Complex systems in mechanical engineering

Complex systems (CS) constitute a challenging frontier in mechanical engineering. CS study the relationships between multiple entities that contribute to a collective behavior often revealing intricate dynamic phenomena. The modeling of such systems requires sophisticated mathematical tools, but often, we verify that present-day human knowledge and scientific tools are far from capturing the overall richness of the system dynamics. Therefore, new theoretical advances and novel challenges posed by applications motivate the development of adequate tools to describe accurately CS.

The special collection focuses on theory and applications of complex dynamical systems in mechanical engineering. The selected 11 papers illustrate the broad impact of several emerging techniques in this challenging area.

In the paper “Anti-disturbance inverse optimal control for spacecraft position and attitude maneuvers with input saturation,” Chutiphon Pukdeboon presents a new anti-disturbance inverse optimal translation and rotation control scheme for a rigid spacecraft with external disturbances and actuator constraint. In the first phase, an inverse optimal controller with input saturation is designed. In the second phase, a new sliding mode disturbance observer is proposed to compensate for the total disturbances. Lyapunov analysis is employed to ensure the finite-time convergence of observer error dynamics. Numerical simulations are presented to validate the performance of the developed controller. ¹

The paper “Decoupling control of a 5-degree-of freedom bearingless induction motor based on least squares support vector machine inverse,” by Ling Wan, Zebin Yang, Xiaodong Sun, Zheng Chen, and Lin Chen, proposes a strategy based on least squares support vector machine inverse for controlling a 5-degree-of-freedom bearingless induction motor. A mathematical model is derived based on least squares, and the particle swarm optimization scheme is used to optimize the parameters. A decoupling algorithm is developed and simulation and experimental results are presented to verify the effectiveness of the strategy. ²

In “Dynamic modeling of dual-arm cooperating manipulators based on Udwadia–Kalaba equation,” Jia Liu and Rong Liu formulate a generalized dynamical equation for modeling multi-link planar manipulators. They obtain the constraint relationship and the dynamical equation of a dual-arm cooperating manipulator subject to a desired trajectory by means of the Udwadia–Kalaba equation. Simulation results prove the effectiveness of the method. ³

The article “Dynamic responses of a wind turbine drivetrain under turbulent wind and voltage disturbance conditions,” by Chengwu Li, Yunpeng Zhou, Teik C Lim, and Guohua Sun, studies the effects of turbulent wind and voltage disturbance on a wind turbine drivetrain. The model is able to account for the dynamic interaction between turbulent wind, voltage disturbance, and mechanical system. A parametric study is performed to understand the influences of generator and gearbox parameters on the drivetrain system dynamics. ⁴

In the paper “Dynamical analysis of fractional order model of immunogenic tumors,” Sadia Arshad, Dumitru Baleanu, Jianfei Huang, Yifa Tang, and Maysaa Mohamed Al Qurashi investigate the fractional order model of the cytotoxic T-lymphocyte response to a growing tumor cell population. They show that tumor growth rate, source rate of immune cells, and death rate of immune cells play vital role in tumor dynamics, and the system undergoes saddle-node and transcritical bifurcation based on these parameters. The effect of cancer treatment is discussed by varying the values of relevant parameters. Numerical simulations validate the analytical results. ⁵

The paper “Electromechanical Integrated Magnetic Gear,” authored by Xiu-hong Hao, Hong-fei Zhang, and Ji-de Men, proposes a new type of magnetic gear, integrating the traditional modules of field-modulated magnetic gear, drive, and control. The system can generate a high torque at low speed and has extensive applications. ⁶

In the manuscript “Mechanism design and motion ability analysis for wheel/track mobile robot,” Dengqi Cui, Xueshan Gao, and Wenzeng Guo study a wheel/track mobile robot with a one-way tail rod. First, the mechanical structure of the wheel/track mobile robot is designed and the hardware composition of its control system is given. Second, the variable structure model is established using the geometry analysis. Analysis under different conditions is performed. Simulation and experiments demonstrate the robot performance. ⁷

The paper “Multi-routing planning design of Y-type urban rail transit,” by Xinmiao Zhao, Quanxin Sun, Yuting Zhu, Yong Ding, Cunrui Ma, and Zhijie Chen, investigates routing planning for Y-type urban rail transit, aiming to minimize the passenger travel time and train operating distance. The multi-objective model is converted into a single-objective model by giving weight values to the objectives. A genetic algorithm is adopted to obtain optimal solutions for the problem. Results for a case study show that when the weight of the passenger travel time increases to a certain level, the optimal solution changes from a two-routing planning to a three-routing planning, and the latter one can better meet the characteristics of the passenger. ⁸

In “Particle swarm optimization used with proportional-derivative control to analyze nonlinear behavior in the atomic force microscope,” Chin-Tsung Hsieh, Her-Terng Yau, Cheng-Chi Wang, and Yi-Sheng Hsieh investigate the nonlinear probe behavior in an atomic force microscope, caused by different excitation frequencies, and analyze the subsequent regulation using particle swarm optimization in combination with proportional-derivative control. They examine the system dynamic behavior using phase portrait, bifurcation diagrams, Poincaré maps, and the maximum Lyapunov exponent. The authors show that the nonlinear behavior and chaotic state can be suppressed to improve stability and performance. ⁹

The paper “Research on impacts of mechanical vibrations on the production machine to its rate of change of technical state,” by Štefánia Salokyová, Radoslav Krehel’, Martin Pollák, and Marek Kočiško, studies the mechanical vibrations in machine tools, and its effects on the machined parts, tool life, and noise during operation. Turning experiments on a lathe TOS SV 18RB demonstrate the importance of avoiding certain working velocities during machining. ¹⁰

Finally, in “Two-step sine movable tooth drive,” Lizhong Xu, Wentao Song, and Ran Li propose a two-step sine movable tooth drive that is able to realize small radial size and large speed ratio simultaneously. The authors analyze not only the force and torque in the drive system but also the influence of the main parameters in the output torque. The results obtained show that the output torque generated is much larger than the one produced by single-step sine movable tooth drives. ¹¹