Guidance, Control, And Stability Of Spinning Missiles

Spinning missiles are extensively applied in the guidance weapon because of theiradvantages in simplifying control elements, reducing production costs, facilitating tominiaturization, enhancing the compatibility of system, fitting the jet impulse arrangement,etc. With the trends of diversification, intelligentization, collaborative integration and lowcost, spinning missiles have more potential and promising application in the future.However, the spinning of the airframe induces serious dynamical cross-coupling betweenpitch and yaw, and may further cause flight instability in the form of a divergent coningmotion. Therefore, more attention should be paid to the coning motion stability whenguidance and control systems are designed. Meanwhile, the dynamical cross-coupling maynot only affect the response accuracy of guidance and control systems but also result in badperformance of the missile. Therefore, the decoupling design approach should bedeveloped.In the paper, the mathematical models of spinning missiles in the form of complexsummation are formulated. Both the frames and the system equations for accelerationautopilot, classical three loop autopilot, path following guidance, body pursuit guidance,and homing proportional navigation are obtained respectively. Based on the complexcoefficient system stability criterion, the sufficient and necessary condition of coningmotion stability for spinning missiles with lateral acceleration autopilots and three loopautopilots are analytically derived and further verified by numerical simulations. It is notedthat the stable region of the design parameters for the autopilot shrinks significantly underthe spinning condition and the autopilots designed by independent channel method cannotensure the stability of spinning missiles. Generally, the control coupling induced by thedelay and lag of actuators is the major factor for coning motion instability. And the locationof accelerometers also has great effect on the autopilot stability and the relevant treatmentshould be included. It is observed that the stable region for design parameters is furthernarrowed when an integrator is introduced into the acceleration autopilot while thesteady-state accuracy is dramatically improved. The sufficient and necessary conditions ofconing motion stability for spinning missiles with guidance loops are also analyticallyderived. And the stable regions for design parameters of path following, body pursuit, andhoming proportional navigation are illustrated by case study. It is noted that stable regions of guidance parameters shrink due to spinning, and improperly designed parameters willlead to a divergent coning motion of missile. In additional, numerical simulations indicatethat the coning motion has great effect on guidance precision, and the greater the spinningrate, the larger the miss distance.To address the dynamical coupling during guidance and control system design, a novelstate-feedback decoupling controller design method is proposed by taking the advantages ofsymmetrical characteristic of the coupling. The complex coefficient method is utilized andthe complex feedback gains are obtained by eigenvalue placement, then the couplingbetween pitch and yaw is eliminated by cross-compensating and the desired performancecan be achieved. On the basis of physical configuration of missile control system, theobtained controllers are transformed into acceleration autopilot and three loop autopilot,and their adaptive capability can be easily achieved by gain-scheduling table andinterpolation. Numerical results verify the excellent decoupling performance.To improve the adaptive capability to rapid time varying parameters of guidance andcontrol system, the robust gain-scheduling technology based on parameter-dependentLyapunov function (PDLF) is presented. By defining the spinning missiles as affineparameter-dependent linear parameter varying system (LPV), the parameter-dependentdynamic output-feedback controller is developed, which can ensure the inner stability and a-suboptimal H performance. By Bounded Real Lemma, the design of the controller canbe transformed to the convex optimization problem restricted by Linear Matrix Inequalities(LMI). Meanwhile, the integrated autopilot scheme is developed which combinescross-compensating decoupling with robust gain-scheduling. From simulation, it isobserved that the proposed scheme is perfect in robust stability, feasibility, lessconservatism, well adaptive capability and decoupling performance.