• Journal of KSNVE
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• v.3 no.3
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• pp.231-243
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• 1993

The dynamic characteristics of two types of mathematical models for a rigid body suspension system are analyzed and compared in this paper. One is a linearized model which is commonly used in the engine mount system analysis, the other is a nonlinear model which usually applied to the pendulum type system. The typical 3 d.o.f's mathematical model, for convenience, is chosen as a simulation model, because it has fundamental dynamic characteristics of suspension system. Time responses and unbalance responses of the rigid body, transmitted forces and torques are simulated by using the mathematical model. From the results of computer simulation, it is approved that he nonlinear model is valid and the linearized model gives erroneous results in the case of the pendulum type suspension system. In addition, in this study the effects of design change on the dynamic characteristics of the suspension system are investigated. Mount locations, mount angles, lengths, stiffness and damping coefficients of suspension bars are chosen as design parameters.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.2 no.2
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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.

• Proceedings of the KIEE Conference
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• 1998.07g
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• pp.2309-2311
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• 1998

The attitude control of a double inverted pendulum with a periodical disturbance at link top is dealt in this paper. The proposed system is consisted of the double inverted pendulum and a disturbance link. The lower link is hinged on the plate to free for rotation in the vertical plane. The upper link is connected to the lower link through a DC motor. The DC motor is used to control the posture of the pendulum by adjusting the position of the upper link. The periodical disturbance can be generated by the additional link attached at the end of link 2 through another DC motor, which is the modeling of a posture for a biped supporting with one leg. The motor for the joint simulates the knee joint(or hip joint) and the disturbance for the legs moving in air. The algorithm for controlling a proposed inverted pendulum is consisted of a state feedback control and a fuzzy logic controller. The fuzzy controller keeps the center of gravity of the biped within the specified range through the nonlinear feedback compensator. The state feedback control takes over the role to maintain a desired posture regardless the disturbance at the link top. In these case, the change of the angle and COG of an upper link is compensated with on-line. Simulations with a mathematical model are conducted to show the validity of the proposed controller.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.60 no.2
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• pp.407-415
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• 2011

In this study, we propose the design of optimized fuzzy controller for the rotary inverted pendulum system by using differential evolution algorithm. The structure of the differential evolution algorithm has a simple structure and its convergence to optimal values is superb in comparison to other optimization algorithms. Also the differential evolution algorithm is easier to use because it have simpler mathematical operators and have much less computational time when compared with other optimization algorithms. The rotary inverted pendulum system is nonlinear and has a unstable motion. The objective is to control the position of the rotating arm and to make the pendulum to maintain the unstable equilibrium point at vertical position. The output performance of the proposed fuzzy controller is considered from the viewpoint of performance criteria such as overshoot, steady-state error, and settling time through simulation and practical experiment. From the result of both simulation and practical experiment, we evaluate and analyze the performance of the proposed optimal fuzzy controller from the comparison between PGAs and differential evolution algorithms. Also we show the superiority of the output performance as well as the characteristic of differential evolution algorithm.

• Journal of applied mathematics & informatics
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• v.14 no.1_2
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• pp.251-266
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• 2004

We consider a controlled nonlinear mechanical system described by the Lagrange equations. We determine the control forces $Q_1$ and the restrictions for the perturbations $Q_2$ acting on the mechanical system which allow to guarantee the asymptotic stability of the program motion of the system. We solve the problem of stabilization by the direct Lyapunov's method and the method of limiting functions and systems. In this case we can use the Lyapunov's functions having nonpositive derivatives. The following examples are considered: stabilization of program motions of mathematical pendulum with moving point of suspension and stabilization of program motions of rigid body with fixed point.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1996.10a
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• pp.227-233
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• 1996

The Inverted Pendulum has been one of most popular nonlinear dynamic systems for the exploration of control techniques. This paper presents a new linear optimal control techniques and nonlinear neural network learning methods. The multiayered neural networks are used to add nonlinear effects on the linear optimal regulator(LQR). The new regulator can compensate nonlinear system uncertainties that are not considered in the LQR design, and can tolerated a wider range of uncertainties than the LQR alone. The new regulator has two neural networks for modeling and control. The neural network for modeling is used to obtain a more accurate model than the given mathematical equations. The neural network for control is used to overcome deficiencies by adding corrections to the linear coefficients of the LQR and by adding nonlinear effects on the LQR. Computer simulations are performed to show the applicability and a more robust regulator than the LQR alone.

