Stabilization of second-order systems using a P/I-delayed controller

Abstract

The present paper describes the stabilization and control of second-order systems using a proportional plus integral delayed controller (P/I-delayed controller). The stabilization of closed-loop control systems using a controller comprehends several techniques to increase the control circuit’s stability. Even in some simple second-order plants, the classical PI controller cannot be applied to pursue the closed-loop stability, although the design requisites, for example, constant reference tracking capability. In this paper, the control will be analyzed using a P/I-delayed controller. The main goal of this article is to obtain the global stability region (the region of global stability) in the two-dimensional $$\left({k_{p},k_{i} } \right)$$ plane for the delay-based P/I-delayed controller and to verify the control using the designed controller. The stabilization of linear-time invariant (LTI) systems with time delay in an integral part of the P/I-delayed controller will be studied in detail. Two typical examples, namely the control of an unstable plant and the control of a stable plant, are used as benchmarks to verify the proposal’s effectiveness. The simulation results show that the presented stabilization method is effective and practically applicable in both analysis and control. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.