Lyapunov Truncation for Low-Order Modeling of Linear Time-Invariant Unmanned Rotorcraft Flight Dynamics
DOI:
https://doi.org/10.18196/jrc.v6i4.27251Keywords:
Model Order Reduction, Lyapunov Truncation, Flight Dynamics, Linear Time-Invariant Systems, Gramian-Based Reduction, Stability Preservation, Unmanned Rotorcraft, Lyapunov EquationAbstract
This study addresses model order reduction for unmanned rotorcraft flight dynamics, specifically focusing on the development of computationally efficient, low-order representations for fourth-order linear time-invariant (LTI) models. The research contribution is a systematic evaluation of the Lyapunov Truncation (LT) algorithm in the context of rotorcraft dynamics, where the need for reduced-order models is motivated by real-time control and simulation requirements in autonomous aerial vehicles. The LT method exploits controllability and observability Gramians to identify dominant state directions, but it inherently relies on the assumptions of linearity and time-invariance. The reduction process yields models of third, second, and first order, which are comparatively assessed using time-domain (RMSE), peak error, frequency-domain (total error), and statistical reliability metrics. Results show that the second-order reduced model achieves a 50% reduction in system complexity, with RMSE as low as 0.0537 rad/s in the lateral-to-pitch channel and relative errors consistently below 200% for all channels. Maximum deviations remain under one unit for most channels, and total frequency-domain error is minimized at this order (1519.48). In contrast, first-order models exhibit RMSEs exceeding 1000% in certain channels and peak deviations above 4 units, highlighting limitations in preserving stability margins and transient behaviors. Overall, the study demonstrates that second-order Lyapunov Truncation achieves the optimal balance between computational efficiency and dynamic fidelity, supporting its adoption for practical control-oriented reduction of LTI unmanned rotorcraft models within their valid operational envelope.
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