非线性系统时间最优模型预测控制

发布时间：2018-06-17 14:03

本文选题：非线性模型预测控制 + 利普希茨条件　；参考：《辽宁工程技术大学》2017年硕士论文

【摘要】：模型预测控制发展至今,线性系统的预测控制理论已经比较成熟了,并且可以有效的处理带有约束的系统、优化求解目标,使得在线计算量足够小,广泛的应用于工业过程中,但是,实际上,大部分工业过程的系统都是非线性的,而且非线性系统的复杂性、多样性和不确定性等因素,其稳定性、鲁棒性、在线优化计算的复杂度都大大增加,因此本文针对带有约束的非线性系统,提出了时间最优的非线性模型预测控制算法,用来求解优化非线性系统,具体内容如下:1.基于Jacobian线性化将非线性系统线性化能够推导产生一系列的凸优化问题,而且产生的线性化误差在Lipschitz条件下确定上边界范围。然后采用双重控制模式策略,在离线情况下构造一系列椭圆集来描述t步可行区域,每个椭圆集的平衡点根据上一个椭圆来选取,最后再根据在线计算合适的输入使系统稳定。采用逐步倒退计算的方法能够确保迭代的可行性和稳定性,数值例子表明算法大大减少了计算负担,证明了算法的有效性。2.针对一类基于多线性模型的约束非线性系统,首先基于间隙度量(gap metric)在操作范围内通过网格化取点将非线性系统进行划分,然后确定最小的线性模型库可以得到一系列线性模型集,这一类线性模型集可以精确估计非线性系统,其次根据鲁棒约束的模型预测控制算法,在离线条件下每一个子模型可以设计一个离线的局部控制器,可以根据模型集构造一些列不变椭圆集合;在线计算合适的输入,使初始状态能够很快的到达目标区域,而且离线计算的方式可以减少在线计算的负担,使得优化求解能够更快更有效的进行,在线条件状态在构造的不同子模型椭圆区域之间的转换能够确保闭环系统的稳定性。最后连续搅拌反应釜(CSTR)验证了算法的可行性。
[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.
【学位授予单位】：辽宁工程技术大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TP273

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