This work presents a unique control approach to improve the stability and performance of dynamic systems by combining Fractional Synergetic Control (FSNC) with Funnel Control (FC). The key innovation is the introduction of a new macro-variable for Synergetic Control (SNC), designed based on FC principles and \(PI^\mu \) controllers, to improve stability and accuracy by integrating fractional-order (FO) theory with SNC. To overcome the difficulties caused by nonlinearities and uncertainties in control systems, the proposed controller makes use of the enhanced flexibility of FSNC and the error-confining powers of FC. The FSNC-FC technique is first validated using Simulink/Matlab and then confirmed by experiments on the water level control system. According to simulation studies, the FSNC-FC controller performs faster in terms of overall system stability, quick trajectory tracking, and robustness against disturbances compared to classical FC, classical SNC, FSNC, and Proportional-Integral FC (PI-FC) controllers. Specifically, the FSNC-FC controller achieves a settling time of 9.56 s, a rise time of 8.17 s, a relative error of \(2.1 \times 10^{-4}\) , and eliminates overshoot. Compared to existing methods, it reduces settling time by \(6\%\) and improves tracking accuracy by \(70\%\) . Experimental validation confirms the FSNC-FC controller’s superior performance in regulating water levels and improving control accuracy, further highlighting the controller’s dependability and effectiveness in practical settings. Experimental results show steady-state errors below \( 1.5\%\) and a \( 25\% \) faster response time compared to benchmark controllers. Furthermore, the proposed controller’s stability was confirmed by the use of Lyapunov technique, indicating its resilience and efficiency in real-world scenarios.
