的同类智能体LQR控制

本文考虑具有一般线性时不变动态特性的多智能体系统优化控制问题. 将智能体之间的通讯拓扑结构建模成具有自环的无向多图, 每个子系统就是一个节点, 每个节点的控制行为只与本身及邻居节点有关. 由于反馈矩阵具有块对角结构约束, 本文研究的LQR控制问题本质上是一类结构优化问题. 最小化系统LQR性能指标等价于最小化单个智能体性能指标和. 基于线性矩阵不等式得到系统的次优性能指标, 指出LQR性能域是凸集. 由此多智能体系统的LQR控制转化为若干个子系统的LQR控制, 可以通过求解系数是Laplacian矩阵最小最大特征值的两个矩阵不等式得到反馈增益. 数值例子验证了方法的有效性.     

具有次优保性能滑动模态的静态输出反馈滑模控制

针对一类不确定系统,提出了一种具有次优保性能滑模面的静态输出反馈滑模控制方法.首先将滑模面的设计问题等价为一个对称矩阵的求解问题,基于等效控制法,推导了保性能滑模面存在的充分条件.然后基于迭代线性矩阵不等式(iterative linear matrix inequality,ILMI)方法,给出了次优保性能线性滑模面的求解算法,最后基于线性矩阵不等式(linearmatrix inequality,LMI)方法,设计了输出反馈滑模控制器,使得闭环系统渐近稳定且切换函数能在有限时间内到达零.该方法首次实现了输出反馈滑模面的优化,且具有保守性小、无需对被控系统模型进行坐标变换的优点.仿真结果验证了本文方法的优越性.     

二级倒立摆系统的实时稳定控制实验研究

为实现二级倒立摆系统的实时稳定控制,以深圳固高直线二级倒立摆装置作为控制对象,在MATLAB环境下,利用基于二次型最优控制理论的线性二次型(Linear Quadratic Regulator,LQR)最优控制器,成功实现了该装置的实时稳定控制。为引入新的控制策略,采集二级倒立摆实时控制过程中的LQR控制器数据作为样本,经过自适应神经模糊推理系统(Adaptive Neuro-Fuzzy Inference System,ANFIS)工具箱训练并生成出一种新型模糊神经网络控制器,应用到装置上同样实现了实时平衡。结果表明,新型控制器较LQR控制器控制效果更优,也为成功实现装置的实时平衡提供了一种新的思路和解决方法。     

随机时滞系统的时滞相关无源控制

研究随机时滞系统的时滞相关无源性分析和控制问题. 利用Lyapunov-Krasovskii方法和松弛矩阵方法, 得到时滞相关的无源性条件. 基于该条件设计时滞相关的随机无源控制器. 文中的结果以线性矩阵不等式(Linear matrix inequalities, LMIs)表示, 可以利用标准的凸优化算法进行有效求解. 通过一个数值例子说明本文方法的有效性.     

An improved robust model predictive control approach to systems with linear fractional transformation perturbations

In this paper, a robust model predictive control approach is proposed for a class of uncertain systems with time-varying, linear fractional transformation perturbations. By adopting a sequence of feedback control laws instead of a single one, the control performance can be improved and the region of attraction can be enlarged compared with the existing model predictive control (MPC) approaches. Moreover, a synthesis approach of MPC is developed to achieve high performance with lower on-line computational burden. The effectiveness of the proposed approach is verified by simulation examples.     

Price-driven coordination method for solving plant-wide MPC problems

In large-scale model predictive control (MPC) applications, such as plant-wide control, two possible approaches to MPC implementation are centralized and decentralized MPC schemes. These represent the two extremes in the “trade-off” among the desired characteristics of an industrial MPC system, namely accuracy, reliability and maintainability. To achieve optimal plant operations, coordination of decentralized MPC controllers has been identified as both an opportunity and a challenge. Typically, plant-wide MPC problem can be formulated as a large-scale quadratic program (QP) with linking equality constraints. Such problems can be decomposed and solved with the price-driven coordination method and on-line solutions of these structured large-scale optimization problems require an efficient price-adjustment strategy to find an “equilibrium price”. This work develops an efficient price-adjustment algorithm based on Newton’s method, in which sensitivity analysis and active set change identification techniques are employed. With the off-diagonal element abstraction technique and the enhanced priced driven coordination algorithm, a coordinated, decentralized MPC framework is proposed. Several case studies show that the proposed coordination-based decentralized MPC scheme is an effective approach to plant-wide MPC applications, which provides a high degree of reliability and accuracy at a reasonable computational load.     

