Design and Real-Time Control of a Flexible Arm

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Frank, Gilbert H.
Krishnaprasad, P.S.
As specified robotic manipulators have been designed to lift and accurately move small loads, the need for machines with lightweight, low inertia links has been noted. Such designs imply that some structural rigidity must be sacrificed, shifting the mechanical resonance spectrum lower in frequency toward the frequencies of interest to the system controller. These lower resonant frequencies with equal or lower damping cause larger absolute end-effector overshoot, in the absence of compensation schemes. One method employed to regain system performance, the observer-controller, involves implementation of a control law utilizing feedback from estimates of all the states of a model of the link (plant) including those states not directly measurable. A particular example of the observer-controller based on a reduced order model of a single link flexible arm is developed in this paper. A plant was designed and built for this experiment consisting of a thin, 36 inch long, aluminum beam connected fixed-free to a motorized hub. Hub angular position, hub rate, and beam tip acceleration are physically measurable. The plant interfaces with an IBM PC AT through an electronics chassis which also drives the motor. An observer-controller for the plant resides as a software program in the PC. The model is developed from a model identification experiment using the beam tip accelerometer as a sensor. The University of Maryland optimization package, DELIGHT.MaryLin, is used to determine the feedback gains required to place the closed loop poles of the plant according to performance constraints specified by the designer. Test results were recorded using a step input by measuring plant tip motion vs. time and comparing the results with the DELIGHT.MaryLin simulation. We conclude that the resonant modes of the plant can, to a certain extent, be controlled by this method and that the observer-controller scheme is a viable tool in this context.