• Title/Summary/Keyword: mathematical pendulum

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CMAC Learning Controller Implementation With Multiple Sampling Rate: An Inverted Pendulum Example (다중 샘플링 타임을 갖는 CMAC 학습 제어기 실현: 역진자 제어)

  • Lee, Byoung-Soo
    • Journal of Institute of Control, Robotics and Systems
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    • v.13 no.4
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    • pp.279-285
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    • 2007
  • The objective of the research is two fold. The first is to design and propose a stable and robust learning control algorithm. The controller is CMAC Learning Controller which consists of a model-based controller, such as LQR or PID, as a reference control and a CMAC. The second objective is to implement a reference control and CMAC at two different sampling rates. Generally, a conventional controller is designed based on a mathematical plant model. However, increasing complexity of the plant and accuracy requirement on mathematical models nearly prohibits the application of the conventional controller design approach. To avoid inherent complexity and unavoidable uncertainty in modeling, biology mimetic methods have been developed. One of such attempts is Cerebellar Model Articulation Computer(CMAC) developed by Albus. CMAC has two main disadvantages. The first disadvantage of CMAC is increasing memory requirement with increasing number of input variables and with increasing accuracy demand. The memory needs can be solved with cheap memories due to recent development of new memory technology. The second disadvantage is a demand for processing powers which could be an obstacle especially when CMAC should be implemented in real-time. To overcome the disadvantages of CMAC, we propose CMAC learning controller with multiple sampling rates. With this approach a conventional controller which is a reference to CMAC at high enough sampling rate but CMAC runs at the processor's unoccupied time. To show efficiency of the proposed method, an inverted pendulum controller is designed and implemented. We also demonstrate it's possibility as an industrial control solution and robustness against a modeling uncertainty.

Control of Rotary Inverted Pendulum using ANFIS (ANFIS를 이용한 수평회전형 도립진자의 제어)

  • Min, Hyun-Ki;Ryu, Chang-Wan;Ko, Joe-Ho;Yim, Wha-Yeong
    • Proceedings of the KIEE Conference
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    • 1998.07b
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    • pp.681-683
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    • 1998
  • Fuzzy Inference System is to trans late and be concrete with human expert in to mathematical equation. It is easy to be applied for Nonlinear System and the know ledge can be applied at that. With using the rule according to the Knowledge, when it is realized simulations must be required repeatedly and small vibration is generated in steady state, too. In this paper, we applied the system to the methodology of optimization with self-learn ing by us ing ANFIS(Adaptive Network-based Fuzzy Inference System) which makes use of back-propagation and least square method at a first order Sugeno Fuzzy System. In order to show the effect of Algorithm, we demonstrated it by us ing Rotary Inverted Pendulum.

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Stabilzed Control of an Inverted Pendulum Cart System Using the Optimal Regulator (최적 Regulator를 이용한 도립진자 시스템의 안정화 제어)

  • 박영식;최부귀
    • The Journal of Korean Institute of Communications and Information Sciences
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    • v.15 no.4
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    • pp.315-323
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    • 1990
  • A design technique of dynamic stabilization controller for the intrinsic unstable inverted pendulum system is introduced. Mathematical modelling with the more complex nonlinearity and the stabilized control theory presented by C.D.Johnson are adapted to this system by using the state-space approach. And the Stabilized controller with the designed optimal regulator type which can be fastly tracked and can be accurately counteracted aginst all effects of the constant distrubances and the parameteric variations is simulated and is implemeted successfully on the microcomputer.

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Modeling of vibration protection by shape memory alloy parts with an account of latent heat

  • Fedor S. Belyaev;Margarita E. Evard;Aleksandr E. Volkov;Maria S. Starodubova
    • Smart Structures and Systems
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    • v.33 no.3
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    • pp.243-251
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    • 2024
  • Modeling of vibrations of a rotating pendulum with working shape memory alloy rod has been performed in the frames of a microstructural model taking into account the latent heat release, absorption and the heat exchange during direct and reverse martensitic transformation. It has been shown that the influence of the latent heat, the rate of preliminary deviation of the pendulum from the equilibrium, the rate of heating and cooling can have a significant impact on the vibrations and damping characteristics of the system.

The Analysis of The Kalman Filter Noise Factor on The Inverted Pendulum (도립진자 모델에서 칼만 필터의 잡음인자 해석)

  • Kim, Hoon-Hak
    • Journal of the Korea Society of Computer and Information
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    • v.15 no.5
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    • pp.13-21
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    • 2010
  • The Optimal results of Kalman Filtering on the Inverted Pendulum System requires an effective factor such as the noise covariance matrix Q, the measurement noise covariance matrix R and the initial error covariance matrix $P_0$. We present a special case where the optimality of the filter is not destroyed and not sensitive to scaling of these covariance matrix because these factors are unknown or are known only approximately in the practical situation. Moreover, the error covariance matrices issued by this method predict errors in the state estimate consistent with the scaled covariance matrices and not the issued state estimates. Various results using the scalar gain $\delta$ are derived to described the relations among the three covariance matrices, Kalman Gain and the error covariance matrices. This paper is described as follows: Section III a brief overview of the Inverted Pendulum system. Section IV deals with the mathematical dynamic model of the system used for the computer simulation. Section V presents a various simulation results using the scalar gain.

