基于频域的自抗扰广义预测控制的稳定性分析

Stability of active disturbance rejection generalized predictive control based on frequency domain

为了克服广义预测控制的在线计算量大这一不足,本文提出了一种自抗扰广义预测控制(ADRC-GPC)算法。并针对一阶非线性不确定系统,推导了新算法的闭环反馈结构,分析了其频域特性,证明了所提算法的稳定性,利用Bode图分析总结了控制器参数选取的原则与规律。分析结果表明:与传统的广义预测控制相比,新算法可以离线求得丢番图方程的通解,且无需辨识被控对象的参数,因此极大地减少了算法的线计算量;仿真结果表明:和β-GPC预测控制算法相比,新算法具有更好的动态性能和更高的控制精度。

Generalized predictive control（GPC） is an advanced control algorithm that has been applied successfully in the process industry,but it has a large online computation burden. To overcome the drawback of GPC,a novel active disturbance rejection generalized predictive control（ADRC-GPC） algorithm was proposed. First,the principle of the ADRC-GPC was introduced. Second,the closed-loop feedback structure of the new algorithm was deduced based on a first-order nonlinear uncertain system,and its frequency domain characteristic was analyzed to verify the stability of the proposed method. Finally,the principles and laws for selecting the parameters of a controller were summarized by utilizing the Bode diagram. Results show that the proposed method could be used to obtain the general solutions of the Diophantine equations offline in comparison with traditional GPC. In addition,identifying the parameters of the controlled objects is unnecessary,so the online calculation burden can be reduced greatly. Compared with the β-GPC method,the proposed scheme has better dynamic performance and higher control precision.