Cascaded Optimization of FOPID Control for a Fast-Forging Press Hydraulic System Using Digital Twins and Dual-Layer PSO

PID control is widely adopted in fast-forging press hydraulic systems. However, it often fails to deliver satisfactory performance under variable operating conditions due to its fixed control parameters. To tackle this problem, this paper proposes a control strategy that combines digital twin (DT) technology with cascaded particle swarm optimization (PSO). In the outer-layer optimization, a twin model is first built in MATLAB/Simulink. By combining real-time sensor data with PSO, the outer-layer optimization identifies the optimal effective bulk modulus of the hydraulic oil. This procedure updates the twin model and enables real-time mapping between the twin model and the physical system. Based on the updated twin model, the inner-layer optimization employs PSO to tune the fractional-order PID (FOPID) controller parameters (Kp, Ki, Kd, λ, and μ) online. The optimal parameters are then applied to the physical system to enhance control performance. Experimental results show that, compared with single-layer PSO-FOPID control, the proposed strategy reduces settling time by 9.36% and overshoot by 2.216 percentage points under no-load conditions. Under loaded forging conditions, it reduces settling time by 12.7% and overshoot by 0.2 percentage points, thereby improving the system’s response speed and position-tracking accuracy.