• Journal of the Korean Society of Fisheries and Ocean Technology
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• v.31 no.2
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• pp.178-189
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• 1995

In this pater, authors derive the state - space equiation about the patallel - type inverted pendulum which is adopted as control object, and constitute the control system by $H_\infty$control theory. The modeling error is unavoidably existed by linearization error, and so on. We regard this modeling error which is determined from the identification through frequency response as unstructured model uncertainty. An augmented state - space equiation with frequency weighting function is constructed for application of the $H_\infty$theory, and the mixed sensitivity problem is considered. The weighting functions are determined in consideration of the model uncertainty and the response of system in frequency region. The $H_\infty$controller is designed by using software package for controller design. From results of response simulation, the control system designed with $H_\infty$theory guarantees low sensitivity for disturbance as well as robustness against the model uncertainties.

• Proceedings of the KSME Conference
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• 2007.05a
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• pp.405-408
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• 2007

Vestibular hair cells, the sensory receptors of vestibular organs, selectively amplify miniscule stimuli to attain high sensitivity. Such selective amplification results in compressive nonlinear sensitivity, which plays an important role in expanding dynamic range while ensuring robustness of the system. In this study, negative stiffness mechanism, a mechanism responsible for the selective amplification by vestibular hair cells, is applied to a simple mechanical system consisting of an array of inverted pendulums. The structure and working principle of the system have been inspired by gating spring hypothesis proposing that opening and closing of transduction channels contributes to the global stiffness of vestibular hair bundle. Parameter study was carried out to analyze the effect of each parameter on the compressive nonlinearity of suggested model.

• Journal of Institute of Control, Robotics and Systems
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• v.15 no.12
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• pp.1216-1222
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• 2009

This article describes a simple method for generating the walking trajectory for the biped humanoid robot. The method used a simple inverted model instead of complex multi-mass model and a reasonable explanation for the model simplification is included. The problem of gait trajectory generation is to find the solution from the desired ZMP trajectory to CoG trajectory. This article presents the analytic solution for the bipedal gait generation on the bases of ZMP trajectory. The presented ZMP trajectory has Fourier series form, which has finite or infinite summation of sine and cosine functions, and ZMP trajectory can be designed by calculating the coefficients. From the designed ZMP trajectory, this article focuses on how to find the CoG trajectory with analytical way from the simplified inverted pendulum model. Time segmentation based approach is adopted for generating the trajectories. The coefficients of the function should be designed to be continuous between the segments, and the solution is found by calculating the coefficients with this connectivity conditions. This article also has the proof and the condition of solution existence.

• Journal of the Korea institute for structural maintenance and inspection
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• v.25 no.3
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• pp.21-30
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• 2021

Architectural cultural properties suffer a lot of damage due to various environmental factors. In order to preserve damaged cultural properties, preventive preservation and long-term preservation management are becoming more important. Therefore, research on a scientific non-destructive testing method applicable to regular inspection is required. For related research, DangGan with a high flag-pole shape was selected as the subject of study among various cultural properties. Among the preserved DangGans, a basic study was conducted on the analysis technique to evaluate the structural stability by selecting Treasure No. 49 Naju SeokDangGan. An idealized model was presented and a multi-degree of freedom equation of motion was derived. In addition, an equation for estimating the critical stiffness value for each joint position is presented.

• Proceedings of the KIEE Conference
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• 2006.10c
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• pp.108-110
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• 2006

This paper deals with a tracking problem for nonlinear systems using its T-S fuzzy model and internal model. We extend the internal model of linear systems to an internal model of T-S fuzzy systems to accompany with state error of zero. A sufficient condition of the existence of a tracking controller for T-S fuzzy systems is expressed by linear matrix inequalities. A system of inverted pendulum on cart is illustrated to verify our method.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.57 no.7
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• pp.1247-1253
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• 2008

A design method of a T-S fuzzy model based reduced order nonlinear unknown input observer(NUIO) is presented. The fuzzy NUIO is designed based on the parallel distributed compensation(PDC) concept. It consists of a number of the linear UIOs, each of which is designed for each local linear model in the T-S fuzzy model of a class of nonlinear systems. The fuzzy NUIO provides not only the state estimates insensitive to the unknown inputs, for example, disturbances and faults etc., but also the estimates of the unknown inputs. Therefore, It can be employed in the state feedback control and disturbance rejection control of a class of nonlinear systems with unknown disturbances. It also applied to the robust residual generation for the fault detection and isolation systems and to the design of fault tolerant control systems. As an example, the NUIO is applied to an inverted pendulum system to show the state and disturbance estimation performance and to illustrate the fuzzy reduced order NUIO design method.

• Proceedings of the KIEE Conference
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• 1999.07b
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• pp.630-632
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• 1999

In this paper, we develop intelligent digitally redesigned PAM and PWM fuzzy controllers for nonlinear systems. Takagi-Sugeno fuzzy model is used to model the nonlinear systems and a continuous-time fuzzy-model-based controller is designed based on the extended parallel-distributed-compensation method. The digital controllers are determined from existing analogue controllers. The proposed method provides an accurate and effective method for digital control of continuous·time nonlinear systems and enables us to efficiently implement a digital controller via pre-determined continuous-time TS fuzzy-model-based controller. We have applied the proposed method to the balancing problem of the inverted pendulum to show the effectiveness and feasibility of the method.

• 제어로봇시스템학회:학술대회논문집
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• 1998.10a
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• pp.185-189
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• 1998

This paper addresses analysis and design of a fuzzy model-based-controller for the control of uncertain SISO nonlinear systems. In the design procedure, we represent the nonlinear system by using a Takagi-Sugeno fuzzy model and construct a global fuzzy logic controller via parallel distributed compensation and sliding mode control. Unlike other parallel distributed controllers, this globally stable fuzzy controller is designed without finding a common positive definite matrix for a set of Lyapunov equations, and has good tracking performance. The stability analysis is conducted not for the fuzzy model but for the real underlying nonlinear system. Furthermore, the proposed method can be applied to partially known uncertain nonlinear systems. A numerical simulation is performed for the control of an inverted pendulum, to show the effectiveness and feasibility of the proposed fuzzy control method.

• Journal of Institute of Control, Robotics and Systems
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• v.8 no.11
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• pp.941-947
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• 2002

Two methods of constructing T-S fuzzy model which is equivalent to a given nonlinear system are presented. The first method is to obtain an equivalent T-S fuzzy model by using the sum of linearly independent scalar functions with constant real matrix coefficients. The sum of products of linearly independent scalar functions is used in the second method. The former method is to formulate the procedures of T-S fuzzy modeling dealt in many examples of previous publications; the latter is a new method. By comparing the number of linearly independent functions used in the two methods, we can easily find out which method makes fewer rules than the other. The nonlinear dynamics of an inverted Pendulum on a cart is used as an equivalent T-5 fuzzy modeling example.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2002.12a
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• pp.122-125
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• 2002

This paper proposes a stability condition in switched system and then, introduce design method of fuzzy-model-based controller which guarantees the stability. Takagi-Sugeno(75) fuzzy model is employed to design a switching-type fuzzy-model-based ,controller. Furthermore, it is proposed that the design method stabilizing continuous and discrete-time 75 fuzzy model respectively. Each controller in each subspace stabilize the subsystem respectively. In order to guarantee the stability of the global system, it is required to guarantee the stability condition in boundaries with subsystems. The condition which guarantees the stability in boundaries is presented in this paper. Inverted Pendulum system is employed to execute computer simulations. In this computer simulation, the performance of the proposed controller is verified by the control result.