A Study on the Performance of Fuzzy Inference Engine (퍼지 추론부의 성능 향상에 관한 연구)

  • 우찬일;신인철;유종상
    • Proceedings of the Korea Society for Industrial Systems Conference
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    • 1997.11a
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    • pp.105-116
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    • 1997
  • The fuzzy logic controller was used effectively for the controlling of unmeasured parameter and inaccurate mathematical modeling was designed. In this paper, we proposed that the method of reducing the vibration at the target point on calculating the membership degree about input value without a look-up table was proposed. And its effectiveness in the inverted pendulum was acquired.

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Fuzzy Inference System Based Multiple Neural Network Controllers for Position Control of Ultrasonic Motor (퍼지 추론 시스템 기반의 다중 신경회로망 제어기를 이용한 초음파 모터의 위치제어)

  • Choi, Jae-Weon;Min, Byung-Woo;Park, Un-Sik
    • Journal of the Korean Society for Precision Engineering
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    • v.18 no.4
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    • pp.209-218
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    • 2001
  • Ultrasonic motors are newly developed motors which are expected to be useful as actuators in many practical systems such as robot arms or manipulators because of several advantages against the electromagnetic motors. However, the precise control of the ultrasonic motor is generally difficult due to the absence of appropriate and rigorous mathematical model. Furthermore, owing to heavy nonlinearity, the position control of a pendulum system driven by the ultrasonic motor has a problem that control method using multiple neural network controllers based on a fuzzy inference system that can determine the initial position of the pendulum in the beginning of control operation. In addition, and appropriate neural network controller that has been learned to operate well at the corresponding initial position is adopted by switching schemes. The effectiveness of the proposed method was verified and evaluated from real experiments.

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Design of a Two-wheeled Balancing Mobile Platform with Tilting Motion (횡방향 틸팅 기능을 갖는 이륜 밸런싱 모바일 플랫폼 설계)

  • Kim, Sangtae;Seo, Jeongmin;Kwon, SangJoo
    • Journal of Institute of Control, Robotics and Systems
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    • v.20 no.1
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    • pp.87-93
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    • 2014
  • Conventional two-wheeled balancing robots are limited in terms of turning speed because they lack the lateral motion to compensate for the centrifugal force needed to stop rollover. In order to improve lateral stability, this paper suggests a two-wheeled balancing mobile platform equipped with a tilting mechanism to generate roll motions. In terms of static force analysis, it is shown that the two-body sliding type tilting method is more suitable for small-size mobile robots than the single-body type. For the mathematical modeling, the tilting-balancing platform is assumed as a 3D inverted pendulum and the four-degrees-of-freedom equation of motion is derived. In the velocity/posture control loop, the desired tilting angle is naturally determined according to the changes of forward velocity and steering yaw rate. The efficiency of the developed tilting type balancing mobile platform is validated through experimental results.

Balance Control of a Biped Robot Using the ZMP State Prediction of the Kalman Estimator (칼만예측기의 ZMP 상태추정을 통한 이족로봇의 균형제어기법)

  • Park, Sang-Bum;Han, Young-Jun
    • Journal of the Korean Institute of Intelligent Systems
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    • v.16 no.5
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    • pp.601-607
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    • 2006
  • This paper proposes a novel balance control scheme of a biped robot to predict the next position of ZMP using Kalman Filter. The mathematical model of the biped robot is generally approximated by 3D-LIPM(3D-Linear Inverted Pendulum Mode), but it cannot completely express the robot's dynamics. The stability of the biped robot depends on whether the ZMP(Zero Moment Point) position is in the stability region or out of. And the internal error between the robot mechanism and its model could affect the stability of a robot. Therefore, the proposed balance control not reduces the internal error, but also timely generates the proper control. The experiment of the proposed balance control is simulated on the virtual workspace where the biped robot may encounter with various difficulties.

Monitoring and vibration control of a fluid catalytic cracking unit

  • Battista, Ronaldo C.;Varela, Wendell D.;Gonzaga, Igor Braz N.
    • Smart Structures and Systems
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    • v.29 no.4
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    • pp.577-588
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    • 2022
  • Oil refineries' Fluid Catalytic Cracking Units (FCCU) when in full operation may exhibit strong fluid dynamics caused by turbulent flow in the piping system that may induce vibrations in other mechanical and structural components of the Unity. This paper reports on the experimental-theoretical-computational program performed to get the vibration properties and the dynamic response amplitudes to find out alternative solutions to attenuate the excessive vibrations that were causing fatigue fractures in components of the bottle like reactor-regenerator of an FCC unit in operation in an existing oil refinery in Brazil. Solutions to the vibration problem were sought with the aid of a 3D finite element model calibrated with the results obtained from experimental measurements. A short description of the found solutions is given and their effectiveness are shown by means of numerical results. The solutions were guided by the concepts of structural stiffening and dynamic control performed by a nonlinear pendulum controller whose mechanical design was based on parameters determined by means of a parametric study carried out with 2D and 3D mathematical models of the coupled pendulum-structure system. The effectiveness of the proposed solutions is evaluated in terms of the fatigue life of critical welded connections.