一种基于分数阶卡尔曼滤波器的模型预测控制器的设计与实现

针对一类分数阶线性系统，设计了一种基于分数阶卡尔曼滤波器的模型预测控制器。采用分数阶微分的Grunwald-Letnikov定义对被控对象的分数阶状态空间模型进行离散化，构造了一种分数阶卡尔曼滤波器，并将该滤波器得到的状态估计应用于预测控制系统的最优状态反馈控制中。将所提出的方法用于一种黏弹性阻尼系统的控制，仿真结果表明该预测控制器在设定值跟踪、抗噪声扰动等方面都有良好的控制性能；分数阶微分的短记忆长度不仅会影响分数阶卡尔曼滤波器的估计精度，还会对预测控制器的性能产生重要影响。

Design and implementation of a model predictive controller based on a fractional Kalman filter

In this paper, a fractional Kalman filter-based model predictive controller is studied with a fractional order linear system. By using the Grunwald-Letnikov definition of the fractional derivative, the fractional state-space model of the controlled plant is discretely approximated, and a fractional Kalman filter is designed to estimate the unpredictable states, which were then used to give to optimal state feedback control for the system. Simulation results of the control of a viscoelastic damping system show that the proposed predictive controller has good performance in set-point tracing and noise disturbance rejection. Furthermore, it is also found that the length of short memory of the fractional derivative can not only affect the fractional Kalman filter’s accuracy, but also have a significant impact on the performance of the proposed predictive controller.