Guidance And Control With Minimax Command For Angle-Constraint Impact

With the rapid development of guided weapon and the high demand by modern war,more and more weapons are required to attack the target not only with zero miss distance but also with certain impact angles.The extra impact angle constraint doubtless demands better performance of the guidance-control system,which is a big challenge especially for those large stability missiles already with limited maneuverability.To deal with the maneuverability insufficiency suffered by those missiles,there is an urgent need for bringing down the required maneuverability in developing new impact angle constraint guidance and control methods,which has been rarely involved at present.From three design levels,i.e.,the path planning,the guidance law design,and the whole trajectory optimization and control,this dissertation aims at minimizing the peak curvature,the peak acceleration,and the peak angle of rudder reflection,respectively,so that the control saturation can be avoided to the utmost and the large impact angle attack can be realized with high precision under low maneuverability.In the first part of investigation,the terminal guidance problem is idealized to a fundamental geometry problem,and the minimax curvature path connecting two oriented points in a plane is proved.First,in the framework of minimax optimal control,a one-side bending optimal curve is proved through trial-and-error method.Second,by designing auxiliary problems and employing the infinitesimal method,a complete mathematical proof is provided for obtaining the existence conditions and specific forms of the optimal paths under the restrictions of none and one inflection point,respectively.Compared to the previous trial-and-error approach,the mathematical proof is superior in revealing the geometrical nature,considering the whole plane,and guaranteeing the solutions' uniqueness.Third,based on the optimal path obtained,the circular-line guidance law(CLGL)and circular-circular guidance law(CCGL)are proposed for zero autopilot-lag systems,which can effectively reduce the peak curvature.Finally,depending on the relationship between the minimax curvature path and other optimal paths such as Dubins path,an indirect idea for solving minimax problems is proposed.In the second part,a near-minimax acceleration guidance law with consideration of the first-order autopilot lag is proposed based on CLGL and CCGL.First,the failure mechanisms of the original guidance laws are proved and verified through simulations.Then in the terminal guidance phase,the switch point and the lag compensation term are designed to make the guidance law switch to the compensated polynomial guidance law(CPGL).It is proved that the switch point is bound to exist and the maximum acceleration always appears at this point,which not only maintains the law's optimality but also satisifies the terminal constraints.Simulation results indicate that the hybrid guidance law can be applied to situations with large initial angle deviations.In the earlier guidance phase,by switching to the circular phase in advance,the increase in the guidance command caused by its discontinuous change is effectively reduced.Also,the condition is given for ensuring that each of the guidance phases can be conducted successfully.Combining the two improvements above,the hybrid front-modified CL-CPGL(FCL-CPGL)and front-modified CC-CPGL(FCC-CPGL)are proposed.Comparison studies with the numerical solutions validate the near-optimality of the proposed guidance law.In the third part,the peak rudder deflection is minimized by exploiting the optimization potential of the departure angle and the rudder's deflection angle throughout the whole trajectory.By adopting a series of new ideas and methods such as reverse thinking,the hypothesis that the maximum rudder angle generates the maximum overload,an analysis method based on the range-impact angle curve,an inverse interpolation criterion and so on,the launch angle and rudder deflection angle for the whole trajectory are obtained.Then depending on the peak value of rudder deflection,the closed-form guidance command in terms of rudder deflection angle for terminal guidance is provided through the integrated guidance and control design.Simulation study validates the feasiblilty and effectiveness of the proposed approach,and it is shown that the sliding mode controller parameters adjusted by the known rudder deflection angle can be applied to a wider range of guidance scenario.