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Research Papers

# Parameter Estimation of Multibody Models of Unstable Systems From Experimental Data, With Application to Rotorcraft Vehicles

[+] Author and Article Information
Carlo L. Bottasso1

Dipartimento di Ingegneria Aerospaziale, Politecnico di Milano, Via La Masa 34, I-20156 Milano, Italycarlo.bottasso@polimi.it

Fabio Luraghi, Andrea Maffezzoli, Giorgio Maisano

Dipartimento di Ingegneria Aerospaziale, Politecnico di Milano, Via La Masa 34, I-20156 Milano, Italy

Here and in the following, quantities related to the plant (the true system, as opposed to a model of it) are indicated using the notation $(⋅)˜$.

1

Corresponding author.

J. Comput. Nonlinear Dynam 5(3), 031010 (May 18, 2010) (10 pages) doi:10.1115/1.4001390 History: Received July 25, 2009; Revised March 08, 2010; Published May 18, 2010; Online May 18, 2010

## Abstract

In this paper, we consider the problem of estimating the parameters in mathematical models of complex systems from experimental observations; the methods and procedures that we develop are general, but in this work we make specific reference to the problem of parameter estimation for multibody-based rotorcraft vehicle models from flight test data. We consider methods that are applicable to unstable systems, since rotorcraft vehicles are typically unstable at least in certain flight regimes. Unstable vehicles must be operated in closed-loop, and this must be explicitly accounted for when formulating parameter estimation methods. We describe two alternative classes of methods in the time domain, namely, the recursive filtering and the batch optimization methods. In the recursive approach, we formulate a novel version of the extended Kalman filter that accounts for the presence of unobservable states in the model. In the case of the batch optimization methods, we present a formulation based on a new single-multiple shooting approach, specifically designed for models with slow and fast solution components. We perform some initial steps toward the validation of the proposed procedures with the help of applications regarding manned and unmanned rotorcraft vehicles.

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## Figures

Figure 1

The problem of parameter estimation

Figure 2

Parameter estimation using the direct approach

Figure 3

Hybrid single-multiple shooting approach

Figure 4

System and model predicted pitch rate time history for a longitudinal stick doublet maneuver: with interference model (solid line) and without interference model (dash-dotted line). Left: EKF; right: OEM. Note: Labels on the y axis were eliminated to protect proprietary information.

Figure 5

System and model predicted pitch acceleration time history for a longitudinal stick doublet maneuver: with interference model (solid line) and without interference model (dash-dotted line). Left: EKF; right: OEM. Note: Labels on the y axis were eliminated to protect proprietary information.

Figure 6

At left: small rotorcraft UAV with steel rods and IMU, suspended at a pivot point. At right: detail of the pivot.

Figure 7

Sketch of the body model with reference frames. The inertial earth-fixed reference frame E of unit vectors (e1,e2,e3) is centered at the pivot point O, whereas the body-attached reference frame B of unit vectors (b1,b2,b3) is centered at G.

Figure 9

Validation problem, Euler angles. Solid line: IMU-measured response. Dashed line: computed response for converged parameter estimation.

Figure 11

RUAV estimation problem, angular velocity body-attached components. Solid line: IMU-measured response. Dashed line: computed response for converged parameter estimation.

Figure 10

Validation problem, progress of moments of inertia with standard deviations. Horizontal line: “exact” CAD-derived values. Light band: error bounds.

Figure 8

CAD model of the object of known inertial properties used for the validation of the procedure

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