Title: NON-LINEAR STATE FEEDBACK CONTROL FOR NEAR OPTIMAL INTERCEPT IN THREE DIMENSIONS
Abstract: The paper describes the development of an analysis tool to obtain missile performance data for optimal implementation of aerodynamic and thrust magnitude controllable missiles. The objective is to establish which motor type and aerodynamic configuration is best suited to any one of several Air Force missions. Optimal control solutions are derived to define the guidance and thrust magnitude control for air-launched tactical rockets. Constraints such as maximum lift coefficient, maximum load factor, and minimum and maximum velocity and thrust are enforced. The control solutions are non-linear and in a feedback form suitable for on-board implementation. Numerical results from a simulation study are presented which validate the operation of the control solutions. Background The direct application of optimal control theory to the intercept control problem requires the solution of a two-point boundary value problem. Further, the problem is complicated by aerodynamic non-linearities associated with lift, thrust and drag, and control constraints forced by structural and angle of attack limits. These complications result in large computation time so that the resulting solution is unsuitable for both missile performance evaluation and implementation on an airborne digital computer. In the presence of these formidable difficulties, the approach taken here is to obtain a near optimal solution to the problem based on singular perturbation theory [l-31. This method provides an inherently analytic solution to the optimal control problem that satisfies all optimality conditions, while enforcing a broad class of state and control constraints. This is achieved by reducing the original problem to a series of lower order problems that are easily solved. Model order reduction is achieved by initially ignoring the faster (transient) dynamics. These are later accounted for in separate boundary layer analyses. The theory insures that the composite solution (outer plus boundary layers) provides a good approximation to the original problem. The resulting control law is in feedback form and due to its analytic structure is suitable for implementation in an on-board computer. There are several distinguishing features of this study as compared to previous research. Reference [4] considered a similar problem but restricted the analysis to two dimensions. Reference [5] develops the optimal three dimensional control for transport aircraft based on an energy state approach. While this is valid for the transport aircraft problem, the high thrusttweight ratios of
Publication Year: 1979
Publication Date: 1979-01-01
Language: en
Type: article
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Cited By Count: 2
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