Time and place: Friday, May 14, 5:50-6:20, 202 Chernoff HallTitle: Flexible Manipulator Control Accommodating Passivity
Violations: Theory and Experiments (½ hour)Abstract: The passivity and small gain theorems are fundamental
results of input-output stability theory; both have been extensively used in
robotics and aerospace control, for example. The passivity theorem states
that the negative feedback interconnection of a passive system and a very
strictly passive system (i.e., input strictly passive with finite gain) is
stable. The small gain theorem states that the negative feedback
interconnection of two systems is stable provided the loop gain is strictly
less than one.
Although the passivity theorem is extremely powerful, the passive nature of the nominal plant to be controlled is often destroyed via unmodeled sensors and actuators which, for example, add time and/or phase delay. These passivity violations disallow the use of the passivity theorem nominally guaranteeing closed-loop stability. Utilizing the small gain theorem is possible provided the plant has finite gain (which is probable), but the controllers may be overly conservative owing to the small gain requirement. This is especially true in the context of flexible manipulator control where the modes of the structure are modestly damped, resulting in very large gain. To recover some of the high gain feedback characteristics of passivity-based control, various authors have investigated "mixing" or "blending" the passivity and small gain properties of systems [1,2,3]. Essentially, the passive nature of the plant being controlled will be exploited when passive properties hold, and the finite gain characteristics of the plant will be exploited when passivity is violated. This allows high gain feedback within the passive bandwidth of the plant, and gain limited feedback when passivity is violated. This control structure naturally fits with physically realizable systems because all real systems roll-off at high frequency (i.e, mass-spring-damper systems, RLC circuits, etc.). In this talk stability and control of systems which possess hybrid properties, that is those that possess both passive and finite gain properties, will be discussed. Two practical and challenging problems will be addressed: the tip control of a one-link flexible manipulator, and the joint control of a two-flexible manipulator. Both of theses systems are nominally passive, but passivity is destroyed by sensor dynamics. Synthesis of hybrid controllers via frequency weighting will be presented, along with experimental results.
References |