An Increased Nonlinear Coupling Motion Controller for Underactuated Multi-TORA Systems: Theoretical Design and Hardware Experimentation

In mechanical engineering, multi-translational oscillator with rotational actuator (multi-TORA) systems have been introduced to study the self-synchronized phenomenon as well as to investigate the vibration damping problem associated with many vibrational mechatronic systems, e.g., hand-held drills. Due to the lack of available actuators, multi-TORA systems are typically underactuated. Multi-TORA systems consist of a series of single TORA subsystems connected to and coupled with each other by elastic springs. For practical multi-TORA systems, the plant parameters are usually unknown or difficult to measure. Moreover, they exhibit strong nonlinear coupling behaviors. These factors bring much difficulty for both controller design and analysis. The control problem for underactuated multi-TORA systems with parametric uncertainties is challenging and still open. To address the above issues, this paper proposes a nonlinear increased motion control scheme for multi-TORA systems with parametric uncertainties. Specifically, a novel energy function is constructed and some extra coupling terms are introduced into the proposed controller for improving the transient performance. Then, based on Lyapunov techniques, we rigorously prove the asymptotic stability for the equilibrium point of the closed-loop system. As far as we know, this paper gives the first smooth control law to yield global asymptotic control results for underactuated multi-TORA systems suffering from unknown/uncertain plant parameters. To verify the effectiveness of the proposed controller, a series of hardware experiments are carried out on a self-built double-TORA hardware testbed, which indicate that the controller achieves effective control results in various conditions.