Initial Experiments on the End-Point Control of a Flexible One-Link Robot

It has been known for some time ( Gevarter 1970) that if a flexible structure is controlled by locating every sensor exactly at the actuator it will control, then stable operation is easy to achieve. Nearly all commercial robots are controlled in this way, for this reason. So are most flexible spacecraft. Conversely, when one attempts to control a flexible struc ture by applying control torques at one end that are based on a sensor at the other end, the problem of achieving stability is severe. Solving it is an essential step for better control in space: the space-shuttle arm is a cogent example. The next generation of industrial robots will also need such control capability, for they will need to be much lighter in weight ( to achieve quick response with modest energy), and they will need to achieve greater precision by employing end-point sensing. A set of experiments has been constructed to demonstrate control strategies for a single-link, very flexible manipulator, where the position of one end is to be sensed and precisely positioned by torquing at the other end. The objective of this first set of experiments is to uncover and solve problems related to the control of very flexible manipulators where sen sors are not colocated with the actuator. The experimental arrangement described here is also a test bed for new designs for flexible-structure controllers, designs that use insensitive, reduced-order control and adaptive control methods, for example. This paper describes the experimental arrangement, model identification, control design, and first experimental results. Some interesting results are the following. First, good stability can be achieved for such noncolocated systems, and reponse can be achieved that is effectively three times faster than the first natural cantilever period of the system: but a good model of the system dynamics and rather sophisticated control algorithms are essential to doing so. Even then, the system will always be conditionally stable. In addition to the tip sensor, a colocated rate sensor and nearly colocated strain gauges have been found to be very useful for achieving good closed-loop performance, that is, high gain and high band width. Second, there is an ultimate physical limit to achiev able response time, namely, the time required for a wave to travel the length of the member. Well-designed controllers can approach this limit. Third, the use of end-point sensing makes less critical the elaborate dynamic conditioning of position-command signals— "model-following " differentia tors, feed-forward, and the like—such as are typically needed in present-generation robots that use "dead reckoning" in lieu of end-point sensing. With end-point sensing, feedback alone ( suitably conditioned) is sufficient to whip the tip to the commanded position and hold it there precisely. Even more important, a shift in, for example, workpiece with respect to robot base, no longer produces an error.