Robust constrained trajectory tracking for magnetically controlled linear actuators with hysteresis

This paper extends the results of the dual-loop proportional and derivative controller discussed in [1] to magnetically controlled linear (MCL) actuator systems with state and input constraints and unknown but bounded disturbances. These actuators include both electromagnetic and smart actuators, such as moving coil, moving iron controllable, linear reluctance, magnetostrictive, and magnetically controlled shape memory alloy actuators. MCL actuators exhibit complex hysteresis with minor-loop closure and output saturation. In the aforementioned papers, the authors discuss how to utilize two output feedbacks for trajectory tracking control of disturbance-free hysteretic systems. In the case of MCL actuators, one can utilize both position feedback and induced voltage feedback to derive the input current. However, if the trajectory to be tracked is not known in its entirety, the output measurements are perturbed, or the plant contains parameters with uncertainties, then the system is no longer disturbance-free. The controller must achieve tracking under such exogenous disturbances while keeping the input current within its rated conditions. Here, sufficient conditions on controller gains are derived for ultimate bounded control while maintaining the input current within the rated conditions and maintaining closed-loop system stability for bounded input disturbance signals.