Controller compensator conversions to estimator-controller forms

In this paper, the problem of converting linear time-invariant compensators to their corresponding state estimator- or observer-based feedback control forms is considered for the case of not necessarily strictly proper plants and controllers. For the full-order state estimator-controller conversion case, subtle but important differences between two earlier works are noted and discussed; as well, sufficient conditions for an invariant property involving the product of candidate control feedback and estimator update gain parameters are given, and for the specific case of single-input single-output systems having a specified plant and controller model, it is shown how this product always is equal to a constant. In the reduced-order state observer-controller conversion case based upon the method of Luenberger, new necessary conditions for the existence of real-valued solutions are specified, and explicit corresponding analytic design equations are provided. Within this particular reduced-order framework, these results highlight how general candidate solutions only are available under certain specific a priori conditions. Simulations of conversion results when applied to a conventional hard disk drive plant and discrete-time control system additionally are presented, and concordance results demonstrate the effectiveness and feasibility of such transformation schemes.