控制能量约束时不稳定过程最优控制与仿真

Optimal Control and Simulation for Unstable Processes under Control Energy Constraint

在最优控制问题的研究中,工业过程控制领域中不稳定系统的控制难度比较大,且在许多控制系统设计中控制能量可能成为重要的性能指标。对控制能量存在约束时不稳定过程的最优控制问题进行了研究与仿真,优化问题的难点在于性能指标的表示与最小化。首先基于不稳定过程的互质分解,由敏感度函数和控制敏感度函数定义了一个包含跟踪误差和控制能量在内的性能指标,采用谱分解最小化该性能指标,从而为不稳定系统导出了一种最优的控制器设计方法,可使系统获得最优的控制性能。仿真结果进一步说明了方法的有效性。

The unstable system is difficult to be controlled in industry process control domain and control energy may become an important performance index in many control system design.This paper has investigated optimal control and simulation for unstable processes under control energy constraint and the key of the optimization is the expression and minimization of the performance index.Firstly,based on prime factorization of unstable process,a performance index containing tracking error and plant input energy is defined,which is represented by sensitivity function and control sensitivity function.Then,utilizing spectral factorization to minimize the performance criterion,an optimal controller design method is derived for unstable processes,which can be used to obtain optimal system performance under control energy constraint.The validity of the obtained result can be illustrated by simulation research.