Two-stage suboptimal discrete-time regulators for continuous-time stiff dynamic systems

Abstract A two-stage design method is developed for design of linear quadratic regulators (LQRS) with regional pole assignment for a large-scale continuous-time stiff dynamic system and its observer, which do not exhibit a two-time scale structure explicitly. The method also provides a procedure to convert the designed analog LQR and observer to an equivalent digital LQR and observer, respectively, for digital implementations. First, the large-scale stiff dynamic system is block-decomposed into two block-decoupled subsystems according to their own characteristics via the fast and stable matrix sign algorithm. Next, a sequential design procedure is used to design a LQR with regional pole placement for each subsystem. The same procedure is then carried out to design an optimal observer. For implementation of the designed analog LQR using a digital LQR, the designed analog LQR and observer are converted into an equivalent digital LQR and observer, respectively, via a digital redesigned method. A practical stiff system is used as an illustrative example to demonstrate the effectiveness of the proposed method.