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.