Dynamics and control of quasirational systems

Abstract

Systems having transfer functions of the form documentclass{article}pagestyle{empty}begin{document}$$ G_P (s) = frac{{P_1 (s) - P_2 (s)e^{ - t_d s} }}{{Q(s)}}, $$end{document} where P 1 ( s ), P 2 ( s ) and Q ( s ) are polynomials, are called quasirational distributed systems (QRDS). They are encountered in processes modeled by hyperbolic partial differential equations. QRDS can have an infinity of right half-plane zeros which causes large phase lags and can result in poor performance of the closed-loop system with PID controllers. Theory on the asymptotic location of zeros of quasipolynomials is used to predict the nonminimum phase characteristics of QRDS and formulas are presented for factoring QRDS models into minimum and non-minimum phase elements. A generalized Smith predictor controller design procedure for QRDS, based on this factorization, is derived. It uses pole placement to obtain a controller parameterization that introduces free poles which are selected to satisfy robustness specifications. The use of pole placement allows for the design of robust control systems in a transparent manner. Controller selection is generally better, simpler and more direct with this procedure than searching for optimal PID controller settings.