Initial investigation into the complementary use of black box and physics-based techniques in rotorcraft system identification

  • Susanne Seher-WeißEmail author
  • Johannes Wartmann
Original Paper


Accurate linear helicopter models are needed for control system development and simulation and can be determined by system identification when appropriate test data are available. Standard methods for rotorcraft system identification are the frequency domain maximum likelihood method and the frequency response method that are used to derive physics-based linear state-space models. Also the optimized predictor-based subspace identification method (PBSIDopt), a time domain system identification method that yields linear black box state-space models, has been successfully applied to rotorcraft data. As both methods have their respective strengths and weaknesses, it was tried to combine both techniques. The paper demonstrates the successful complementary use of physics-based frequency domain methods and the black box PBSIDopt method in the areas of database requirements, accuracy metrics, and model structure development using flight test data of DLR’s ACT/FHS research rotorcraft.


System identification Black box Maximum likelihood Predictor-based subspace 

List of symbols

\(a_x\), \(a_y\), \(a_z\)

Longitudinal, lateral, and vertical acceleration (m/s\(^2\))

\(\varvec{A}\), \(\varvec{B}\), \(\varvec{C}\), \(\varvec{D}\)

State-space matrices (continuous time)

\(\mathrm {CR}_j\)

Cramer–Rao bound of the jth parameter

\(\varvec{\mathcal {F}}\)

Fischer information matrix


Cost function

L, M, N

Moment derivatives


Model order


Number of model outputs

p, q, r

Roll, pitch and yaw rates (rad/s)


Measurement noise covariance matrix

u, v, w

Airspeed components (aircraft fixed) (m/s)

\(\varvec{u}\), \(\varvec{x}\), \(\varvec{y}\)

Input, state, and output vectors

X, Y, Z

Force derivatives

\(\delta _{\mathrm{{lon}}}\), \(\delta _{\mathrm{{lat}}}\)

Longitudinal and lateral cyclic inputs (%)

\(\delta _{col}\), \(\delta _{\mathrm{{ped}}}\)

Collective and pedal inputs (%)

\(\phi\), \(\theta\)

Roll and pitch attitude angles (rad)

\(\varvec{\varTheta }\)

Unknown model parameters



Active control technology/flying helicopter simulator




German Aerospace Center


Frequency response


Maximum likelihood


Optimized predictor-based subspace identification (method)


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Copyright information

© Deutsches Zentrum für Luft- und Raumfahrt e.V. 2019

Authors and Affiliations

  1. 1.German Aerospace Center (DLR)Institute of Flight SystemsBraunschweigGermany

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