Three-Stage Feedback Controller Design With Applications to Three Time-Scale Linear Control Systems

Abstract

This paper presents a new technique for design of full-state feedback controllers for linear dynamic systems in three stages. The new technique is based on appropriate partitioning of the linear dynamic system into linear dynamic subsystems. Every controller design stage is done at the subsystem level using only information about the subsystem (reduced-order) matrices. Due to independent design in each stage, different subsystem controllers can be designed to control different subsystems. Partial subsystem level optimality and partial eigenvalue subsystem assignment can be achieved. Using different feedback controllers to control different subsystems of a system has not been present in any other known linear full-state feedback controller design technique. The new technique requires only solutions of reduced-order subsystem level algebraic equations. No additional assumptions were imposed except what is common in linear feedback control theory (the system is controllable (stabilizable)) and theory of three time-scale linear systems (the fastest subsystem state matrix is invertible)). The local full-state feedback controllers are combined to form a global full-state controller for the system under consideration. The presented results are specialized to the three time-scale linear control systems that have natural decomposition into slow, fast, and very fast subsystems, for which numerical ill conditioning is removed and solutions of the design algebraic equations are easily obtained. The proposed three-stage three time-scale feedback controller technique is demonstrated on the eighth-order model of a fuel cell model.

Two-stage multirate state feedback control designs for systems with slow and fast eigenvalue modes

“…Hence, the use of singular perturbation techniques may not be feasible always. Instead, the use of similarity transformations to derive decoupled subsystems could be a more promising method (Gajic et al, 2017). Because of this, the proposed two-stage MSFC design uses similarity transformations.…”

Multi-Timescale-Based Partial Optimal Control of a Proton-Exchange Membrane Fuel Cell

“…Terms 1 , 2 , 3 ,B 2 ,B 3 , α 12 ,α 13 andβ 2 are spelled out in the Appendix A.2. Comments on the required computational power needed to solve those iterative equations and achieved precision and convergence rate are provided in [39].…”

“…Coupling analysis showed that some sort of the decoupling control strategy would optimize the system performance. The recent approach presented in [38][39][40], tackle the coupling interference between physical variables represented as states in the model, by investigating PEMFC subsystems as systems with multiple time scales. It was suggested and demonstrated in [41] that PEMFC has at least three distinct characteristic time scales, processes with response time less than 1s, approximately 100s and more than 1000s.…”

“…This approach in controlling large scale systems with multiple time scales is applied to nuclear reactors [56]. Future work: Our group specialized this design for 2 timescale systems [57] and expanded the work to 3 timescale systems [39,58]. The multistage design framework is quite universal and future research directions could include the possible expansion to 4 timescale systems, which is already outlined in [59].…”