Error-Domain Conservativity Control to Transparently Increase the Stability Range of Time-Discretized Controllers

Abstract

Time-discretization introduces an explicit time dependency for control laws that were originally designed to depend exclusively on an error variable: At different times, the control actions at the same error value might differ. Integrating the control action over the error reveals that this time dependency translates into the energy. It can directly cause active behavior when energy values at given error values decrease over time, potentially destabilizing the system. In this work, we aim to prevent energy values at given error values from decreasing over time. To this end, energies are recorded when error values are encountered for the first time. Linear interpolation of the recorded energy values provides a lower limit for energy as a function of the error value. This limit is enforced using an adaptive damping. The main contributions of this work include increasing the stability range with minimal amplitude control modifications, while promoting a symmetric behavior of control actions and energy. The approach's characteristics are shown in simulation and validated in experiments.