• Earthquakes and Structures
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• v.24 no.6
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• pp.405-413
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• 2023

Various methods have been used to strengthen structures against earthquakes. Isolator systems are among the methods to control the structure's response. Instead of increasing the strength and capacity of the structure, these systems react to earthquakes. In this paper, an isolator system was investigated with the flexible piers of ∨ and ∧ elements, which were perpendicular to each other and connected by a rod hinged at both ends. The behavior of the isolator system was studied. Many structures have non-rigid connections; the effect of this issue was considered in the pendulum column's performance in this paper. Its mathematical equations were derived, solved with MATLAB software, and compared with ABAQUS results. Later on, the isolator system was investigated during different earthquakes. The results show that this mechanism is suitable as an isolator. The period was found to be longer in the flexible pier form. The flexible piers have an influential role in the system's response by reducing the system's stiffness considerably. Among the different damping ratios, those with more than 15% had better results. Finally, the tested model verified the theory.

• Proceedings of the KIEE Conference
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• 1996.07b
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• pp.1104-1106
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• 1996

In this paper, a hierarchical fuzzy controller is proposed for the stabilization control of the inverted pendulum system. The design of controller for that system is difficult because of its complicated nonlinear mathematical model with unknown parameters. Conventional fuzzy control strategy based only on dynamics of pendulum made have failed to stabilize. However, proposed control strategies are to swing pendulum from natural stable up equilibrium point to an unstable equilibrium point and are to transport a cart from an arbitrary position toward a center of rail. Thus, the proposed fuzzy stabilization controller have a hierarchical fuzzy inference structure; that is, the lower level is for inference interface for the virtual equilibrium point and the higher level one for the position control of cart according to the firstly inferred virtual equilibrium point.

• Journal of the Korean Institute of Intelligent Systems
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• v.26 no.2
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• pp.127-134
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• 2016

This paper presents a robust control of a reaction wheel inverted pendulum. To this end, a mathematical model is derived using physical laws, and then parameters in the model are identified as well. Based on the model, a robust position control is designed, which consists of two parts: swing-up control using passivity and robust stabilization control using LMI (Linear Matrix Inequality). When the pendulum starts to move, the swing-up control is applied. If the position of the pendulum is near the desired upright position, the control is switched to the robust stabilization control. This robust control is employed in order to deal with the uncertainties in the inertia of the pendulum dynamics. The performance of the proposed control scheme is validated not only simulation but also real experiment.

• The Journal of Korea Institute of Information, Electronics, and Communication Technology
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• v.16 no.6
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• pp.400-405
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• 2023

Currently, inverted pendulums are being studied in many fields, including posture control of missiles, rockets, etc, and bipedal robots. In this study, the vertical posture control of the pendulum was studied by constructing a rotary inverted pendulum using a 256-pulse rotary encoder and a DC motor. In the case of nonlinear systems, complex algorithms and controllers are required, but a control method using the classic and relatively simple PID(Proportional Integral Derivation) algorithm was applied to the rotating inverted pendulum system, and a simple but desired method was studied. The rotating inverted pendulum system used in this study is a nonlinear and unstable system, and a PID controller using Microchip's dsPIC30F4013 embedded processor was designed and implemented in linear modeling. Usually, PID controllers are designed by combining one or two or more types, and have the advantage of having a simple structure compared to excellent control performance and that control gain adjustment is relatively easy compared to other controllers. In this study, the physical structure of the system was analyzed using mathematical methods and control for vertical balance of a rotating inverted pendulum was realized through modeling. In addition, the feasibility of controlling with a PID controller using a rotating inverted pendulum was verified through simulation and experiment.