多变量预测控制系统稳态解的相容性与唯一性分析  

Compatibility and Uniqueness Analyses of Steady State Solution for Multi-variable Predictive Control Systems

作　　者：邹涛[1] 李海强[2] 丁宝苍[3] 王丁丁[2] 

机构地区：[1]中国科学院沈阳自动化所研究所,沈阳110016 [2]浙江工业大学信息工程学院,杭州310023 [3]西安交通大学电子与信息工程学院,西安710049

出　　处：《自动化学报》2013年第5期519-529,共11页Acta Automatica Sinica

基　　金：国家自然科学基金(61074059;61174095;60934007);中国科学院重点部署项目(KGZD-EW-302);浙江省自然科学基金(Y12F030052)资助~~

摘　　要：多变量控制系统在结构形态上可以划分为方系统和非方系统,非方系统可进一步划分为胖系统和瘦系统.对瘦系统和胖系统,预测控制系统分别可能出现输出静差和输入稳态值不确定问题.本文从控制输入与被控输出稳态关系入手,将上述问题归结为非齐次线性方程组的相容性与唯一性问题.通过非齐次方程组解的判定定理分析了多变量预测控制系统稳态解出现相容性和唯一性问题的原因,并由此给出了双层结构控制策略及解决方案.上层稳态优化方法从理论上解决了瘦系统的相容性问题,并从胖系统的无穷多个相容解中找到最优解.下层集成控制输入目标的预测控制从根本上保证了胖系统控制输入稳态解的唯一性,并实现了方系统与非方系统预测控制在算法描述上的统一.仿真结果验证了本文提出的双层结构预测控制算法的有效性,即多变量预测控制系统稳态解既是相容的又是唯一的.The multi-variable control systems can be structurally classified into the square and non-square ones,with the latter further into fat and thin ones.For the fat and thin,the output offset and non-determinedness of the steady state input,respectively,can occur in predictive control systems.From the steady-state relationship between the control input and the controlled output,the two issues are tackled as the compatibility and uniqueness,respectively,of the nonhomogeneous linear equations set.The reason why the compatibility and uniqueness issues can arise is analyzed based on the determination theorem for non-homogeneous linear equations set,and the solutions based on the double-layer（two-layer） control structure are given.The upper level steady state optimization not only tackles the compatibility issue for the thin system,but also finds the optimal solution from the infinite many consistent ones for the fat system.The lower level predictive control algorithm,integrated with the control input target,guarantees the uniqueness of the steady state solution for fat system,and algorithmically unifies both the square and nonsquare systems.Simulation results have validated the effectiveness of the double-layered predictive control algorithm,i.e.,the steady state solutions of the multi-variable predictive control system are consistent and unique.

关 键 词：模型预测控制 稳态优化 双层结构 相容性 唯一性 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程]