Stability guaranteed auto-tuning algorithm of a time-delay controller using a modified Nussbaum function

Abstract

Time-delay control (TDC) has been widely used to control various systems thanks to its simplicity and robustness. The control distribution matrix of TDC is assumed to be constant and tuned heuristically. However, the constant TDC control gain could degrade the system control performance and even cause the closed-loop system to become unstable when the system parameters are substantially changing, resulting in the violation of the stability criterion of TDC. We propose an algorithm for automatic tuning of the TDC gain in order to guarantee stability by using a modified Nussbaum function. Thus, the closed-loop system controlled by TDC with the modified Nussbaum function is proven to be semi-globally uniformly ultimately bounded. The auto-tuned gain satisfies the stability criterion of TDC and the proposed method can widen the range of implementable dynamic systems. Simulations are conducted to verify the simplicity, robustness, and guaranteed stability by auto-tuning of the proposed method.