In this paper, a new design method with performance improvements of multiloop controllers for multivariable systems is proposed. Precise expression is developed to show the relationship between the dynamic- and steady-state characteristics of the multiloop control system and its parameters. First, an equivalent transfer function (ETF) is introduced to decompose the multivariable system, based on which the multiloop controller parameters are calculated. According to the ETF matrix property, an analytical expression for the PI controller for multivariable systems is derived in terms of substituting the ETF matrix for the inverse open-loop transfer function. In the proposed controller design method, no approximation of the inverse of the process model is needed, implying that this method can be applied to some multivariable systems with high dimensions. The simulation results obtained from several examples demonstrate the effectiveness of the proposed method.

中文翻译：

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时滞多变量系统的解析多环控制

提出了一种改进多变量系统多环控制器性能的新设计方法。开发了精确的表达式以显示多环控制系统的动态和稳态特性及其参数之间的关系。首先，引入等效传递函数（ETF）分解多变量系统，基于该变量计算多回路控制器参数。根据ETF矩阵属性，用ETF矩阵代替逆开环传递函数，得出了用于多变量系统的PI控制器的解析表达式。在提出的控制器设计方法中，不需要过程模型逆函数的近似值，这意味着该方法可以应用于某些具有高维的多变量系统。从几个实例获得的仿真结果证明了该方法的有效性。