s.h. jalali naini

A complete miss distance analysis of true proportional navigation is carried out due to initial heading error, step target maneuver, and seeker noise sources assuming a first-order control system using forward and adjoint methods. For this purpose, linearized equations are utilized for deterministic and stochastic analyses. Worst case analysis shows that the maximum value of the final time-miss distance plots reduces by increasing the value of the effective navigation ratio due to initial heading error and step target acceleration. The number of peaks of these curves obeys the relation of the effective navigation ratio minus 1 (or 2) due to heading error (or step target maneuver). Moreover, the normalized miss coefficients due to seeker noise sources and miss due to random target maneuver are computed and approximate formulas are presented using the curve fitting method. This leads to an approximate formula for miss distance budget. Therefore, optimum values of the effective navigation ratio and control system time constant are obtained. Finally, the preferred values of these parameters are calculated for increased RMS miss of 5%, 10%, and 20% compared to its minimum value for two scenarios.

This study presents the miss distance analysis of the first-order explicit guidance law due to seeker noise using the adjoint method. For this purpose, linearized equations are utillized and the adjoint model is developed. Then the first-order equations are obtained and converted into nondimensional ones. The analysis is carried out for different values of the power of the alpha function, defined as the time decrease rate of the zero-effort miss distance to unit control input. The unity power gives the first-order optimal guidance strategy, minimizing the integral of the square of the commanded acceleration during the total flight time.The seeker and control system is assumed as a fifth-order binomial transfer function. Due to computational error and stability consideration, the effective navigation ratio is kept constant for very small time-to-go until intercept, which its effect on the miss distance is also investigated. Finally, approximate formulas are obtained using curve fitting method for rms miss distance due to seeker noise.

In this study, the static and dynamic analyses of a modified integral pulse-width pulse-frequency (PWPF) modulator with small error-reset integrator (SE-RI) logical circuit are carried out using grid search method. A set of quasi-normalized equations is utilized in order to reduce the number of parameters, that is, the integrator gain and the maximum torque of modulator are merged to other parameters. The output of the modified integral PWPF (IPWPF) modulator is limited to 50 Hertz.The preferred regions of the IPWPF are chosen by the amount of limitation on fuel consumption and thruster firings. These preferred regions are obtained for different dead zone values of SE-RI circuit. The analyses are performed in two methods with different choices of Schmitt-trigger parameters (i.e., hysteresis or threshold ratio). The proposed regions described by simple inequality relations represent the rectangular regions, which does not give the whole preferred region. As an advantage of the study, the preferred regions are presented graphically instead of rectangular regions by inequality relations.