分布式模型預測控制算法相關研究
發(fā)布時間：2018-10-12 15:42
【摘要】：隨著科學技術的不斷發(fā)展,現(xiàn)代工業(yè)過程呈現(xiàn)出結構復雜、規(guī)模龐大、子系統(tǒng)間能量、物料耦合強烈等特性。分布式模型預測控制(Distributed Model Predictive Control, DMPC)是一種有效的解決大規(guī)模系統(tǒng)控制問題的方法。DMPC的優(yōu)勢在于：(1)減小每個子系統(tǒng)的計算負擔；(2)多個控制器之下可以提高系統(tǒng)的可擴展性；(3)系統(tǒng)的容錯能力強等。DMPC算法的主要設計目標在于：在盡可能簡單的系統(tǒng)通信方式和盡可能少的通信負擔之下達到盡可能好的控制性能,同時保證算法的收斂性和系統(tǒng)的穩(wěn)定性。針對DMPC算法以及控制器設計中的相關問題,本文圍繞DMPC快速算法設計,大系統(tǒng)結構拆解以及MPC控制系統(tǒng)性能評估問題進行研究,取得以下成果：1.針對分布式預測控制大系統(tǒng)拆解問題,提出了一種基于遺傳算法(GA)的最優(yōu)結構分解方法。該方法包括兩個新的拆解指標分別對應分解的兩個階段,包括輸入分組(Input Clustering Decomposition, ICD)以及輸入輸出配對(Input-Output Pairing Decomposition IOPD)。ICD可以用來消除子系統(tǒng)之間輸入的耦合,同時還能平衡各個子系統(tǒng)之間的計算負擔, IOPD是為了找到合適的輸入輸出之間的配對。ICD和IOPD所對應的優(yōu)化問題是通過GA來求解的。2.針對DMPC分布式算法設計問題,提出了一種基于SVD分解的DMPC算法有效降低了子系統(tǒng)間的通信負擔。該方法在無約束的情況下,把集中式MPC在線二次優(yōu)化問題轉到共軛空間進行處理。每個子系統(tǒng)可以獨立并行地求解各自的最優(yōu)控制輸入,全局的最優(yōu)輸入可以由各個子系統(tǒng)的解合并來產(chǎn)生。該方法同樣可以推廣到有約束的情況之下,得到的無約束解首先在共軛空間中并行檢查,然后再根據(jù)奇異值的大小去除小的奇異值所對應的解,最終可以得到帶有約束情況下的最優(yōu)解。3.針對DMPC在線優(yōu)化問題,提出了一種基于有效集方法(active-set)的快速DMPC算法,該算法利用Hessian矩陣的離線求逆來快速求解一個帶約束的分布式有效集二次規(guī)劃問題。根據(jù)無約束解的大小,提出了一種雙模式優(yōu)化策略來加快在線計算速度。該算法可以提前停止迭代,同時可以保證系統(tǒng)穩(wěn)定性,并且易于實現(xiàn)。最后,一種利用前一時刻DMPC最優(yōu)值的暖啟動的策略可以進一步加快算法迭代收斂速度。4.針對串聯(lián)結構DMPC算法的設計問題,提出了一種分布式模型預測算法,該算法利用串聯(lián)結構各個子系統(tǒng)的輸出僅與其上游子和其本身系統(tǒng)輸入相關的特點,對傳統(tǒng)的迭代式DMPC算法進行改進,得到一種非迭代的遞階求解DMPC算法。5.針對MPC性能評估及改進問題,提出了一種在線提升MPC控制系統(tǒng)經(jīng)濟性能的方法。該方法根據(jù)系統(tǒng)在線收集的數(shù)據(jù),利用迭代學習方法不斷在線調(diào)整MPC控制器參數(shù),從而不斷在線提升MPC控制器的經(jīng)濟性能。本文同時也對該方法在分布式MPC系統(tǒng)上擴展的可能性進行了相關討論。
[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.
【學位授予單位】：浙江大學
【學位級別】：博士
【學位授予年份】：2015
【分類號】：TP13
本文編號：2266681
[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.
【學位授予單位】：浙江大學
【學位級別】：博士
【學位授予年份】：2015
【分類號】：TP13
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