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.
This paper proposes a guidance scheme to operate ship defense missiles using dual seekers—radio frequency and strapdown imaging infrared seekers—against the threat of antiship missiles. Key challenges associated with considered operational concept such as the multipath error of an radio frequency seeker, the narrow field of view of an strapdown imaging infrared seeker, and the interference between the target and defense missiles are identified. A guidance scheme that can address these challenges is proposed by combining an optimal guidance law for the midcourse phase and the proportional navigation guidance for the terminal phase. A relationship among interceptor/target velocity, minimum line-of-sight angle for the radio frequency seeker, and the field of view of the strapdown imaging infrared seeker for a successful intercept is analytically derived and graphically presented. Numerical simulations for the engagements between ship defense missiles and an antiship missile demonstrate the validity of the proposed guidance scheme.
In this paper, theoretical analysis on the incremental backstepping control is suggested especially under the existence of model uncertainties. This algorithm is proposed in the previous studies by modifying the backstepping method to reduce model dependency. Because this method is a type of nonlinear control and the model uncertainties are assumed to be considered, it is difficult to have theoretical analysis, which causes lack of understandings about this algorithm. Therefore, this paper suggests closed-loop analysis with simplified dynamics under the model uncertainty. Transfer function is derived and poles, stability condition, steady state error, and settling time are presented. In addition, the effects of model uncertainties and gains are identified through analysis. Proposed analysis is meaningful in terms of establishing critical understandings about the algorithm, even though the simplified dynamics is applied for analysis purpose.
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