Dynamic operability of mimo systems with time delays and transmission zeroes—II. Enhancement

Abstract

Time delays and right half-plane transmission (RHPT) zeroes limit the ability for perfect control in multivariable systems. A numerical evaluation of the RHPT zeroes is required to assess their effect on the closed-loop performance, while the effect of time delays is assessed by an upper and lower response bound. If the design is found to be poorly operable, dynamic operability can be enhanced only by appropriate process design modifications. Multivariable time delay processes usually have infinite transmission zeroes which makes their numerical determination very difficult. To assess the dynamic operability of these systems, a test has been developed that identifies systems with infinite RHPT zeroes and provides information for their fast computation from asymptotic formulas. This work utilizes these developments to identify process design modifications that enhance the dynamic operability of processes with time delays and infinite RHPT zeroes. Results from the theory of distribution of roots of quasi-polynomials are incorporated in a linear programming formulation to identify which delays of the process should be increased and by how much, to result in one with a most finite RHPT zeroes. In certain cases this method removes all zeroes from the RHP. More restricted delay increases identified from the solution of a mixed integer linear programming problem may achieve an optimum lower response bound as well. It is argued that the limitations imposed on the dynamic operability by nonminimum phase elements should not be studied separately when the design is to be modified, but should be considered simultaneously in a unified approach that addresses the interaction of process design and control. Several examples illustrate these concepts and verifies the results.