Discrete-Time Nonlinear Control Technique for Trajectory Tracking of Hybrid Reluctance Actuator

To empower precise manipulation of flexible nanoscale objects, the Hybrid Reluctance Actuators (HRA) prove to be the most effective type of actuator, capable of applying forces with a very high resolution to the dynamic system. In this paper, the circuit model of the HRA is formulated by incorporating equations governing structural uncertainties, extracting nonlinear state-space equations. Stability control laws are considered for position and velocity control modes, ensuring stable and accurate performance. The actuator system imposes constraints leading to saturation limitations on the electromagnetic force. By using a mapping of the actuator constraints to the desired trajectory, the system will track a modified desired trajectory instead of the primary one. Due to the complex direct dynamic relationships of the actuator, explicit relationships for its inverse dynamics cannot be derived. Therefore, an adaptive lookup table is employed to address this issue, updated at each time step, determining the relationship between the control input and the electromagnetic force. System dynamics equations along with the controller are simulated in the MATLAB environment. Simulation results in two different tracking scenarios demonstrate the accuracy of the designed control system with a 2 nm precision, while adhering to the saturation range of input voltage.