火箭发动机燃烧过程的鲁棒非脆弱H_∞控制

The robust non-fragile H_∞ control for the combustion process in rocket motor

针对某液体火箭发动机燃烧室的燃烧过程,设计了鲁棒非脆弱H_∞状态反馈控制器。首先,基于一种新型的时滞分割法和交互式凸组合技术,借助于构造一个包含四重积分项的Lyapunov-Krasovskii泛函(LKF),并利用新的积分不等式方法给出了LMI形式的时滞相关有界实判据;其次,在有界实判据的基础上,采用矩阵的合同变换以及变量替代技巧将燃烧过程非线性矩阵不等式线性化,通过求解线性矩阵不等式得到相应的非脆弱H_∞控制器的可行解。模拟结果验证了本文设计方法的有效性。

In this study we dealt with the robust non-fragile H∞controller for the combustion process in liquid propellant rocket motor chambers.In developing a less conservative H∞performance analysis criterion,we introduced a Lyapunov-Krasovskii functional comprising quadruple-integral term.Then,based on a new delay-partitioning method,the reciprocally convex combination technique and the integral inequality approach(IIA),we formulated the bounded real criterion in terms of linear matrix inequalities(LMIs).Furthermore,based on this bounded real criterion,we translated the nonlinear matrix inequality into the linear matrix inequality by using the matrix congruent transformation and the variable substitution technique,and obtained the parameter expression of non-fragile H∞controller by solving the feasible linear matrix inequality.The numerical examples we provided showed the effectiveness of the proposed theoretical results.