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High-fidelity rotorcraft simulation model: analyzing and improving linear operating point models

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Abstract

The simulation of the helicopter motion is a central component in flight control design, handling quality studies, and the understanding of physical effects. At best, the flight test results fulfill the expectations from the simulation. Even though identification and simulation techniques for linear models were continuously developed in the past, the fidelity achieved with existing tools is still insufficient—based on the experience with the research rotorcraft EC135 ACT/FHS. This paper is about the improvement of the simulation fidelity for the bare and stabilized vehicle. A pragmatic procedure is presented that updates a given linear (physics-based) model by adding (not physics-based) models and systems. Methods used are inverse simulation, partial closed-loop analysis, and model stitching. The paper shows how to combine these methods in a certain framework so that the simulation fidelity is significantly improved. Comprehensible examples as well as data from the research rotorcraft ACT/FHS are documented to provide the reader with more insights.

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Notes

  1. Note that any measurement such as flight states, atmospheric states, etc. can be used to describe the tuned inputs. Reference [18] shows additional possible modeling approaches. For the application to ACT/FHS models and data, the input model as depicted in Fig. 2 is sufficient to improve the bare vehicle’s simulation fidelity (based on experience).

  2. Identified state-space models of the ACT/FHS—as documented in Ref. [5]—are all fully controllable and observable and the multiple input multiple output MIMO system only has left halfplane zeros.

  3. For ACT/FHS data, the low-pass filter has its \(3\hbox { dB}\) magnitude decrease at 50 rad/s.

  4. For flight tests with the ACT/FHS, multistep and doublet inputs are performed for different feedback configurations. Sweeps have not been applied as partial closed-loop control responses are validated for a plant model with good simulation fidelity for small control deflections. This means, an adaptation is expected for large control deflections and with little changes on the modeling structure. Multistep responses are used for validation. Doublet signals are used for modeling and for excitation of weakly damped oscillatory modes. In total, up to ten test signals with different feedback configurations have been recorded per control axis in five to ten minutes of flight time.

Abbreviations

ACT/FHS:

Active Control Technology / Flying Helicopter Simulator

\(\mathbf A _{\xi _{op}}, \mathbf B _{\xi _{op}}\) :

Identified matrices: dynamic, input,

\(\mathbf C _{\xi _{op}}, \mathbf D _{\xi _{op}}\) :

Output, and feedthrough (at \(\xi _{op}\))

\(\mathbf A _{a,\xi _{op}}, \mathbf B _{a,\xi _{op}}\) :

Additional matrices for parameter tuning

\(\mathbf A ', \mathbf B '\) :

Residual matrices

\(\mathbf A (\xi ), \mathbf B (\xi )\) :

Interpolated matrices

\(\mathbf f (\mathbf x ,\mathbf u )\) :

Nonlinear system vector

G :

Frequency response

\(\mathbf I\) :

Unity matrix

\(J_{{\text {G}}}\) :

Root mean square error of frequency response data

q :

Pitch rate (rad/s)

\(T_{\text {f}}\) :

Time constant, low-pass filter

u :

Forward speed (m/s)

\(\mathbf u\) :

Control vector

\(\mathbf x\) :

State vector

\(\mathbf x _s\) :

Simulated state vector as part of the inverse simulation

\(\mathbf y\) :

Output vector

\(\mathbf y _r\) :

References (filtered measurements)

\(\delta _x\) :

Longitudinal control (%)

\(\varvec{\varDelta }_m\) :

Input uncertainty

\(\varvec{\varDelta }_{m,s}\) :

Stochastic part of \(\varvec{\varDelta }_m\)

\(\varvec{\varDelta }_{m,d}\) :

Deterministic part of \(\varvec{\varDelta }_m\)

\(\theta\) :

Pitch attitude (rad)

\(\xi\) :

Interpolation variable, i.e., aerodynamic velocity

\(\omega\) :

Frequency (rad/s)

1:

First partition of a vector

2:

Second partition of a vector

f :

Filtered value

\(is\) :

Inverse simulated value

m :

Measured value

T :

Trim value

\(\xi _{op}\) :

Operating point (i.e., characterized by airspeed)

\(\varDelta \square\) :

Perturbed value “\(\square\)”

\(\square ^{\text {T}}\) :

Transpose of the value “\(\square\)”

\(\dot{\square }\) :

Derivative \(\partial \square /\partial t\)

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  1. Institute of Flight Systems, Deutsches Zentrum für Luft- und Raumfahrt, Brunswick, Germany

    Steffen Greiser

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Greiser, S. High-fidelity rotorcraft simulation model: analyzing and improving linear operating point models. CEAS Aeronaut J 10, 687–702 (2019). https://doi.org/10.1007/s13272-018-0345-9

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