發(fā)布時(shí)間：2018-05-22 07:39

  本文選題：預(yù)見(jiàn)控制 + 離散提升技術(shù)　； 參考：《北京科技大學(xué)》2017年博士論文

【摘要】：在預(yù)見(jiàn)控制理論和多采樣率系統(tǒng)理論豐碩研究成果的基礎(chǔ)上,本文進(jìn)一步將預(yù)見(jiàn)控制理論與多采樣率系統(tǒng)理論相結(jié)合,研究了幾種不同類型的多采樣率系統(tǒng)的最優(yōu)預(yù)見(jiàn)控制問(wèn)題.本文主要作了以下幾方面的研究工作:(1)研究了具有輸入多采樣率特點(diǎn)的時(shí)變離散時(shí)間系統(tǒng)的最優(yōu)預(yù)見(jiàn)控制問(wèn)題.利用離散提升技術(shù),把多采樣率時(shí)變離散時(shí)間系統(tǒng)轉(zhuǎn)化成一個(gè)形式上的單采樣率系統(tǒng).然后引入一階前向差分算子并結(jié)合差分算子的性質(zhì)構(gòu)造擴(kuò)大誤差系統(tǒng).利用時(shí)變系統(tǒng)最優(yōu)控制的有關(guān)結(jié)果,得到原系統(tǒng)的最優(yōu)預(yù)見(jiàn)控制輸入,并通過(guò)矩陣分解,實(shí)現(xiàn)了 Riccati方程的降階.(2)研究了一類輸入多采樣率不確定離散時(shí)滯系統(tǒng)的魯棒預(yù)見(jiàn)控制問(wèn)題.首先利用離散提升技術(shù),分別將輸入時(shí)滯和多采樣率特點(diǎn)從形式上消除.再根據(jù)預(yù)見(jiàn)控制的基本方法,對(duì)不確定系統(tǒng)構(gòu)造其對(duì)應(yīng)的擴(kuò)大誤差系統(tǒng),然后對(duì)其相應(yīng)的標(biāo)稱系統(tǒng)設(shè)計(jì)帶有預(yù)見(jiàn)作用的控制器.最后根據(jù)Lyapunov穩(wěn)定性理論并結(jié)合矩陣范數(shù)的性質(zhì),得到其閉環(huán)系統(tǒng)的魯棒穩(wěn)定性判據(jù).(3)研究了一類具有干擾預(yù)見(jiàn)的輸出多采樣率離散時(shí)間系統(tǒng)的最優(yōu)預(yù)見(jiàn)控制問(wèn)題.利用系統(tǒng)狀態(tài)與穩(wěn)態(tài)時(shí)的狀態(tài)值之差代替以往差分算子的方法構(gòu)造擴(kuò)大誤差系統(tǒng),并引入積分器來(lái)消除靜態(tài)誤差,進(jìn)而給出原系統(tǒng)預(yù)見(jiàn)控制器的設(shè)計(jì)方法.(4)研究了一類輸出采樣周期整數(shù)倍于輸入采樣周期的雙率離散時(shí)間系統(tǒng)的最優(yōu)輸出調(diào)節(jié)器的設(shè)計(jì)問(wèn)題.利用提升技術(shù)將原系統(tǒng)轉(zhuǎn)化為單采樣率增廣系統(tǒng).然后根據(jù)最優(yōu)調(diào)節(jié)理論并通過(guò)矩陣的合同變換,修正了性能指標(biāo)函數(shù),進(jìn)而得到原系統(tǒng)的最優(yōu)輸出調(diào)節(jié)器.并在此方法的基礎(chǔ)上,研究了一般雙率離散時(shí)間系統(tǒng)的最優(yōu)預(yù)見(jiàn)控制問(wèn)題,給出了一般雙率離散時(shí)間系統(tǒng)的提升狀態(tài)空間模型.結(jié)合預(yù)見(jiàn)控制理論,得到原系統(tǒng)帶有預(yù)見(jiàn)補(bǔ)償?shù)目刂破?上述所有的情況都對(duì)定理成立的條件給出了嚴(yán)格的數(shù)學(xué)證明,并且數(shù)值仿真結(jié)果驗(yàn)證了所提出的研究方法的有效性.
[Abstract]:On the basis of the abundant research results of the theory of foresight control and the theory of multi-sampling rate system, this paper further combines the theory of foresight control with the theory of multi-sampling rate system. The optimal foresight control problem for several different types of multi-sampling rate systems is studied. In this paper, we study the optimal foresight control problem for time-varying discrete time systems with input multi-sampling rate. The discrete lifting technique is used to transform the time-varying discrete time system with multiple sampling rates into a single sampling rate system. Then the first order forward difference operator is introduced and the extended error system is constructed by combining the properties of the difference operator. By using the results of optimal control for time-varying systems, the optimal predictive control input of the original system is obtained, and the matrix decomposition is used. The problem of robust predictive control for a class of uncertain discrete time-delay systems with multiple input sampling rates is studied. Firstly, the discrete lifting technique is used to eliminate the characteristics of input delay and multi-sampling rate respectively. Then according to the basic method of foresight control, the corresponding extended error system is constructed for uncertain system, and then the corresponding nominal system is designed with predictive controller. Finally, according to the Lyapunov stability theory and the properties of matrix norm, the robust stability criterion of the closed-loop system is obtained. The optimal predictive control problem for a class of discrete-time systems with multi-sampling rate output with disturbance foresight is studied. The extended error system is constructed by using the difference between the state value of the system and that of the steady state instead of the previous difference operator, and an integrator is introduced to eliminate the static error. Furthermore, the design method of predictive controller for the original system is given. (4) the design of optimal output regulator for a class of double-rate discrete time systems with an output sampling period integer times greater than the input sampling period is studied. The lifting technique is used to transform the original system into a single sampling rate augmented system. Then, according to the optimal adjustment theory and the matrix contract transformation, the performance index function is modified, and the optimal output regulator of the original system is obtained. On the basis of this method, the optimal foresight control problem for general double rate discrete time systems is studied, and the lifting state space model of general double rate discrete time systems is given. Combined with the theory of foresight control, the controller with predictive compensation in the original system is obtained. In all the above cases, strict mathematical proof is given for the conditions under which the theorem is established, and the numerical simulation results verify the validity of the proposed method.
【學(xué)位授予單位】：北京科技大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2017
【分類號(hào)】：TP13

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