热力系统的分数阶特性及其动态矩阵控制

Dynamic matrix control for thermal systems with fractional order characteristics

在热力系统的控制设计或面向控制的特性分析时,目前广泛使用的是整数阶微分方程或者整数阶传递函数。研究表明:大量的热力系统采用分数阶描述比整数阶描述更精确,但是分数阶控制系统研究中存在着控制器参数整定困难等问题。本文基于动态矩阵控制是一种采用系统阶跃响应系数的非参数模型控制算法的特点,将其应用于分数阶系统的控制。因此只需获得系统的阶跃响应模型,从而避免了对于分数阶系统获取分数阶参数模型的困难以及获取整数阶参数模型的必然性模型失配问题,而且动态矩阵控制器参数整定相对简单,鲁棒性强。仿真结果证实该算法对分数阶系统的控制是可行且有效的。

Integer-order differential equation or integer-order transfer function is widely used for design of thermal sys- tem controller or analysis of control-oriented performance. For lots of thermodynamic systems, fractional-order descrip- tion is more accurate than integer-order description. But the study of fractional-order system control shows that it is dif- ficult to get suitable controller parameters. Dynamic matrix control is a non-parametric model control algorithm which u- ses step response coefficients. Based on this characteristic, dynamic matrix control is applied to fractional-order sys- tems. It only needs the step response of the system, which avoids the difficulty of obtaining the parameter model of frac- tional-order system and avoids model mismatch problem when getting integer-order parameter model. Moreover parame- ter tuning of dynamic matrix controller is relatively simple and the controller has a good robustness. Numerical simula- tions show that the algorithm is feasible and effective for fractional-order systems.