MPC-Based Sliding Mode Control of Dual-Inertia System Analysis

The servo drive system serves as the core power unit in high-end equipment such as industrial robots and computerized numerical control (CNC) machine tools, where mechanical resonance and shaft torque ripple induced by elastic deformation and backlash severely degrade motion accuracy and system stability. Conventional resonance suppression approaches, predominantly based on PI control and notch-filter-augmented PI control, suffer from critical limitations: high sensitivity to resonant frequency variations, inability to systematically enforce physical shaft torque constraints, poor robustness against parameter uncertainties and external disturbances, and significant degradation of dynamic performance when resonance is aggressively suppressed. This paper establishes a two-inertia elastic system model to investigate the effects of elastic deformation and backlash nonlinearities, revealing the mechanisms of mechanical resonance and torque ripple, and proposes control strategies for resonance suppression and shaft torque ripple limitation. A novel hierarchical control architecture is designed, consisting of a Luenberger-observer-based model predictive control (MPC) speed controller, and a super-twisting sliding mode controller (ST-SMC) for the current loop. Luenberger observer-based MPC with ST-SMC strategy is to simultaneously obtain: (a) enhanced robustness via state estimation, (b) superior dynamic performance via SMC, and (c) guaranteed shaft torque constraint satisfaction via MPC. Compared with conventional PI control and notch-filter-based PI control, simulation results demonstrate that Luenberger observer-based MPC with ST-SMC strategy effectively suppresses resonance, limits shaft torque ripple, and enhances the system’s disturbance rejection capability.