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Prediction of Angular Acceleration for Practical Realization of Incremental Nonlinear Trajectory-tracking Control for Aircrafts

Jun-Young An and Chang-Joo Kim*
International Journal of Control, Automation, and Systems, vol. 20, no. 4, pp.1250-1265, 2022

Abstract : This study proposes a novel algorithm to accurately predict the angular acceleration required for incremental nonlinear control design. To this end, the angular acceleration of the body as well as the Euler angles provided by the navigation system are used to interpolate the attitude trajectories using a Hermite-spline polynomial. By differentiating the resultant trajectory function, the angular acceleration can be predicted accurately. This study proposes three different algorithms using cubic, quartic, and quintic Hermite-spline predictors. The accuracies achieved using these algorithms were investigated by applying them to rotorcraft responses with the doublet and linear-cusp types of lateral-cyclic control. The simulation results are compared to those obtained using conventional first and fifth-order backward-difference formulas (BDFs) and those obtained using washout filters to evaluate the relative accuracy. The results verified that the cubic Hermite-spline algorithms predict the angular acceleration more accurately than conventional BDFs, regardless of the sampling rate and abruptness of the maneuver. The proposed algorithms were applied to incremental backstepping control design to evaluate the effect of the sampling rate on the controller performance. Further, the attitude-rate response type for manned rotorcraft and autonomous trajectory-tracking control for unmanned aircraft were designed and simulated with different sampling rates, ranging from 25 Hz to 200 Hz. The proposed algorithms outperform the first-order BDF in terms of trajectory-tracking accuracy. The fifth-order BDF failed to provide stable control for all examined sampling rates. The washout filter demonstrated relatively poor performance, even making the rotorcraft flight partially unstable. The commanded attitude-rate trajectory was tracked well even with a 25 Hz sampling rate using the proposed methods. The autonomous transient-turn can be accomplished with a sampling rate greater than 75 Hz; therefore, the proposed algorithms can be implemented with considerably lesser computational resources than those of conventional BDFs to achieve the same level of prediction accuracy.

Keyword : Acceleration prediction, incremental backstepping control, incremental dynamics, nonlinear control, rotorcraft, trajectory tracking.

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