Hybrid systems of linear partial differential (PDE) and ordinary
differential (ODE) equations accurately model a variety of electromechanical
flexible systems. Models of smart structures, lightweight robots, magnetic
bearing rotors, and web/fiber handling machinery, for example, involve
distributed parameter material models and lumped parameter sensors and
actuators. High performance operation of these systems requires the development
of active feedback controllers that compensate for material flexibility. Due to
the lack of control design tools for hybrid ODE/PDE systems, however, many
researchers discretize the PDE subsystem using approximate methods such as
finite elements. Unfortunately, a controller that stabilizes the discretized
model may destabilize the high frequency modes of the actual distributed system
(i.e. spillover instability). Use of a large number of modes to approximate
the PDE subsystem often results in a complex, high-order control algorithm.
In this seminar, implementable, low order controllers are developed for two hybrid ODE/PDE beam systems. First, boundary force controllers are developed for a cantilevered Euler-Bernoulli beam with an end mass. An exact model knowledge controller exponentially stabilizes the beam displacement given the mechanical system parameters and measurements of the shear, shear-rate, and velocity at the end of the beam. The exact model knowledge controller is then redesigned as an adaptive controller that asymptotically stabilizes the beam displacement while compensating for parametric uncertainty. Second, voltage level controllers are derived for an electrically-driven, flexible link gantry robot. The electrical subsystem dynamics for a permanent magnet brushed DC motor couple with the distributed link dynamics. An integrator backstepping boundary control law is developed that provides a stabilizing control force on the flexible link using the motor voltage input. A velocity observer estimates the gantry velocity, eliminating one feedback sensor. Experimental results demonstrate the improved performance provided by the controllers.