發(fā)布時(shí)間：2018-06-17 14:03

  本文選題：非線性模型預(yù)測(cè)控制 + 利普希茨條件�。� 參考：《遼寧工程技術(shù)大學(xué)》2017年碩士論文

【摘要】：模型預(yù)測(cè)控制發(fā)展至今,線性系統(tǒng)的預(yù)測(cè)控制理論已經(jīng)比較成熟了,并且可以有效的處理帶有約束的系統(tǒng)、優(yōu)化求解目標(biāo),使得在線計(jì)算量足夠小,廣泛的應(yīng)用于工業(yè)過(guò)程中,但是,實(shí)際上,大部分工業(yè)過(guò)程的系統(tǒng)都是非線性的,而且非線性系統(tǒng)的復(fù)雜性、多樣性和不確定性等因素,其穩(wěn)定性、魯棒性、在線優(yōu)化計(jì)算的復(fù)雜度都大大增加,因此本文針對(duì)帶有約束的非線性系統(tǒng),提出了時(shí)間最優(yōu)的非線性模型預(yù)測(cè)控制算法,用來(lái)求解優(yōu)化非線性系統(tǒng),具體內(nèi)容如下:1.基于Jacobian線性化將非線性系統(tǒng)線性化能夠推導(dǎo)產(chǎn)生一系列的凸優(yōu)化問(wèn)題,而且產(chǎn)生的線性化誤差在Lipschitz條件下確定上邊界范圍。然后采用雙重控制模式策略,在離線情況下構(gòu)造一系列橢圓集來(lái)描述t步可行區(qū)域,每個(gè)橢圓集的平衡點(diǎn)根據(jù)上一個(gè)橢圓來(lái)選取,最后再根據(jù)在線計(jì)算合適的輸入使系統(tǒng)穩(wěn)定。采用逐步倒退計(jì)算的方法能夠確保迭代的可行性和穩(wěn)定性,數(shù)值例子表明算法大大減少了計(jì)算負(fù)擔(dān),證明了算法的有效性。2.針對(duì)一類基于多線性模型的約束非線性系統(tǒng),首先基于間隙度量(gap metric)在操作范圍內(nèi)通過(guò)網(wǎng)格化取點(diǎn)將非線性系統(tǒng)進(jìn)行劃分,然后確定最小的線性模型庫(kù)可以得到一系列線性模型集,這一類線性模型集可以精確估計(jì)非線性系統(tǒng),其次根據(jù)魯棒約束的模型預(yù)測(cè)控制算法,在離線條件下每一個(gè)子模型可以設(shè)計(jì)一個(gè)離線的局部控制器,可以根據(jù)模型集構(gòu)造一些列不變橢圓集合;在線計(jì)算合適的輸入,使初始狀態(tài)能夠很快的到達(dá)目標(biāo)區(qū)域,而且離線計(jì)算的方式可以減少在線計(jì)算的負(fù)擔(dān),使得優(yōu)化求解能夠更快更有效的進(jìn)行,在線條件狀態(tài)在構(gòu)造的不同子模型橢圓區(qū)域之間的轉(zhuǎn)換能夠確保閉環(huán)系統(tǒng)的穩(wěn)定性。最后連續(xù)攪拌反應(yīng)釜(CSTR)驗(yàn)證了算法的可行性。
[Abstract]:With the development of model predictive control, the predictive control theory of linear system has been mature, and it can effectively deal with the system with constraints, optimize the target, so that the on-line calculation is small enough, widely used in industrial processes. However, in fact, most industrial process systems are nonlinear, and the complexity, diversity and uncertainty of nonlinear systems, such as stability, robustness, and complexity of on-line optimization computation, are greatly increased. Therefore, in this paper, a time optimal nonlinear model predictive control algorithm is proposed for nonlinear systems with constraints, which is used to solve the optimal nonlinear systems. The main contents are as follows: 1. Linearization of nonlinear systems based on Jacobian linearization can generate a series of convex optimization problems, and the resulting linearization errors determine the upper boundary range under Lipschitz conditions. Then a series of elliptic sets are constructed to describe the t-step feasible region under the condition of off-line using dual control mode strategy. The equilibrium points of each ellipse set are selected according to the previous ellipse. Finally, the system is stabilized according to the appropriate input calculated online. The feasibility and stability of iteration can be ensured by the method of stepwise retrogressive computation. Numerical examples show that the computational burden is greatly reduced and the validity of the algorithm is proved. For a class of constrained nonlinear systems based on multilinear models, the nonlinear systems are partitioned by meshing points in the operating range based on gap metric. Then a series of linear model sets can be obtained by determining the smallest linear model base. This kind of linear model set can estimate the nonlinear system accurately, and then according to the robust constraint model predictive control algorithm, An off-line local controller can be designed for each submodel under off-line conditions, and some column invariant elliptic sets can be constructed according to the model set, and the appropriate input can be calculated online so that the initial state can reach the target region quickly. Moreover, the off-line computing method can reduce the burden of on-line computation, so that the optimization solution can be carried out faster and more effectively. The conversion of on-line conditional states between elliptic regions of different submodels can ensure the stability of the closed-loop system. Finally, CSTR verifies the feasibility of the algorithm.
【學(xué)位授予單位】：遼寧工程技術(shù)大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：TP273

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