Data-Driven Dead-Zone Compensation via Projection in Predictive Control Setting

Actuator dead-zones are a common and troublesome nonlinearity in motion control: a band of commanded effort over which the plant does not respond, leaving a steady-state offset or a limit cycle. This paper proposes a data-driven architecture that compensates such mismatches without a model of the plant and without any parameterization of the dead-zone. The central idea is to identify, alongside the velocity-form predictor used for control, a second absolute subspace predictor. Because the absolute predictor carries no integral action, it behaves as a data-driven steady-state sensor, so a persistent actuator mismatch appears as a proportional prediction residual. Embedding this residual as a proxy in a behavioral Hankel matrix reduces the mismatch estimate to a single fixed orthogonal projection evaluated online, with no dynamic estimator, no injected probing signal, and no run-time prediction-error computation. Integrated into a subspace predictive controller, the framework is shown to be recursively feasible and practically input-to-state stable, and it recovers offset-free tracking once the dead-band traversal settles. The approach is validated in real time on a sixth-order, lightly damped Quanser multi-DOF torsion system, whose complex-conjugate poles give a lightly damped open-loop response, achieving offset-free tracking across a $\pm 0.18$\,V actuator dead-band. A second study on a high-precision power amplifier shows that the same architecture rejects dead-time-induced nonlinearities in fast-switching power electronics.