Ball on a beam: stabilization under saturated input control with large basin of attraction

This article is devoted to the stabilization of two underactuated planar systems, the well-known straight beam-and-ball system and an original circular beam-and-ball system. The feedback control for each system is designed, using the Jordan form of its model, linearized near the unstable equilibrium. The limits on the voltage, fed to the motor, are taken into account explicitly. The straight beam-and-ball system has one unstable mode in the motion near the equilibrium point. The proposed control law ensures that the basin of attraction coincides with the controllability domain. The circular beam-and-ball system has two unstable modes near the equilibrium point. Therefore, this device, never considered in the past, is much more difficult to control than the straight beam-and-ball system. The main contribution is to propose a simple new control law, which ensures by adjusting its gain parameters that the basin of attraction arbitrarily can approach the controllability domain for the linear case. For both nonlinear systems, simulation results are presented to illustrate the efficiency of the designed nonlinear control laws and to determine the basin of attraction

Upaya Orang Tua Membina Pendidikan Agama Islam Anak di Dusun Embun Pagi Jorong Padang Galanggang

This study aims to analyze the efforts of parents to foster their children's Islamic religious education. The focus of the study is on three things, namely the form of effort, supporting factors, and obstacles. This study analyzes the efforts made by parents in Embun Pagi Hamlet, Jorong, Padang Galanggang. The research method used is a descriptive study-based qualitative. Data collection techniques used are observation, interviews, and documentation studies. The data obtained were then analyzed using the Miles and Huberman technique, namely data reduction, data display, and conclusions. The results of the study explain that the form of efforts taken are involving children in non-formal religious education, fostering children's religious practices at home, involving children in religious traditions based on local wisdom, familiarizing children to grow up in the surau. The supporting factors for the implementation and success of these efforts are the high motivation and expectations of parents for their children, coupled with a religious village environment. However, there are also inhibiting factors, namely the busyness of parents at work which is an obstacle to not being able to fully control the religious development of children