Perfect control for nonminimum-phase unstable systems defined in the multivariable continuous-time state–space framework — An inverse-based approach

• Published in: ISA transactions 2023-09, Vol.140, p.84-96
• Main Authors: Majewski, Paweł, Hunek, Wojciech P., Piskorowski, Jacek
• Format: Article
• Language: English
• Subjects: Continuous-time LTI systems; Nonminimum-phase systems; Nonunique right inverses; Perfect control; Stability; State–space representation
• ISSN: 0019-0578; 1879-2022
• DOI: 10.1016/j.isatra.2023.05.020

In this paper, a new perfect control law dedicated to nonminimum-phase unstable LTI MIMO systems governed in the continuous-time state–space domain is proposed. Two algorithms are investigated, one of which has turned out to be definitely accurate. Henceforth, the inverse model control-based formula can be applied to any right-invertible plants having more input than output variables. Last, not least, through the application of some generalized inverses, the perfect control procedure guarantees the structural stability behavior even for unstable systems. Thus, the notion of the nonminimum-phase property should be understood in terms of a possible achieveability covering the entire class of LTI MIMO continuous-time plants. Theoretical and practical simulation examples performed in the Matlab/Simulink environment confirm the feasibility of the newly introduced approach. •A new perfect control law devoted to nonminimum-phase unstable systems is offered.•The IMC-originated approach is derived from the application of generalized inverses.•A new method certifies a stability for unstable and nonminimum-phase systems.•A new procedure is associated with the continuous-time state–space MIMO framework.•Theoretical and practical scenarios confirm the correctness of the new solution.