• 한국과학교육학회지
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• 제26권5호
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• pp.611-619
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• 2006

The aims of this study are to investigate science high school students' understanding of velocity and acceleration of a simple pendulum bob, and to investigate their understanding of inertia and gravitational force in the motion of a pendulum bob when the tension is removed. For the study, 46 students that had already studied the physical, concepts in simple pendulum were sampled from a science high school in a large city in Korea. For a comparison with general high school students' conceptions, 49 students were sampled from a general high school in the same city. The test tool for the investigation consisted of four drawing and simple-answering type questions developed by the authors. The outcomes of the study revealed that a substantial number of science high school students have misconceptions concerning acceleration in pendulum motion, and that many of them do not understand the relationship between force and acceleration. In addition, the results of the study showed that more than 30% of the students drew the path of a bob going along the tangential direction at the highest point of the motion, and approximately 20% of them drew the path of a bob falling straight down at the lowest point of the motion.

• Coupled systems mechanics
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• 제6권2호
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• pp.127-139
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• 2017

During the last decades, Pendulum Bearings with one or more concave sliding surfaces have been dominating bridge structures. For bridges with relative small lengths, the use of classical pendulum bearings could be a simple and cheaper solution. This work attempts to investigate the effectiveness of such a system, and especially its behavior for the case of a seismic excitation. The results obtained have shown that the classical pendulum bearings are very effective, mainly for bridges with short or intermediate length.

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제2권2호
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• pp.109-114
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• 2002

Various inverted pendulum systems have been frequently used as a model for the performance test of the proposed control system. We first identify a rotary-type inverted pendulum system by the Euler-Lagrange method and then design a FLC (Fuzzy Logic Controller) fur the plant. FLC`s are one of useful control schemes fur plants having difficulties in deriving mathematical models or having performance limitations with conventional linear control schemes. Many FLC`s imitate the concept of conventional PD (Proportional-Derivative) or PI (Proportional-Integral) controller. That is, the error e and the change-of-error are used as antecedent variables and the control input u the change of control input Au is used as its consequent variable for FLC`s. In this paper we design a simple-structured FLC for the rotary inverted pendulum system. We also perform some computer simulations to examine the tracking performance of the closed-loop system.

• Journal of Advanced Marine Engineering and Technology
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• 제23권2호
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• pp.168-175
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• 1999

Unlike a general inverted pendulum system which is moved on the cart the proposed inverted pendulum system in this paper has an inverted pendulum which is moved on the two-degree-of-freedom parallelogram link. The dynamic equation of the pendulum system activated by the DD(Direct Drive)motor includes many nonlinear terms and has the high degree of freedoms. The problem is followed hat the exact mathmatical equations can not be analized by a general linear theory However the neural network trained by a simple learning method can control the dynamic system with hard nonlinearities. Learning procedure is the backpropagation algorithm with super-visory signal. The plant inputs obtained by the designed neural network in this paper can stabilize the pendu-lem and get the servo control. Experiment results have proce the effectiveness of the designed neural network controller.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2005년도 ICCAS
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• pp.690-693
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• 2005

In this paper, a hybrid PD-servo state feedback control algorithm for swing up inverted pendulum system is proposed. It consists of two parts. The first part is the PD position control for swinging up the pendulum from the natural pendent position to around the upright position and the second part is the servo state feedback control for stabilizing the inverted pendulum in upright position. The first controller is PD controller and it is tuned to control the position of the pendulum by moving the cart back and forth until the pendulum swings up around the upright position. Then the second controller will be switched to stabilize the inverted pendulum in its upright position. The controller in this stage is the servo state feedback controller designed by pole placement. Experimental results of PD type swinging up control system, of stabilizing servo state feedback control system and of the proposed hybrid PD-servo state feedback control system to swing up and stabilize inverted pendulum show that the proposed method is effective and reliable for actual implementation while it is simple.

• 한국정보전자통신기술학회논문지
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• 제16권6호
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• pp.400-405
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• 2023

현재 도립진자는 많은 분야에서 연구 중이며 미사일, 로켓, 등의 자세 제어와 2족 보행 로봇 등에 응용되고 있다. 본 연구에서는 256펄스의 로터리 엔코더와 DC 모터를 이용한 회전형 도립진자(Rotary Inverted Pendulum)를 구성하여 회전형 역 진자의 수직 자세 제어를 연구하였다. 비선형 시스템의 경우 복잡한 알고리즘과 제어기가 필요하지만 고전적이며 비교적 간단한 PID(Proportional Integral Derivation)알고리즘을 이용한 제어 방법을 회전형 도립진자 시스템에 적용하였으며 간단하지만 원하는 성능을 높이는 방안을 연구하였다. 본 연구에서 사용된 회전형 도립진자 시스템은 비선형적이고 불안정한 시스템으로 선형화된 모델링에서 마이크로칩 사의 dsPIC30F4013 임베디드 프로세서를 이용한 PID 제어기를 설계 및 구현하였다. 보통 PID 제어기는 하나 혹은 두 가지 이상을 조합하여 설계하며 우수한 제어 성능에 비해 구조가 간단하며 제어 이득 조정이 다른 제어기들에 비해 비교적 쉽다는 장점이 있다. 본 연구에서는 시스템의 물리적 구조를 수학적 방법으로 분석하고 모델링을 통한 회전형 도립진자의 수직 균형을 위한 제어를 실현하였다. 또한 회전형 역 진자를 이용하여 PID 제어기로 제어가 가능한지 시뮬레이션과 실험을 통하여 그 타당성을 검증하였다.

