连续搅拌釜的非线性模型稳定性判据及算法

摘要

针对具有强非线性、时变、有纯滞后等复杂特性的连续搅拌釜(CSTR)反应过程,提出了一种非线性鲁棒模型预测控制方法.先根据搅拌釜中物料反应和温度波动机理,强鲁棒性的系统参数假设在凸多面体中,然后,在温度工作稳定平衡点离散线性化具有高度非线性特点的系统方程.合理建立系统预报方程,提出可保成本性能指标函数并计算李雅普诺夫函数的差分.采用双线性和线性矩阵不等式(BMI和LMI)技术处理鲁棒模型预测控制系统,给出了保持较优性能条件下的闭环系统稳定性判定标准.其次,考虑稳定标准的条件中存在双线性矩阵不等式,设计相应的凸优化算法,便于利用matlab中LMITOOLBOX求解.最后,通过系统仿真实验,与已有数值结果对比,说明了所提理论的正确性和算法的有效性、优越性.%A control method of nonlinear robust prediction model was proposed for continuous stirred tank reaction (CSTR) process with complex characteristics,as strong nonlinear,time-varying and pure delay.Firstly,according to the mechanism of material reaction and temperature fluctuation,strong robust system parameters were set in convex polyhedron,and discrete linearization method was applied to deal with the system equation with highly nonlinear characteristics at temperature equilibrium point.By establishing system forecast equation and cost performance index function,difference of lyapunov function was calculated.By utilizing bilinear and linear matrix inequality (BMI and LMI) to deal with the robust model predictive control system,the criterion for judging the stability of the closed loop system was formed under the condition of keeping the better performance.Secondly,for bilinear matrix inequalities were considered in the condition of stability criteria,the corresponding convex optimization algorithm was designed,which was easy to realize by using LMI TOOLBOX in Matlab.Finally,system simulation results illustrated the correctness,effectiveness and superiority of the proposed theory and algorithm,compared with the existing numerical results.