Application of nonlinear control theory in weapon guidance and control

This thesis considers the application of nonlinear control theory in two subjects pertinent to weapon applications. Initially, Section 2 considers the development of a simple nonlinear autopilot for a Laser Guided Bomb (LGB). Later a nonlinear autopilot design is developed using a Pulse-Width Modulated (PWM) controller derived from the method developed by Bemelli-Zazzera et al4. This is applied to an LGB utilising a “bang-bang” actuator, enabling the control surfaces to achieve a pseudo-proportional response. The PWM design stems from an equivalent Pulse Amplitude Modulated controller, which required a design technique to be developed for a linear autopilot and, in addition, simulation of an electro-mechanical actuator. Simulation demonstrated that the PWM controller can achieve the desired response but the design must incorporate actuator dynamics. Section 3 considers the use of nonlinear control theory to examine the nonlinear intercept equations using a Proportional Navigation (PN) guidance law. Using a simple heuristic example, PN is introduced and vector algebra used to develop a simple model of the intercept. The model is then used to illustrate the importance of the kinematic gain. Using the method pioneered by Ha et al16, Lyapunov theory is used to demonstrate that PN is a robust guidance law. Although generally derived assuming the target maintains rectilinear flight, Lyapunov theory is used to demonstrate interception is always possible provided the pursuer has sufficient manoeuvre advantage over the target. Noting that many missiles incorporate a 1 directional warhead, Lyapunov theory is used to design a time-varying rate bias that controls the direction of approach to the target. Simulation demonstrates that the guidance requirements are indeed achieved by this law but additional effort is required by the control system. In Section 3 it is demonstrated that the PN guidance law will always ensure an intercept, i.e. it does not by itself generate miss-distance. In the final part of Section 3, using adjoint software designed by Zarchan42, it is demonstrated that miss-distance develops in practical systems as the result of sub-system dynamics