Fixed-point FPGA implementation of advanced linear controllers for real-time double-pendulum crane stabilisation

Uncontrolled payload oscillations in double-pendulum container-crane systems hinder positioning, safety and efficiency. We present a quantitative comparison of four linear controllers – parallel dual PID, hybrid parallel dual PID–LQR, LQRI and Lyapunov-based pole placement (LPP) – using a double-pendulum model incorporating cable dynamics, payload coupling and nonlinearities, linearised. The main novelty is a complete hardware-in-the-loop validation framework implemented on an Artix-7 XC7A200 T FPGA using fixed-point arithmetic, enabling direct comparison between floating-point simulation and FPGA performance under nominal and disturbed conditions. Results show the hybrid PID–LQR delivers the best overall performance: the fastest fall time (1,70 s versus 9,20 s for LPP), superior steady-state accuracy (1,75 × 10−7 rad versus 1,71 × 10−3 rad for LQRI) and markedly improved disturbance rejection (161% undershoot versus 1,344% for LQRI). Parallel dual PID is most energy-efficient (1,001 J, 99.85% lower than LPP at 664 J). LQRI suffers catastrophic FPGA degradation (energy ×338). Findings guide embedded controller selection for fixed-point FPGAs.