基于多项式平方和规划的航空发动机鲁棒LPV/PI控制

针对航空发动机常规(proportion integration,PI)控制器设计过程中难以保证鲁棒性及参数适应性差等问题,提出了一种基于线性变参数(linear parameter varying,LPV)模型及多项式平方和(sum of squares,SOS)规划的控制器设计方法.结合传递函数模型下的鲁棒稳定条件及弱对偶定理给出了多项式描述的LPV模型鲁棒稳定条件,并转化为便于求解的SOS规划问题.根据发动机非线性模型获取不同转速下的传递函数模型,并利用多项式拟合的方法建立发动机LPV模型.根据所提出的定理构造出SOS规划问题,并求解得出LPV/PI控制器.最终以某型双轴涡扇发动机为被控对象,在包线内不同点进行了阶跃仿真,结果表明:高压转子转速控制系统的稳态误差为0,调节时间小于3s. 

Robust LPV/PI control for aero-engine based on polynomial sum of squares programming

A controller design method based on the model and polynomial sum of squares(SOS) programming was put forward for the conventional PI controller of aero-engine featuring poor adaptability and difficulty to guarantee robustness. Combining the robust stability conditions of transfer function model and the weak duality theorem, the robust stability conditions of linear parameter varying(LPV) model depicted by polynomial were proposed. Using the frequency response method, a family of transfer function models was obtained from non-linear model. And then these transfer functions were used to get LPV model by polynomial fitting method. With the proposed theorem and the LPV model, the controller design problem could be transformed into SOS programming problem, which was solved to obtain the linear parameter varying/proportion integration(LPV/PI) controller. Finally the controller was applied to a turbofan engine model. And step simulation results show that the settling time of this high pressure rotor speed control system is less than 3 seconds, and the steady state error is zero.