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Predictive control for linear constrained systems : linear control performance and constrained control strategy

线性约束系统的预测控制：线性控制性能和约束控制策略

基本信息

批准号：
15560384
负责人：
KOJIMA Akira
金额：
$ 1.79万
依托单位：
Tokyo Metropolitan University (2005)Tokyo Metropolitan Institute of Technology (2003-2004)
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2003
资助国家：
日本
起止时间：
2003 至 2005
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-15560384/
关键词：
constrained system preview control model predictive control H-infinity control H2 control

项目摘要

Model predictive control (MPC) has become a standard control strategy for constrained multivariable systems. The essential part of the MPC strategy is that the optimal control problem is solved on line over a finite-horizon and the first value of the resulting control signals is applied. In the general MPC systems, it is observed that a linear appropriate control works in the unconstrained region around the equilibrium point and the auxiliary compensation is additionally applied in case when some of the system constraints turn to be active. Motivated by this observation, this research project clarifies the following feature on the predictive control: 1) performance limitation of linear predictive control systems, and 2) derive a model predictive control, which enables to elaborate the performance in the linear control regions. For H2 or LQ control problems, a control strategy, which clarifies the linear control performance with account of the compensation in the constrained regions, is obtained. The results are summarized as follows.1) For unconstrained linear systems, the H-infinity and H2 preview control problems are solved. Furthermore it is shown that analytic solution for H-infinity preview and delayed control problem is obtained based on the framework of finite-dimensional operations.2) LQ control problem for continuous-time linear systems is solved. It is clarified that the control consists of linear LQ control and additional auxiliary signals, which make up the linear LQ control in case when the constraints work.The control laws obtained by 1), 2) are applied to an inverted pendulum system and the strength and limitation are further discussed.

模型预测控制（MPC）已成为约束多变量系统的标准控制策略。 MPC 策略的基本部分是在有限范围内在线求解最优控制问题，并应用所得控制信号的第一个值。在一般 MPC 系统中，可以观察到线性适当控制在平衡点周围的无约束区域中起作用，并且在某些系统约束变得活跃时另外应用辅助补偿。受这一观察的启发，本研究项目阐明了预测控制的以下特征：1）线性预测控制系统的性能限制，2）推导模型预测控制，该模型能够详细说明线性控制区域的性能。对于 H2 或 LQ 控制问题，获得了一种控制策略，该策略阐明了考虑约束区域补偿的线性控制性能。主要研究结果如下：1)对于无约束线性系统，解决了H-无穷大和H2预览控制问题。进一步证明了基于有限维运算框架得到了H-无穷远预演和延迟控制问题的解析解。2)解决了连续时间线性系统的LQ控制问题。明确了该控制由线性LQ控制和附加辅助信号组成，在约束条件下，它们构成了线性LQ控制。将1）、2）得到的控制律应用于倒立摆系统，并进一步讨论了其强度和局限性。