Adaptive Autobalancing Boundary Control for a Flexible Rotor

Abstract:

In this project, we design a control strategy for a spinning rotor with an unbalanced disk attached to its free end. The control strategy is composed of a boundary torque applied to the clamped end, and two boundary forces and two boundary torques applied to the free-end. At the clamped-end, the boundary torque ensures that the rotor tracks a desired angular velocity trajectory, while at the free-end, the boundary forces and torques ensure that the rotor displacement is regulated at every point along the length of the rotor. Under the assumption of exact model knowledge, we first develop a model-based control law which exponentially achieves the control objectives. We then illustrate how the model-based control law can be redesigned as an adaptive controller which asymptotically achieves the same control objectives while compensating for parameteric uncertainty associated with unbalanced operation. Simulation results illustrate controller performance.

Theory

Over the last decade, the study of the effects of flexiblility on lightweight body-beam systems has been propelled into the limelight. Motivated, for example, by the prohibitive cost of placing equipment in space, many structural designers and control researchers have focused on lightweight mechanical systems with rigid and flexible components. Mathemtically, such systems are often characterized by a combination of ordinary differential equations (ODEs), partial differentialk equations (PDEs), and a set of boundary conditions. Often, there exists a dynamic coupling between the rigid and flexible components; which makes the design of high-performance controllers for such systems very complex.

The nonlinear boundary control law for the nonlinear, hybrid body-beam model requires the following measurements at the boundaries of the rotor:

  • Displacement of the beam,
  • Shear force experienced by the beam,
  • Curvature of the beam, and
  • Time rates of change of the above quantities

While the model-based control law which assume exact knowledge of the system parameters exhibits exponential regulation, the asymptotic control law which estimates the system parameters online exhibits asymptotic regulation

Simulation results.

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