Maximizing lower bound stability measure of finite precision PID controller realizations by nonlinear programming

This paper introduces a new lower bound stability measure with finite-word-length (FWL) considerations that provides a larger measure than existing bounds and gives a better estimation of the stability robustness of sampled data system with FWL controller implementations. The optimal realization problem of the digital PID controller with FWL considerations is addressed. This parametrization problem is formulated as a nonlinear programming problem with a maximum of four independent variables. A strategy based on Rosenbrock's hill climbing algorithm to solve the optimal realization problem of digital PID realizations is developed, and the methodology is applied to a steel rolling mill to illustrate the effectiveness of the new measure.