By Michael Stevens
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Additional info for 30 Minutes to Solve That Problem
8. Here the original output of interest [miss distance or y(tF)] becomes an impulsive input to the adjoint system, and the two original system inputs (target maneuver and heading error) become two adjoint outputs. A simulation of the adjoint block diagram will yield y as a function of ﬂight time y(tF). This means that in an adjoint simulation we obtain the miss distances due to both a step target maneuver and initial heading error for various ﬂight times—all obtained in one computer run! ADJOINT MATHEMATICS The impulse response of the adjoint system h* and the impulse response of the original system h are related by hÃ ðtF À tI ; tF À tO Þ ¼ hðtO ; tI Þ where tI and tO are the impulse application and observation times, respectively, of the original system.
Numerical examples will be presented that demonstrate the power and utility of the adjoint approach. Performance projection comparisons will be made from nonlinear engagement simulation results and adjoint solutions. HOMING LOOP It is convenient to take the linearized engagement equations of Chapter 2 and draw them in block diagram form as is shown in Fig. 1. This type of block diagram is known as a homing loop because it is drawn as a feedback control system. In this diagram missile acceleration is subtracted from target acceleration to form a relative acceleration.
METHOD OF ADJOINTS AND THE HOMING LOOP 39 captures the effect of ﬂight control-system time constant on miss distance. The jaggedness in the nonlinear results is due to the approximate way in which the miss distance is computed. 0002 s. 0002). In this section we have shown the very important result that, when the homing loop has guidance system dynamics, the linearized guidance system model yields very accurate miss distance performance projections for both heading error and target maneuver disturbances.