Linear Fractional Transformation modeling of multibody dynamics around parameter-dependent equilibrium
This paper proposes a new Linear Fractional Transformation (LFT) modeling approach for uncertain Linear Parameter Varying (LPV) multibody systems with parameter-dependent equilibrium. The most common procedure relies on the polynomial fitting of a set of Linear Time Invariant models over a grid of equilibrium points, which may be time consuming and miss worst-case configurations. An alternative is the symbolic linearization of the nonlinear equations, but it is often computationally heavy for complex systems. The proposed approach relies on the linearization of the equations at the substructure level before assembly of the multibody system. The linearized model is obtained under the form of a block-diagram, from which the LFT representation can be derived as a continuous function of the uncertain, varying and design parameters. Thus, the model covers all plants within the specified bounds without introducing conservatism or fitting errors. The method can be extended to boundary conditions, bodies and kinematic joints others than those addressed in this paper by deriving their individual linearized models. Targeted engineering applications include modeling of uncertain LPV systems, robust vibrations control, robust gain scheduling, integrated control/structure co-design. Two numerical applications: gain scheduling for a LPV robotic arm, and control/structure co-design of a stratospheric balloon with on-board telescope, are proposed to illustrate the approach.
- Pub Date:
- September 2021
- Electrical Engineering and Systems Science - Systems and Control
- This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible