Improved closed-loop stability for fixed-point controller realizations using the delta operator (Q2710021)

Due to truncation errors, a stable closed-loop system may achieve a lower than predicted performance or even become unstable when the infinite precision control law is implemented with a fixed-point digital processor. To improve the closed-loop stability when the control law is implemented, the authors develop a state-space approach that selects the control law realization to optimize a stability-related objective function using the delta operator. They derive a mapping function between the optimal delta and forward-shift finite-precision control law realizations and it is shown both analytically and numerically that for sufficiently fast sampling the optimal delta realizations have better finite word length properties than the optimal forward-shift realizations. Furthermore, a delta \(H_\infty\) control law has been designed for a teleoperation system and a comparison has been made between the delta control law and the forward-shift control law which demonstrates the improvement of a closed-loop stability by using the delta representation.