Inversion Impossible‪?‬

Under the terms of the US/German MoU (Helicopter Aeromechanics) the Task IX - Modeling and Simulation for Rotorcraft Systems - is defined:

”The overall objective of this task is to improve the modeling accuracy and understanding of helicopter dynamics and control. Improved modeling and understanding of the important issues can be used to increase the fidelity of ground-based simulations, thus allowing early pilot evaluation during the development of new control systems, compatibility checks for improved safety, decreases in experimental flight testing, and hence a reduction in costs and risks.”

One of the recent subtasks under Task IX has been a disturbance rejection study [1], resulting in a UH-60 Black Hawk control equivalent turbulence simulation model [2].

Figure 1: Turbulence model extraction

As illustrated in Figure 1 the basic idea is to have a pilot loosely stabilize a helicopter in a turbulent (input T ) environment (e. g. hovering on the leeward side of a high building), and measure the pilot control inputs (P ) and the reaction (rates, velocities, . . . ) of the helicopter (x). In the off-line extraction phase the measured reaction x (which includes the reaction of the helicopter to both the turbulence and the pilot input) is fed into an inverse model of the helicopter, resulting in the corresponding control input P+T that would be necessary to produce the measured reaction. Again, P+T includes turbulence and pilot input. If the measured pilot input P is subtracted, an equivalent turbulence input Teq remains.

This equivalent turbulence input can then directly be used as an additional control input in any kind of simulator; without the need to gain and implement more complex turbulence models.

During the actual model extraction approach [1] it became clear that

”Ideally, an exact numerical inverse of the coupled MIMO model would be used.”

This paper will therefore present and discuss different approaches to invert dynamical systems.