Offset-free 3DOF Ball and Plate Tracking Control Using Velocity-form Integral MPC

This paper proposes a disturbance-observer-assisted velocity-form integral model predictive control (MPC) structure for reference trajectory tracking on a physical three-degree-of-freedom (3DOF) Ball and Plate system. Under the small-angle assumption, the system dynamics are approximated as decoupled linear subsystems along the x- and y-axes, allowing identical MPC controllers to be applied independently to each axis. Conventional nominal-model-based MPC can exhibit steady-state tracking offsets because of model–plant mismatches, including plate-zero alignment uncertainty, actuator mismatch, sensor noise, velocity estimation errors, and residual cross-axis coupling. To mitigate these effects, a velocity-form integral MPC is formulated using state and input increments, with an augmented state containing an accumulated output term for offset-free tracking. However, direct use of state increments can make the controller sensitive to measurement noise and velocity estimation errors. Therefore, a Luenberger-observer-based disturbance observer reconstructs the system state using the innovation between the nominal model’s one-step prediction and the measured output. The reconstructed state is used to form the observer-based augmented state, improving the reliability of the initial condition for MPC prediction. Experimental results show that the proposed controller achieves stable trajectory tracking on the physical system and reduces steady-state tracking offsets under constant disturbances.