应用Lyapunov方法分析自旋导弹动态逆控制器鲁棒性

针对自旋导弹的强非线性特性,设计了二时间尺度分离非线性动态逆控制器.给出了带有气动系数不确定性的控制系统状态空间表达式,利用Lyapunov方法分析了控制器的鲁棒稳定性,并结合舵机性能限幅给出了使系统稳定的内回路时间常数完整边界.通过仿真给出了保证控制系统稳定的气动系数拉偏边界.结果表明:当气动系数向使弹体系统静稳定方向拉偏时,内回路时间常数可取范围较大,反之可取范围逐渐减小直至无法使系统稳定;当内、外回路时间常数比例增加时,控制器对气动系数不确定性的敏感度增加.与三回路控制器相比,动态逆控制器鲁棒性较差,但响应的稳定性较好.

Spinning missile dynamic inversion controller robustness analysis using Lyapunov methods

A two time-scale separation based nonlinear dynamic inversion controller was designed for the spinning missile. A state-space formulation of the control system with the aerodynamic coefficient uncertainties was presented. The nonlinear controller robustness was analyzed using Lyapunov methods. Associating with the actuator's capability, the bound of inner loop time constant was obtained. The aerodynamic coefficient uncertainties boundary was calculated. The result demonstrates that the advisable range of inner loop time constant is large when the uncertainties vary to make the airframe static stable, vice versa. The controller becomes more sensitive against the uncertainties when the inner and outer loop time constant scale increases. Comparing with the three loop controller, the dynamic inversion controller is less robust, but more stable.