基于分形测度的非线性系统多模型切换控制

Multi-model Switch Control for Nonlinear Systems Based on Fractal Dimension Measurement

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 linearized locally and represented by a multi-model structure,the model＇s switching operation will affect the system＇s performances unfavorably.A novel switching strategy that Fractal Dimension Measurement acts as a switch criterion is proposed to reduce the unfavorable influence.After a nonlinear system is linearized in the equilibrium points,its linear switching models can be established.On the base of this,Euclid Norm used to describe the distance between the real-time operating point and the balance point and its fractal dimension measurement are calculated.Considering that the norm has a greater undulation in the system＇s transient process and its fractal dimension measurement acts as a token of the system＇s breaking change,using fractal dimension measurement as a switch criterion for the multi-model control can make switching become ease,and can optimize the system performances and realize the good result control for the system.A model predictive control strategy based on Laguerre functions is used to design the optimal controller for each linearized sub-system.The simulation results indicate the validity of the proposed method,and the method provides a good effect for the control of superheated steam temperature.