Trajectory-Tracking Controller Design of Rotorcraft Using an Adaptive Incremental-Backstepping Approach

Abstract

This paper treats a robust adaptive trajectory-tracking control design for a rotorcraft using a high-fidelity math model subject to model uncertainties. In order to control the nonlinear rotorcraft model which shows strong inter-axis coupling and high nonlinearity, incremental backstepping approach with state-dependent control effectiveness matrix is utilized. Since the incremental backstepping control suffers from performance degradation in the presence of control matrix uncertainties due to change of flight conditions, control system robustness is improved by combining the least squares parameter estimator to estimate time varying uncertainties contained in the control effectiveness matrix. Also, by selecting a suitable gain set by investigating the error dynamics, a uniform trajectory-tracking performance over operational flight envelope of the rotorcraft is ensured without resorting to the conventional gain scheduling method. To evaluate the proposed controller, comparative results between IBSC and Adaptive IBSC are provided in this paper with sequential maneuvers from the ADS-33E-PRF. The proposed method shows improved tracking performance under variations in control effective matrix in the flight simulation. Robust and stable parameter estimation is also guaranteed due to the implementation of the DF-RLS algorithm for the least squares estimator.

Robust Trajectory-Tracking Control of a Rotorcraft Using Immersion-and-Invariance-Based Adaptive Backstepping Control

“…Equation (22) states that the TF-ABSC meets input-to-state stability (ISS) with respect to d and _ d. Therefore, it is not only the system that converges to a bounded region, but also, the radius of convergence in the trajectory-tracking solution can arbitrarily be reduced by increasing γ i . However, the boundedness of both _ d and d must be guaranteed.…”

“…As a result, estimation results for d4 and d5 may show poor accuracy, since slack variables are assigned to the roll and pitch axes in this controller. Even so, when the disturbed system is controllable, the performance and the stability for the TF-ABSC can be guaranteed due to the stability proof in Equation (22).…”

“…Previous studies have been conducted to effectively cope with the rotorcraft's underactuated system while extending controllers' robustness against existing uncertainties [22,23]. Both approaches are based on driving incremental dynamics out of the original dynamics, and the slack variable approach has been used to reduce design parameters and simplify the control structure.…”

“…In Ref. [22], an adaptive incremental backstepping controller (AIBSC) is designed to estimate the uncertain control effectiveness matrix based on the LS method. While the simulation studies using the AIBSC have validated that the separately designed modular LS estimator can identify the unknown control effectiveness matrix, the main limitation of such an approach is that the stability of the closed-loop system can only be guaranteed under the certainty equivalence principle.…”

“…The I&Ibased DOB is then combined with an adaptive backstepping control (ABSC). To effectively reduce design parameters and simplify the design process, a slack-variable approach [22][23][24][25] is adopted to deal with the underactuated system rather than the traditional hierarchical approach [26] or block-BSC approach [27]. The combined ABSC structure with the I&I-based DOB can effectively decouple the adaptive components and the slack variable update laws.…”