多变量分数阶滞后系统预测控制参数解析调优

Analytical Tuning of Predictive Control for a Multivariable Fractional Dead Time System

提出了一种针对各子系统由一阶加分数阶滞后模型描述的多变量系统模型预测控制参数解析调优方法.首先推导了多变量分数阶滞后系统的状态空间模型;其次,基于该模型构建模型预测控制优化问题,并获得了控制信号的解析表达式;再次,对闭环控制系统进行解耦分析,揭示了模型预测控制器参数与系统闭环性能间的定量关系,通过将参数调优问题转化为极点配置问题,得到能够保证闭环系统性能的模型预测控制器参数取值的解析表达式;最后通过仿真实验验证了本文所设计的参数解析调优算法的有效性.

In this study,we propose an analytical model predictive control(MPC)tuning approach for a multivariable system described by first order plus fractional dead time model for each subsystem.Initially,the multivariable fractional dead time system is transformed into the state space form.Subsequently,an MPC optimization problem is constructed based on the aforementioned model,and an analytical expression can be obtained for the control signal.In addition,the decoupling analysis of the closed-loop control system reveals the quantitative relation between the predictive controller parameters of the model and the closed-loop performance of the system.Therefore,the parameter tuning problem can be redefined as a pole placement problem,and the MPC tuning formulas that ensure closed-loop performance are developed.Finally,the simulation results denote the effectiveness of the proposed analytical parameter tuning method.