航空发动机增益调度控制的多项式平方和规划方法

针对现有的线性变参数(linear parameter varying,LPV)控制器设计方法都是关于仿射参数依赖系统而没有专门针对多项式描述的LPV系统这一现状,提出了一种基于多项式平方和(sum of squares,SOS)规划的增益调度控制设计方法,并将其用于转速大范围变化时的航空发动机高压转子转速及压比控制.根据发动机非线性模型获取不同转速下的状态空间模型,并利用多项式拟合的方法建立发动机线性变参数模型.给出能够保证无静差的增益调度控制结构,利用有界实定理和多项式平方和理论推导出能够保证闭环系统鲁棒稳定的SOS约束条件,并形成控制器求解的SOS规划问题,通过求解获得多项式描述的增益调度控制器.分别以LPV模型和发动机非线性模型为对象做阶跃仿真,结果表明:高压转子转速/发动机压比控制系统的调节时间在2s以内,稳态误差不超过0.1%. 

Self-scheduled control method for aero-engine based on sum of squares programming of polynomial

Given that existing LPV(linear parameter varying) controller design methods is for affine system but not for polynomial LPV system, a self-scheduled control method based on SOS(sum of squares)programming was put forward for the high pressure rotor speed and pressure ratio controller design.The state-space models were obtained under different rotor speeds by non-linear model, and then these state-space models were used to get engine LPV model by polynomial fitting method. A self-scheduled control structure was proposed to ensure no static error. Combining bounded real theory with SOS theory, the robust stability conditions of the closed-loop system were obtained as SOS constraints, leading to the SOS programming to get gain scheduled controller. LPV model and engine nonlinear model were both used to examine the controller. Results show that the settling time of the high-pressure rotor speed/engine pressure ratio control system is less than 2s, and the steady state error is less than 0.1 percent.