This paper introduces a new design methodology for impact angle control guidance (IACG) laws. The proposed methodology can extend any proven homing guidance laws to their impact angle control versions if the expressions of the estimated terminal flight path angles under those guidance laws are given. The time derivatives of the estimated terminal flight path angles are obtained as functions of the guidance commands. The IACG versions of the homing guidance laws are derived from those functions and the desired error dynamics of the estimated terminal flight path angle. The guidance law of each IACG version has two terms: The first term maintains the characteristics and capturability of the original guidance law and the second term drives the estimated terminal flight path angle to converge to the specified flight path angle. When a well-understood homing guidance law for a certain combination of target and missile models is given, an IACG law for that combination is easily derived without reformulating the guidance problem again. The usefulness of the proposed method is demonstrated by several examples, deriving new IACG laws for various target and missile models.
This paper suggests closed-loop analysis results for both classical and incremental backstepping controllers considering model uncertainties. First, transfer functions with each control algorithm under the model uncertainties, are compared with the ones for the nominal case. The effects of the model uncertainties on the closed-loop systems are critically assessed via investigations on stability conditions and performance metrics. Second, closed-loop characteristics with classical and incremental backstepping controllers under the model uncertainties are directly compared using derived common metrics from their transfer functions. This comparative study clarifies how the effects of the model uncertainties to the closed-loop system become different depending on the applied control algorithm. It also enables understandings about the effects of additional measurements in the incremental algorithm. Third, case studies are conducted assuming that the uncertainty exists only in one aerodynamic derivative estimate while the other estimates have true values. This facilitates systematic interpretations on the impacts of the uncertainty on the specific aerodynamic derivative estimate to the closed-loop system.
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