Internal models in regulation, stabilization, and tracking

The internal model concept is fundamental in control problems. In linear control systems, internal models have been described in terms of poles in the unstable (bad) region of the complex plane which contain the needed information for the control system to attain the desired objective. It has been erroneously believed for some time that such internal models did not exist in the non-robust regulation problem when a two-input, two-output plant was considered. It is shown here that such internal models always exist not only in regulation, but also in stabilization and tracking if the appropriate physically meaningful maps are considered, thus completely resolving the existing discrepancy between abstract results and intuition on one hand, and linear regulation literature results on the other. Both robust and non-robust control problems are considered and a complete treatment of internal models in all the basic problems is presented.