ILC strategy for progress improvement of economic performance in industrial model predictive control systems

A novel approach to progress improvement of the economic performance in model predictive control (MPC) systems is developed. The conventional LQG based economic performance design provides an estimation which cannot be done by the controller while the proposed approach can develop the design performance achievable by the controller. Its optimal performance is achieved by solving economic performance design (EPD) problem and optimizing the MPC performance iteratively in contrast to the original EPD which has nonlinear LQG curve relationship. Based on the current operating data from MPC, EPD is transformed into a linear programming problem. With the iterative learning control (ILC) strategy, EPD is solved at each trial to update the tuning parameter and the designed condition; then MPC is conducted in the condition guided by EPD. The ILC strategy is proposed to adjust the tuning parameter based on the sensitivity analysis. The convergence of EPD by the proposed ILC has also been proved. The strategy can be applied to industry processes to keep enhancing the performance and to obtain the achievable optimal EPD. The performance of the proposed method is illustrated via an SISO numerical system as well as an MIMO industry process.     

参数不确定广义大系统的保性能分散控制

对一类范数有界时不变参数不确定的连续广义大系统和一个二次型性能指标,研究了其保性能分散控制问题.目的是设计一状态反馈分散控制器,使得对所有容许的不确定性,闭环系统不仅是鲁棒稳定的,而且性能指标有一上界.应用线性矩阵不等式方法,给出了一个用线性矩阵不等式表达的保性能分散控制器存在的充分条件;在此条件可解时,给出了保性能分散控制律的表达式.最后,举例说明了该方法的应用.     

Distributed model predictive control of an experimental four-tank system

A distributed model predictive control (DMPC) framework is proposed. The physical plant structure and the plant mathematical model are used to partition the system into self-sufficient estimation and control nodes. Local measurements at the nodes are used to estimate the relevant plant states. This information is then used in the model predictive control calculations. Communication among relevant nodes during estimation and control calculations provides improvement over the performance of completely decentralized controllers. The DMPC framework is demonstrated for the level control of an experimental four-tank system. The performance of the DMPC system for disturbance rejection is compared with other control configurations. The results indicate that the proposed framework provides significant improvement over completely decentralized MPC controllers, and approaches the performance of a fully centralized design.     

Optimal decentralized control of large scale systems

This paper presents a new optimized decentralized controller design method for solving the tracking and disturbance rejection problems for large-scale linear time-invariant systems, using only low-order decentralized controllers. To illustrate the type of results which can be obtained using the new optimized decentralized control design method, the control of a large flexible space structure is studied and compared with the standard centralized LQR-observer controller. The order of the resultant decentralized controller is much smaller than that of the standard centralized LQR-observer controller. The proposed controller also has certain fail-safe properties and, in addition, it can be five orders of magnitude more robust than the standard LQR-observer controller based on their real stability radii. The new decentralized controller design method is applied to a large flexible space structure system with 5 inputs and 5 outputs and of order 24.     

电流型变流器的改进模型预测控制

传统的模型预测控制(MPC)采用脉冲响应的非参数模型作为系统的预测控制模型,计算量大,很难直接应用于实时控制系统.本文提出将传统的MPC进行改进,应用到电流型变流器(CSC)功率因数校正系统中.改进的MPC根据CSC控制量与被控制量的传递函数得出CSC的一阶差分方程作为预测控制模型,同时保留传统MPC反馈校正、动态优化等优点.将此改进的MPC与传统的PID控制进行对比研究,结果表明:改进的MPC用于电流型变流器,比传统的PID控制具有更好的鲁棒性和更快速的动态响应特性.     

LMI solutions for H-two and H-infinity decentralized controllers applied to an aerothermic process

In this paper, we present a linear matrix inequality (LMI)-based solution to implement H-two and Hinfinity decentralized robust control strategies. Appropriate parametrization of optimal H-two and H-infinity controllers is used. The general formulation of the decentralized control design leads to the optimal determination of both the state feedback gains and the observer gains of the decentralized controllers. This formulation is two folds: first, a centralized controller is obtained, and then, a simplified decentralized solution is derived by optimizing only the observer gains. The mathematical determination of these gains is formulated as an LMI optimization problem that can be easily solved using LMI solvers. As an experimental evaluation of these controllers, a real time application to an aerothermic process is carried out. A continuous-time model of the process obtained with a suitable direct continuous-time identification approach is elaborated. Results illustrating the real performance obtained from the H-two and H-infinity decentralized controllers are discussed and compared with the centralized ones.