Stability issues of finite-precision controller structures for sampled-data systems

Abstract

The paper investigates the sensitivity of closed-loop stability with respect to (w.r.t.) finite word length (FWL) effects in the implementation of the digital controller coefficients. Both the shift and delta operators are considered for controller parameterization. Two tractable lower-bound measures of closed-loop stability are studied, and the optimal realization of general FWL controller structures is formulated as a constrained non-linear optimization problem. The emphasis of the paper, however, is on the derivation of a new algorithmic approach for the optimal realization of FWL PID controller structures. It is shown that, for PID structures, the optimization can be decoupled into two unconstrained problems with a maximum of four independent variables. An optimization strategy is developed to provide an efficient computational method for searching the optimal FWL PID controller realization with maximum stability bound and minimum bit-length requirement. Simulation results involving an IFAC benchmark PID controller system are presented to illustrate the effectiveness of the proposed strategy.