Variable Step-Size FxLMS Algorithm Based on Cooperative Coupling of Double Nonlinear Functions

Based on the principle of symmetry, we propose a variable step-size FxLMS algorithm with double nonlinear functions cooperative coupling (DNVSS-FxLMS), aiming to optimize the contradiction between convergence rate and steady-state error in the active pressure pulsation control system of hydraulic systems. The algorithm innovatively couples two types of nonlinear mechanisms (rational-fractional and exponential-function-based), constructing a refined error-step mapping relationship to achieve a balance between rapid convergence and low steady-state error. Simulation experiments were conducted considering the complex time-varying operating environment of a simulation-based hydraulic system. The results demonstrate that, when the system undergoes unstable random changes, the DNVSS-FxLMS algorithm converges at least twice as fast as traditional and existing variable step size algorithms, while reducing steady-state error by 2–5 dB. The proposed DNVSS-FxLMS algorithm exhibits significant advantages in convergence rate, steady-state error reduction, and tracking capability, providing a highly efficient and robust solution for real-time active control of hydraulic system pressure pulsation under complex operating conditions.