Convergence and Energy Analysis for Iterative Adaptive ON-OFF Control of Piezoelectric Microactuators

A technique is presented for estimating the number of iterations needed for convergence of iterative adaptive ON-OFF controllers to optimal switching times, for certain controllers proposed for managing stepping motion in autonomous microrobots. An upper bound on output error as a function of error in ON-OFF switching times is obtained, and lower bounds on the change in switching times from iteration-to-iteration are used to estimate output error evolution. The simulation and experimental results from the test case of a piezoelectric microrobotic leg joint indicate reasonable agreement between estimated and actual error. The use of convergence estimates to improve controller design with respect to total energy consumption is then described.