Linear Stabilization Control for Underactuated RTAC Based on Model Reconstruction

Rotational-translational actuator (RTAC) system has the underactuated characteristics, i.e., it has two states to be stabilized with only one control input. To overcome this problem, a new “actuated” state is constructed as an output by combining the unactuated and actuated states. The lumped disturbance for the reconstructed model, including nonlinear dynamics, external disturbances, and parametric uncertainty of the stiffness coefficient of the spring, is estimated by the linear extended state observer and can be compensated in real-time. The practical states of the controlled RTAC converge to the equilibrium in a steady manner. The corresponding convergence and stability can be backed up by Lyapunov-based analysis. The RTAC with the proposed controller is proved to be stable subject to the disturbances. Specifically, some tuning guidelines for the control gains are presented, and the closed-loop characteristics of the RTAC is illustrated in the frequency domain. The simulations and Monte Carlo test are provided to verify the effectiveness of the proposed controller. Finally, the hardware experiments are performed to further validate the proposed method. The comparisons with the existing methods show that the proposed controller can achieve superior performance.