Optimal Finite-Precision Controller Realizations in Block-Floating-Point Format

The paper analyzes the properties of the controller coefficient perturbation resulting from using finite word length (FWL) block-floating-point arithmetic and investigates the closed-loop stability issue of finite-precision realizations for digital controllers implemented in block-floating-point format. A true FWL closed-loop stability measure is derived which considers both the dynamic range and precision of number representation in block-floating-point format. To facilitate the design of optimal finite-precision controller realizations, a computationally tractable FWL block-floating-point closed-loop stability measure is introduced and the method of computing the value of this measure for a given controller realization is developed. The optimal controller realization is defined as the solution that maximizes the proposed measure, and a numerical optimization approach is adopted to solve for the resulting optimal realization problem. A numerical example is used to illustrate the proposed design procedure.