连续搅拌釜的非线性模型稳定性判据及算法

发布时间：2018-09-16 20:45

【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LMI TOOLBOX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。
[Abstract]:A nonlinear robust model predictive control method is proposed for the (CSTR) process of a continuous stirred tank with complex characteristics such as strong nonlinearity, time-varying and pure hysteresis. Based on the mechanism of material reaction and temperature fluctuation in stirred kettle, the system parameters with strong robustness are assumed to be in convex polyhedron, and then the system equations with highly nonlinear characteristics are discretized and linearized at the temperature stability equilibrium point. The prediction equation of the system is established reasonably, the index function of guaranteed cost is proposed and the difference of Lyapunov function is calculated. The bilinear and linear matrix inequality (BMI and LMI) techniques are used to deal with the robust model predictive control system. The criteria for determining the stability of the closed-loop system under the condition of maintaining better performance are given. Secondly, considering the existence of bilinear matrix inequalities in the condition of stability criteria, a corresponding convex optimization algorithm is designed, which can be easily solved by using LMI TOOLBOX in matlab. Finally, the correctness of the proposed theory and the validity and superiority of the algorithm are illustrated by the system simulation experiments and compared with the existing numerical results.
【作者单位】：辽宁石油化工大学理学院;
【基金】：国家自然科学基金资助项目(60273101)
【分类号】：TQ051.72

【相似文献】