基于常数对角优势补偿阵的多变量控制系统逆Nyquist阵列设计

Inverse Nyquist array for multivariable control system using constant diagonal dominant pre-compensation matrix

化工过程中的多变量系统变量之间往往存在耦合作用,在控制系统设计时一般将传递函数阵对角优势化,对角优势化后按多个单变量系统进行设计。由于传递函数逆阵的对角优势化更容易实现,本文采用伪对角化方法设计常数对角优势补偿阵实现传递函数逆阵的对角优势化,在一个或多个频率点上通过使开环传递函数逆阵每行的非对角项元素模平方之和最小,实现对角优势。然后,利用逆Nyquist阵列设计法对补偿后的系统设计控制器,基于逆Nyquist稳定判据,通过绘制优势度曲线和Gershgorin带判断系统的优势程度,根据Gershgorin带选定反馈矩阵的参数范围,按照单变量控制系统的方法设计动态补偿器,使系统满足动态控制品质的要求。最后通过3个示例说明本文的设计方法简便,且具有良好的控制性能。

There are coupling effects between input and output variables of multivariable system of chemicalprocesses.In control system design,diagonal dominance is usually implemented in transfer function matrix and thenseveral single loop controllers are deployed.Since it is easy to define diagonal dominance by inversing transferfunction,a pseudo diagonal dominance method was used to develop constant diagonal dominant compensationmatrix for inverse transfer function.First,diagonal dominance was obtained by minimizing sum of module valuesquares of off-diagonal elements in each row of inverse open-loop transfer-function matrix at one or more frequencypoints.Then,inverse Nyquist array design method was adopted to design controller for the compensated system.Based on inverse Nyquist stability criterion,diagonal dominance degree was decided from dominance curve andGershgorin diagram.Parameter range of feedback matrix was also selected from Gershgorin diagram.Dynamiccompensators were designed according to method of single variable system,so that the system met quality requirements of dynamic controls.Finally,study on three examples show that the design method is simple and thecontrol performance is excellent.