Plant-input-mapping discretization in state-space form

The digital redesign technique called the Plant-Input-Mapping (PIM) method, which was developed previously in the transfer-function form, has been extended to a state-space based method, making the application of the method to multi-input multi-output systems easier. The transfer-function-based design uses the matched-pole-zero discretization, which is available only for single-input single-output systems, to satisfy the control-zero-principle. In the present study, the role of the principle is interpreted in the form of the uncontrollable modes under an observer-based state feedback structure. The step invariant model of the underlying continuous-time closed-loop system is used as the reference model, and the parameters of the digital controller are determined to match the discrete-time closed-loop system with this reference model. The resulting PIM controller guarantees the stability for any non-pathological sampling intervals as in the conventional transfer-function-based PIM and its superior performances to conventional digital redesign techniques are verified through some numerical simulations.