• 과학교육연구지
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• 제32권1호
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• pp.1-18
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• 2008

본 연구에서는 단진자의 등시성에 대한 이상화 조건을 다루는 8학년 과학교과서와 교사용 지도서를 분석하였다. 진자의 주기는 진폭에 무관하다는 등시성은 진폭이 매우 작은 경우에만 성립한다. 이를 단진자의 등시성에 대한 "이상화 조건"이라 부른다. 대부분의 8학년 과학교과서와 교사용 지도서는 이러한 이상화 조건에 대해 바르게 명시하지 않아 종종 이론과 실험 사이의 불일치를 나타내고 있다. 이러한 이론과 실험 사이의 불일치는 학생들로 하여금 실제 세계로부터 괴리감을 느끼게 하여 물리로부터 멀어지게 하는 경향을 가져다준다. 이러한 문제를 해결하기 위해 본 연구에서는 진폭에 무관한 진자의 등시성을 실험할 수 있는 대안으로 사이클로이드 진자를 제시하고 교실 수업에서 실제 활용할 수 있는 방법에 대해 논의 하였다.

• 한국운동역학회지
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• 제16권3호
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• pp.1-7
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• 2006

The Primary type of swinging motion in human movement is that which is characteristic of a pendulum. The two types of pendulums are identified as simple and compound. A simple pendulum consist of a small body suspended by a relatively long cord. Its total mass is contained within the bob. The cord is not considered to have mass. A compound pendulum, on the other hand, is any pendulum such as the human body swinging by hands from a horizontal bar. Therefore a compound pendulum depicts important motions that are harmonic, periodic, and oscillatory. In this paper one discusses and compares two algorithms of Newton's method(F = m a) and Euler's method (M = $I{\times}{\alpha}$) in compound pendulum. Through exercise model such as human body with weight(m = 50 kg), body length(L = 1.5m), and center of gravity ($L_c$ = 0.4119L) from proximal end swinging by hands from a horizontal bar, one finds kinematic variables(angle displacement / velocity / acceleration), and simulates kinematic variables by changing body lengths and body mass. BSP by Clauser et al.(1969) & Chandler et al.(1975) is used to find moment of inertia of the compound pendulum. The radius of gyration about center of gravity (CoG) is $k_c\;=\;K_c{\times}L$ (단, k= radius of gyration, K= radius of gyration /segment length), and then moment of inertia about center of gravity(CoG) becomes $I_c\;=\;m\;k_c^2$. Finally, moment of inertia about Z-axis by parallel theorem becomes $I_o\;=\;I_c\;+\;m\;k^2$. The two-order ordinary differential equations of models are solved by ND function of numeric analysis method in Mathematica5.1. The results are as follows; First, The complexity of Newton's method is much more complex than that of Euler's method Second, one could be find kinematic variables according to changing body lengths(L = 1.3 / 1.7 m) and periods are increased by body length increment(L = 1.3 / 1.5 / 1.7 m). Third, one could be find that periods are not changing by means of changing mass(m = 50 / 55 / 60 kg). Conclusively, one is intended to meditate the possibility of applying a compound pendulum to sports(balling, golf, gymnastics and so on) necessary swinging motions. Further improvements to the study could be to apply Euler's method to real motions and one would be able to develop the simulator.

• 대한전기학회:학술대회논문집
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• 대한전기학회 2015년도 제46회 하계학술대회
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• pp.85-86
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• 2015

This paper is to study the inverted pendulum system of cart type by using the method of PID control. This system is that inverted pendulum maintain a constant balance from unstable state by moving a cart. It is controlled via the PID controller. PID controller is proposed to maintain a constant balance for nonlinear system such as the inverted pendulum system so PID control is widely used in the industrial field because of superior control performance, easy implementation and relatively simple structure. To design this system, it consist of Encorder and DC motor. Encorder is used to read the angle of the pendulum and DC motor is used to change the angle. We can verify results of experiment through the Matlab simulator via the inverted pendulum system of cart type.

• 대한전기학회:학술대회논문집
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• 대한전기학회 1999년도 추계학술대회 논문집 학회본부 B
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• pp.643-645
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• 1999

In experiment, a real inverted pendulum system has state constraints and limited amplitude of input. These problems make it difficult to design a swing-up controller. To overcome these problems, we design a sliding mode controller considering physical behaviour of the inverted pendulum system. This sliding mode controller uses a switching control action to converge along a specified path derived from energy equation from a state around the path to desired states(standing position). And optimal control method is used to guarantee stability at unstable equilibrium position. The designed controller can be applied to all inverted pendulum systems regardless of the values of their parameters. Compared with previous existing controllers, it is simple and easy to tune. Experimental results are given to show the effectiveness of this controller.