Linear, Parameter Varying Model Reduction for Aeroservoelastic Systems

Abstract

This paper applies a model reduction method for linear parameter-varying (LPV) systems based on parameter-varying balanced realization techniques to a body freedom flutter (BFF) vehicle. The BFF vehicle has a coupled short period and first bending mode with additional structural bending and torsion modes that couple with the rigid body dynamics. These models describe the BFF vehicle dynamics with considerable accuracy, but result in high-order state space models which make controller design extremely difficult. Hence, reduced order models for control synthesis are generated by retaining a common set of states across the flight envelope. Initially the full order BFF models of 148 states are reduced to 43 states using standard truncation and residualisation techniques. The application of balanced realization techniques at individual point designs result in 20 state models. Unfortunately, the application of balanced realization techniques at individual operating conditions results in different states being eliminated at each operating condition. The objective of LPV model reduction is to further reduce the model state order across the flight envelope while retaining consistent states in the LPV model. The resulting reduced order LPV models with 26 states capture the dynamics of interest and can be used in the synthesis of active flutter suppression controllers.

Robustness analysis of linear parameter varying systems using integral quadratic constraints

“…The computational solution of such parameter-dependent LMIs requires some finite-dimensional approximation and is typically more involved. The benefit is that arbitrary parameter dependence can be considered, which appears in many applications, for example, aeroelastic vehicles [6] and wind turbines [7,8], by linearization of nonlinear models.…”

A Survey of Linear Parameter-Varying Control Applications Validated by Experiments or High-Fidelity Simulations

“…Aeroservoelastic control faces the problem of state space representations with a high number of states [43]. Commercially available tools for model-order reduction [44], [198] are employed.…”

Actuator and sensor selection for robust control of aeroservoelastic systems

“…Body Freedom Flutter Vehicle [3], [20] Linear, continuous-time, state-space models of the airframe are generated at constant altitude of 1000 ft from 40 to 90 KEAS (knots equivalent airspeed) with increments of 2 knots. Reduced order models with 17 states [21], [22], describe the aeroservoelastic behavior of the aircraft where three dynamic instabilities (flutter) are observed between 10-120 rad/s starting at 44, 60, and 62 KEAS. The control objective is flutter suppression and structural attenuation of flexible modes.…”