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对于一类可局域线性化和多模型表示的非线性系统,模型的切换会对系统的性能产生不利影响,为了减少这些影响,提出了采用分形测度作为切换判据的方法。非线性系统在平衡点处进行线性化后,可建立非线性系统的线性化切换模型。在此基础上,计算用于描述实时运行点与平衡点之间距离的欧几里德范数及其分形测度。考虑到系统过渡过程中该范数波动较大以及其分形测度可作为系统特征突变的一种度量,用这些范数的分形测度作为系统多模型控制的切换判据,使模型切换易于实现,同时优化了系统的性能,实现系统良好控制。文中采用了基于Laguerre函数的模型预测控制方法为每个线性化子系统设计优化控制器。仿真实验结果表明了提出的方法的有效性,且该方法在过热汽温的控制中取得良好效果。
For a class of nonlinear systems that can be localized linearization and multi-model representation, the switching of the model will have an adverse effect on the performance of the system. In order to reduce these effects, a fractal measure as the switching criterion is proposed. After the nonlinear system is linearized at the equilibrium point, a linearized switching model can be established for the nonlinear system. On this basis, the Euclidean norm and its fractal measure, which are used to describe the distance between the real-time operating point and the equilibrium point, are calculated. Considering that the norm fluctuates greatly during the process of system transition and its fractal measure can be used as a measure of sudden change of system characteristic, the fractal measure of these norm is used as the switching criterion of multi-model control of the system, which makes the model switching easy to implement. Meanwhile, Optimized the system performance, to achieve good system control. In this paper, a model predictive control method based on Laguerre function is used to design an optimal controller for each linearization subsystem. Simulation results show the effectiveness of the proposed method, and the method has achieved good results in the control of superheated steam temperature.