Missile longitudinal autopilot design using backstepping approach

Abstract

The tactical missile autopilot design process is detailed from a backstepping control perspective. Wherein, two autopilot topologies are proposed, i.e. the angle of attack (AOA) autopilot and acceleration autopilot. The nonlinear missile longitudinal dynamics is dealt with firstly to meet the strict feedback form. Control parameters of AOA autopilot are introduced in turn and required to be positive real numbers during the recursive process, however, act with some combination form in the final law. Thus a set of new parameters is presented to simplify the expression and disclose the conservatism of the aforementioned autopilot design. The results show that the positive real requirement on AOA autopilot parameters during step by step design has an unfavorable effect on closed loop system performance. An acceleration autopilot as a tracking problem is then set up and developed. On the one hand, the derivative of measured acceleration containing much noise is included in the law, which is thus not benefit to practical implementation. On the other hand, it's hard to transform the design parameters in the control formula into a compact form similar to the case of AOA autopilot. Two control gains, i.e. k1 and k2, are determined on the basis of step and sine command tracking. The results show that k1 affects mainly system steady state error, and k2 affects mainly response speed. Moreover, k1 is bounded and its upper bound has less relevance with k2. Compared with the traditional linear three-loop acceleration topology, the nonlinear acceleration autopilot based on a backstepping approach exhibits excellent tracking performance and robustness. In spite of good performance, the application of nonlinear autopilot is limited owing to a lack of physical meaning and complex engineering implementation. Actually, the exact mathematical model including aerodynamics and unconventional control strategy of an advanced missile could hardly be obtained from wind tunnel testing data or software simulation. Both linear and nonlinear autopilots could stabilize a static unstable missile. Through the control usage analysis, it can be concluded that actuator resource is the crucial factor in controlling a static unstable missile12.