多变量非方系统多环PI控制器设计

Multi-loop PI Controller Design for Multivariable Non-square Systems

基于等价传递函数(ETF)理论,提出含有多时滞的高维多变量非方系统多环PI(preportional-integral)控制器设计方法.首先,利用等价传递函数与被控过程传递函数的广义逆之间关系推导出ETF的求解通式.接着,基于已获得的ETF,利用IMC-PID(internal model control-proportional integral derivation)原理设计控制器,再利用Maclaurin级数展开获得多环PI控制器参数.所提ETF算法不仅具有更高的精度且适应于高维非方系统.最后通过仿真实例验证了所提算法的简单性和有效性.

Based on the theory of equivalent transfer function（ETF）,we propose a multi-loop PI（ proportional integral） controller design method for high dimensional multivariable non-square systems with time-delays.Firstly,by exploiting the relationship between the ETF and the generalized inverse of transfer function of the non-square systems,an analytical expression of ETF is derived. Then,based on the obtained ETF,the multiloop PI controler parameters are calculated by exploiting IMC-PID（ internal model control-proportional integral derivation） theory with the help of the Maclaurin expansion. The proposed ETF design approach not only has higher accuracy,but is also applicable to high dimensional non-square systems. Finally,several examples are given to demonstrate the simplicity and the effectiveness of the designed method.