Dynamic Stability And Robust Gain-scheduling Control Of Spinning Missiles

This paper focuses on some new problems concerning the dynamic stability of low cost spinning guided artillery rockets and the suitable robust gain-scheduling control methods for missiles with fast time varying parameters in a large operation range.It is founded out that the hinge moment acting on the actuator can lead to an extra out-of-plane moment, which may result in the coning instability of the spinning missile. This explained the unstable coning motion of a guided artillery rocket in the flight trials. Both the linearized equation of motion of spinning missiles and the mathematical model of the actuator under the hinge moment are constructed, and the necessary and sufficient conditions of the coning motion stability are then analytically derived and further validated by numerical simulation. Finally, the effects of key parameters on the dynamic stability limit are discussed as well. Besides, it is noted that the stability of the missile can also be guaranteed by retuning the controller of the actuator.It is noted that the backlash in the actuator can result in a limit circular motion of spinning missiles. The mathematical model of the backlash is constructed and the necessary and sufficient conditions for the existence of a limit circular motion is then derived by the describing function method and further validated by numerical simulation as well. Finally, the effects of key parameters on the amplitude of the limit cycle are discussed. Besides, it is noted that the harmful effects of the backlash in the controlled phase is much less than that in the free flight phase.The quasi-linear method is applied to analyze the stability of controlled spinning missiles under the nonlinear Magnus moment, damping moment and static stable moment, respectively. The stable region and the sufficient conditions for limit circular motions are derived, and further validated by numerical simulation. It is concluded that the controller parameters, which ensure the stability based on linear model, cannot guarantee the stability when taking nonlinear factors into account, and a well designed controller helps to enlarge the stability region and eliminate the limit circular motions completely.A robust gain-scheduling control method based on a partial parameter dependent Lyapunov function(PPDLF) is proposed. Both the offline and online computational costs are significantly reduced compared with the existing methods, thus breaking the technical bottleneck that the PDLF cannot be utilized to systems with a large number of dependent parameters. The autopilots for spinning artillery rockets, which feature a large number of dependent parameters varying fast in a large operation range, are further designed with this method. The numerical simulation shows that the designed controller leads to globally satisfactory dynamic performances, decoupling performances, robustness to parameter uncertainty and self-adaptability to fast time varying parameters along the whole flight trajectory. Besides, the criterion for selecting the dependent parameters is also investigated in the paper.A LPV robust gain-scheduling control method with direct output feedback is proposed. The online computational time for the controller parameters is significantly reduced and enabling the real-time online updating of the controller. Besides, the online calculating cost of the inputs is also reduced. The autopilots for spinning artillery rockets are further designed with this method. The numerical simulation shows that the designed controller leads to globally satisfactory dynamic performances, decoupling performances, robustness and self-adaptability along the whole flight trajectory.