Counterexamples to the Maximum Speed/Energy IMC Theory – A New Geometric Consideration Incorporates the Multivariable Perfect Control Defined in the LTI Discrete-Time State-Space Framework
Wojciech Przemyslaw Hunek, Tomasz Feliks · Cybernetics & Systems · 2020
In this paper, the counterexamples to the general theory related to the state-feedback IMC plants are given and investigated. It is shown, that the maximum-speed multivariable perfect control schemes do not necessitate the maximum-energy of the control input variables. In that way, the IMC peculiarities involving the nonzero perfect control closed-loop poles are indicated, which constitutes a solid counterweight to the well-known general system theory. A new geometric approach results in counterexamples for both full and non-full rank plants, giving rise to the introduction of a complete analytical paradigm in the nearest future. Numerical examples confirm the intriguing issues covering the paper.