Adaptive Control for 3-disk Torsional Pendulum

Method

An existing linear controller is augmented by a neural network-based adaptive element. The basic approach involves formulating an architecture for which the associated error equation has a form suitable for applying previous results for adaptive output feedback control. The approach is applicable to nonlinear systems with both parametric uncertainties and unmodeled dynamics, and does not place any restriction on the relative degree of the regulated output variable.

Experiment

An actuation device, a brushless DC servo motor, applies torque to the bottom disk. The angles of each disk are measured by encoders; A linear model was selected as a rigid body so that the flexible, unmodelled dynamics be emphasized. A lead controller is designed for the regulation of the bottom disk. A disturbance was applied as an external torque to the system using a friction drive motor attached to the rim of the top disk. Collocated sensor/actuator (control of the bottom disk).

In this case, the regulated output (the angle of the bottom disk) has relative degree 2 with respect to the control voltage. An existing controller is designed as a lead controller assuming the system is rigid.

Collocated sensor/actuator (control of the bottom disk)

Non-collocated sensor/actuator (control of the middle disk)

When the middle disk is selected as the regulated variable, the relative degree bocomes 4. A linear controller is designed as a LQG controller.

Related Publications

  1. Augmentation of an existing linear controller with an adaptive elementAnthony J. Calise, Bong-Jun Yang, James I. CraigAmerican Control Conference, Anchorage, AK, May, 2002calise:acc:2002Keywords: augmentation of existing controllers
  2. An Augmenting Adaptive Approach to Control of Flexible Systems Anthony J. Calise, Bong-Jun Yang, James I. CraigAIAA Guidance, Navigation, and Control Conference and Exhibit, Monterey, California, August, 2002calise:gnc:2002Keywords: augmentation of existing controllers
  3. Augmenting Adaptive Approach to Control of Flexible SystemsAnthony J. Calise, Bong-Jun Yang, James I. CraigJournal of Guidance Control and Dynamics, 27(3):387-396, May, 2004calise:jgcd:2004Keywords: augmentation of existing controllers, flexible systems
  4. Augmenting adaptive output feedback control of uncertain nonlinear systems with actuator nonlinearitiesBong-Jun Yang, Anthony J. Calise, Naira HovakimyanAmerican Control Conference, Boston, MA, June, 2004yang:acc:2004Keywords: augmentation of existing controllers, output feedback