Reference Signal Derivative Constraints for Guaranteed Tracking Performance

We formulate a problem to determine a class of reference signals which guarantees a specified level of performance for a tracking system. An algorithm for computing approximate (conservative) solutions to the problem is presented. In particular, derivative constraints on the reference signal and its time derivatives are determined from the full system dynamics. A reference signal satisfying these constraints insures that operating limits are not violated and that the system output tracks the reference signal with a prescribed degree of accuracy. The derivative constraints are computed off-line, without simulation, as a solution to a semi-infinite program. Thus, supervisory planning and control can be performed in the reference signal space without detailed models of the underlying system dynamics. We illustrate the computational algorithm and the application of derivative constraints to reference signal generation for a two-axis computer numerical control cutting tool.