【作者】 王敏；

【导师】 王磊；

【作者基本信息】 大连理工大学 ， 运筹学与控制论， 2022， 硕士

【摘要】 航空发动机是飞机的“心脏”。随着飞行包线的不断扩展,对它的控制性能也提出了更高的要求。由于航空发动机的工作情况复杂,所以本文研究了一类带有外部干扰的涡扇航空发动机最优控制问题,主要内容概括如下:1、基于航空发动机的控制系统,我们考虑外部干扰,研究目标函数为极小极大(Min-Max)型的鲁棒模型预测控制(RMPC)问题。航空发动机的控制系统复杂,为了更好地表达“输入—状态—输出”之间的关系,本文以状态空间的线性离散时不变预测控制模型来展开。RMPC中的滚动优化是优化算法性能优劣的关键所在。首先,将最优控制问题(OCP)转化为带约束的Min-Max凸优化问题;其次,将Min-Max凸优化问题转化为变分不等式问题;下一步,应用邻近点算法(PPA)将变分不等式问题转化为两个二次规划(QP)子问题;然后,分别在两个QP子问题中引入松弛变量,转化为适合用交替方向乘子法(ADMM)求解的两个子问题;最后,应用ADMM算法求解这两个问题。通过求解地面慢车工况的涡扇航空发动机RMPC问题,验证了改进算法(RMPC-ADMM)求解策略的鲁棒性,且应用该算法可以使控制系统更快速地达到目标值。2、由于用于求解可分块凸优化问题的预测—校正算法能在保证收敛的前提下获得良好的效果,所以我们用RMPC-ADMM算法求出预测点后再对预测点进行校正,提出了一种基于ADMM的预测—校正算法(RMPC-NADMM)。具体是通过松弛延拓优化ADMM算法,进一步提高算法的求解效率。通过两组仿真算例验证了RMPC-NADMM算法的有效性。更多还原

【Abstract】 The aero-engine is the "heart" of the aircraft.As the flight envelope continues to expand,higher requirements are proposed for its control performance.Because of the complex working conditions of the aero-engine,this paper studies a class of optimal control problems of turbofan aero-engines with external disturbances.Here the main contents are summarized as follows.1.Based on the aero-engine control system,we study the robust model predictive control(RMPC)problem with a Min-Max type objective function by considering external disturbances.In order to express the relationship " input-state-output" better,this paper uses linear discrete time invariant predictive control model in state space to study the complex control system of aero-engines.The rolling optimization in RMPC is the key to the performance of the optimization algorithm.First,the optimal control problem(OCP)is transformed into a Min-Max convex optimization problem with constraints.Second,the Min-Max convex optimization problem is transformed into a variational inequality problem.Next,the neighborhood point algorithm(PPA)is applied to transform the variational inequality problem into two quadratic programming(QP)subproblems.Then,relaxation variables are introduced into each of the two QP subproblems to transform them into two subproblems suitable for solving by the alternating direction method of multipliers(ADMM).Finally,the ADMM algorithm is applied to solve these two problems.The robustness of the improved algorithm(RMPC-ADMM)strategy is verified by solving the RMPC problem of the turbofan aero-engine in ground slow motion conditions,and the application of the algorithm allows the control system to reach the target value more quickly.The robustness of the improved algorithm(RMPC-ADMM)strategy is verified by solving the RMPC problem of the turbofan aero-engine in ground idling,and the application of the algorithm allows the control system to reach the target value more quickly.2.Since the prediction-correction algorithm used to solve the block convex optimization problem yields good results when convergence is guaranteed.Therefore,we propose an ADMM-based prediction-correction algorithm(RMPC-NADMM)by using the RMPC-ADMM algorithm to find out the prediction points and then correct them.Specifically,we optimize the ADMM algorithm by relaxation prolongation to further improve the solving efficiency of the algorithm.The effectiveness of the RMPC-NADMM algorithm is verified by two sets of simulation cases.更多还原