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The optimal control of a system governed by an elliptic equation has been widely applied in engineering, and it requires twice differentiability. Furthermore, the optimal control cannot effectively deal with unsmooth boundaries. Now, the condition will not be maintained for a long time because this paper suggests a fractal optimal control of a system governed by a fractal variational principle to deal with unsmooth boundaries. The new optimal theory has obvious advantages in low differentiability for an unsmooth boundary problem. The air conditioning in a room is used as an example to show how to maintain maximum comfortableness of the workplace and maximum efficiency of energy saving. [ABSTRACT FROM AUTHOR]

This work focuses on vibration alleviation and energy harvesting in a dynamical system of a spring-pendulum. The structure of the pendulum is modified using an independent electromagnetic harvesting system. The harvesting depends on the oscillation of a magnet in a coil. An endeavor has been made to get both the energy harvesting and mitigation of vibration efficacy of the harvester. The governing kinematics equations are derived using Lagrange's equations and are solved asymptotically using the multiple scales method to achieve the intended outcome as new and precise results. The resonance states are classified, and the influence of various parameters of the studied system is analyzed. Fixed points at steady states are categorized into stable and unstable. The time behavior of the solutions, the modified amplitudes, and phases are examined and interpreted in the light of their graphical plots. Zones of stability and instability are concerned, in which the system's behavior is stable for a wide range of used parameters. This model has become essential in recent times as it uses control sensors in industrial applications, buildings, infrastructure, automobiles, and transportation. [ABSTRACT FROM AUTHOR]

Sonic drilling technology uses the longitudinal vibration of a drill string to realize fast and effective drilling. By setting the top and bottom boundary conditions of the drill string during drilling, a dynamic model of flexible sonic string percussive drilling is established in this article. At a certain drilling depth, with the excitation frequencies as the control parameters, the maximum impact force and rock breaking energy utilization rate are used to evaluate the rock breaking capability of the sonic drilling system under the linear bit–rock model. A surface diagram of the maximum breaking force reached within the working frequencies and at varying drilling depths is obtained. The curve graph of the rock breaking energy utilization rate varying with drilling depth under the first six orders of resonance is also calculated. Analysing the influence of changing drilling parameters on the rock breaking capability of sonic drilling systems can provide theoretical guidance for the actual drilling process. [ABSTRACT FROM AUTHOR]