双回路控制系统PI/PID控制器的解析设计

针对化工双输入输出时滞过程,基于常用的双回路控制结构提出一种解析地设计PI/PID控制器的方法.根据鲁棒控制H2最优性能指标,提出实际期望实现的系统传函矩阵中的对角元.考虑到两个闭环之间的耦合作用,引入动态解调因子设计最优双回路控制器,采用数学有理逼近的方法得到其实际可执行的PI/PID形式.分析了控制系统保证鲁棒稳定性的充要条件,给出基于谱半径的稳定判据.通过仿真实例验证了文中方法相对于近期发展的数值化设计方法的优越性.

Analytical Design of PI/PID Controllers for Double-Loop Control Systems

For chemical and industrial two-input-two-output processes with time delays,an analytical method for designing the PI/PID controllers was proposed based on a double-loop control structure that is often used in practice.According to the robust control H_2 optimal performance specification,the practically desired diagonal elements of the system transfer matrix are suggested,and in view of the coupling action existing between the two closed loops,dynamic detuning factors are introduced to design the optimal double-loop controllers,and their executable PI/PID forms are derived using a mathematical rational approximation approach.At the same time,the sufficient and necessary conditions for holding the control system robust stability are analyzed,and the stability criterion in terms of the spectral radius is presented.A simulation example was included to demonstrate the superiority of the proposed method over recently developed design methods based on numerical calculation.