基于PID对角优势补偿阵的过程多变量控制系统设计

Multivariable control system based on PID diagonal dominant compensation matrix

化工过程一般为多变量系统,输入输出变量之间往往存在耦合作用,常规分散PID控制系统难以保证控制质量。为了削弱多变量系统的耦合作用,基于对角优势的设计准则,通过在若干频率点加权优化,设计PID动态预补偿阵。然后利用正Nyquist阵列设计法对补偿后的系统设计控制器,基于对角优势系统的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,初步确定反馈矩阵的稳定参数范围,再按照单输入单输出系统设计动态补偿器,使得系统满足动态控制品质要求。最后通过示例说明,该方法设计的集中控制系统与分散控制相比,控制性能具有一定的优势,且方法简便,容易实现。

Chemical processes are multivariable systems with often coupled interactions between input and outputvariables,which conventional decentralized PID control system is difficult to maintain good control performance.In order to weaken coupling effect in multivariable system,PID dynamic pre-compensation matrix was designed byweighted optimization of many frequency points and diagonal dominance design criterion.A controller of thecompensated diagonal dominance system was designed using positive Nyquist array design method.According toNyquist stability criterion of diagonal dominance system,stable parameter range of feedback matrix was determinedby plotting dominance degree curve and Gershgorin band.After that,dynamic compensator was designed byfollowing single input single output system principle,which made the closed-loop system meet performancerequirements of dynamic controls.Case studies show that centralized control systems designed by this method aremore advantageous,simpler,and easier than decentralized control system.