Observer-Based Controllers for Two-Wheeled Inverted Robots with Unknown Input Disturbance and Model Uncertainty

In this paper, two controllers with a compound disturbance observer are proposed for a two-wheeled inverted robot (TWIR) with model uncertainty and unknown input disturbance. First, an equivalent linear model of the TWIR with uncertainty and input disturbance is proposed using the Taylor series expansion for the nonlinear model of the TWIR at an equilibrium point, in which the nonlinear part of the Taylor series and the model uncertainty are combined with unknown input disturbance as compound input disturbance. Then, the compound input disturbance is estimated by using the Newton method and reference model. As the estimated compound disturbance is used to compensate for the compound disturbance, the equivalent linear system becomes closely definite without compound input disturbance. Finally, two controllers are proposed using the equivalent linear system. Stability analysis of the proposed control methods is also given. To illustrate the proposed methods, some simulations for the TWIR are performed and compared with the existing methods. The main contribution of this work includes the following: (i) simple controllers based on compound input disturbance observer for trajectory tracking and balancing of TWIRs with unknown input disturbance and model uncertainty are proposed; (ii) the stability of proposed closed-loop control systems is proved; (iii) our proposed methods are simulated and compared with the existing methods.

Optimal design for a novel inerter-based clutching tuned mass damper system

In this article, a clutching inerter damper is introduced into the conventional tuned mass damper to replace the typical damping element. Regarding the limitation of the typical damping element, the reformed clutching tuned mass damper system is more flexible in parameter design than the optimal tuned mass damper, which may be constrained by the manufacturing process to realize the too small or too large damping coefficient. To investigate the effectiveness of the clutching tuned mass damper, some fundamental analyses are first conducted on the clutching tuned mass damper, and results show that the clutching tuned mass damper system can achieve a similar control effect to the optimal tuned mass damper design. Considering the inherent nonlinearity of the clutching tuned mass damper, the equivalent linearization is performed based on the equivalent linearization parameters drawn from the single-degree-of-freedom system with clutching inerter damper. The equivalent linear system of the clutching tuned mass damper system has been proved to be quite accurate to approximate the nonlinear clutching tuned mass damper system. Based on the equivalent linear system, the performance evaluation and optimal design of the clutching tuned mass damper system are carried out by numerical analysis and analytical solution. Results have shown that there is an optimum inertance for the clutching tuned mass damper to achieve the optimal performance, and the optimum inertance is related to the structural damping ratio and the tuned mass ratio. Finally, the effectiveness of the clutching tuned mass damper system and its equivalent linear system in a multi-degree-of-freedom structure is verified by a numerical study.

Balancing of Rotors Supported on Bearings Having Nonlinear Stiffness Characteristics

In real-life applications, multi-disk-rotor systems are supported on bearings with nonlinear flexibility. The balancing of such systems at high speeds is a challenging task. This work presents a method of balancing such systems. The dynamic equations of motion for a nonlinear system are derived first using the influence coefficient method and then Lagrangian equations. An equivalent linear system is found using the optimization principles. Finally, the correct balance weights for the nonlinear system are obtained based on the equivalent linear system. The results thus obtained establish the utility of such a method of balancing nonlinear systems.