Low parametric closed-loop sensitivity realizations using fixed-point and floating-point arithmetic

The Specialized Implicit Form provides a general framework for the analysis and design of digital controller implementations with minimal finite wordlength effects. This paper proposes a measure of the closed-loop transfer function sensitivity to finite wordlength effects that is generalized for both fixed-point and floating-point arithmetic and can be used with the Specialized Implicit Form to analyze the effects of quantization and rounding on the parameters of a digital controller implementation. The measure is computationally tractable and hence amenable to solving the problem of minimizing the parametric sensitivity FWL effect. Furthermore, the sensitivity to the rounding of each individual parameter can be easily obtained. The use of the measure is illustrated with examples.