分布式模型预测控制算法相关研究

发布时间：2018-10-12 15:42

【摘要】：随着科学技术的不断发展,现代工业过程呈现出结构复杂、规模庞大、子系统间能量、物料耦合强烈等特性。分布式模型预测控制(Distributed Model Predictive Control, DMPC)是一种有效的解决大规模系统控制问题的方法。DMPC的优势在于：(1)减小每个子系统的计算负担；(2)多个控制器之下可以提高系统的可扩展性；(3)系统的容错能力强等。DMPC算法的主要设计目标在于：在尽可能简单的系统通信方式和尽可能少的通信负担之下达到尽可能好的控制性能,同时保证算法的收敛性和系统的稳定性。针对DMPC算法以及控制器设计中的相关问题,本文围绕DMPC快速算法设计,大系统结构拆解以及MPC控制系统性能评估问题进行研究,取得以下成果：1.针对分布式预测控制大系统拆解问题,提出了一种基于遗传算法(GA)的最优结构分解方法。该方法包括两个新的拆解指标分别对应分解的两个阶段,包括输入分组(Input Clustering Decomposition, ICD)以及输入输出配对(Input-Output Pairing Decomposition IOPD)。ICD可以用来消除子系统之间输入的耦合,同时还能平衡各个子系统之间的计算负担, IOPD是为了找到合适的输入输出之间的配对。ICD和IOPD所对应的优化问题是通过GA来求解的。2.针对DMPC分布式算法设计问题,提出了一种基于SVD分解的DMPC算法有效降低了子系统间的通信负担。该方法在无约束的情况下,把集中式MPC在线二次优化问题转到共轭空间进行处理。每个子系统可以独立并行地求解各自的最优控制输入,全局的最优输入可以由各个子系统的解合并来产生。该方法同样可以推广到有约束的情况之下,得到的无约束解首先在共轭空间中并行检查,然后再根据奇异值的大小去除小的奇异值所对应的解,最终可以得到带有约束情况下的最优解。3.针对DMPC在线优化问题,提出了一种基于有效集方法(active-set)的快速DMPC算法,该算法利用Hessian矩阵的离线求逆来快速求解一个带约束的分布式有效集二次规划问题。根据无约束解的大小,提出了一种双模式优化策略来加快在线计算速度。该算法可以提前停止迭代,同时可以保证系统稳定性,并且易于实现。最后,一种利用前一时刻DMPC最优值的暖启动的策略可以进一步加快算法迭代收敛速度。4.针对串联结构DMPC算法的设计问题,提出了一种分布式模型预测算法,该算法利用串联结构各个子系统的输出仅与其上游子和其本身系统输入相关的特点,对传统的迭代式DMPC算法进行改进,得到一种非迭代的递阶求解DMPC算法。5.针对MPC性能评估及改进问题,提出了一种在线提升MPC控制系统经济性能的方法。该方法根据系统在线收集的数据,利用迭代学习方法不断在线调整MPC控制器参数,从而不断在线提升MPC控制器的经济性能。本文同时也对该方法在分布式MPC系统上扩展的可能性进行了相关讨论。
[Abstract]:With the continuous development of science and technology, modern industrial processes show the characteristics of complex structure, large scale, strong coupling of energy and materials between subsystems, and so on. Distributed model predictive control (Distributed Model Predictive Control, DMPC) is an effective method to solve large-scale system control problems. The advantages of DMPC are: (1) reducing the computational burden of each subsystem; (2) improving the scalability of the system under multiple controllers; (3) strong fault-tolerant ability of the system. The main design goal of DMPC algorithm is to achieve the best control performance under the simple system communication mode and the minimum communication burden. At the same time, the convergence of the algorithm and the stability of the system are guaranteed. Aiming at the related problems of DMPC algorithm and controller design, this paper focuses on the design of DMPC fast algorithm, the disassembly of large system structure and the performance evaluation of MPC control system. The results are as follows: 1. An optimal structure decomposition method based on genetic algorithm (GA) is proposed to solve the problem of large scale system disassembly in distributed predictive control (DPC). The method consists of two new disassembly indexes corresponding to two stages of decomposition, including input grouping (Input Clustering Decomposition, ICD) and input and output pairing (Input-Output Pairing Decomposition IOPD). ICD can be used to eliminate input coupling between subsystems). At the same time, it can balance the computational burden between subsystems. IOPD is to find the right pairing between input and output. The optimization problem corresponding to ICD and IOPD is solved by GA. 2. To solve the problem of DMPC distributed algorithm design, a DMPC algorithm based on SVD decomposition is proposed to effectively reduce the communication burden between subsystems. In this method, the centralized MPC online quadratic optimization problem is transferred to conjugate space without constraint. Each subsystem can solve its own optimal control input independently and in parallel, and the global optimal input can be generated by merging the solutions of each subsystem. This method can also be extended to the constrained case. The obtained unconstrained solution is checked in conjugate space in parallel, and then the solution corresponding to the small singular value is removed according to the size of the singular value. Finally, the optimal solution with constraints. 3. A fast DMPC algorithm based on efficient set method (active-set) is proposed to solve DMPC online optimization problem. The algorithm solves a constrained distributed efficient set quadratic programming problem by using offline inverse of Hessian matrix. According to the size of the unconstrained solution, a two-mode optimization strategy is proposed to speed up the on-line computation. The algorithm can stop the iteration ahead of time, ensure the stability of the system, and be easy to implement. Finally, a warm start strategy using the DMPC optimal value at the previous time can further accelerate the iterative convergence rate of the algorithm. A distributed model prediction algorithm is proposed for the design of series structure DMPC algorithm. The algorithm utilizes the characteristics that the output of each subsystem of the series structure is only related to the upper runaway and its own system input. The traditional iterative DMPC algorithm is improved to obtain a non-iterative hierarchical DMPC algorithm. 5. Aiming at the problem of MPC performance evaluation and improvement, a method to improve the economic performance of MPC control system on line is proposed. According to the data collected online, the iterative learning method is used to continuously adjust the parameters of the MPC controller on line, so as to improve the economic performance of the MPC controller on line. This paper also discusses the possibility of extending this method to distributed MPC systems.
【学位授予单位】：浙江大学
【学位级别】：博士
【学位授予年份】：2015
【分类号】：TP13

【相似文献】