Properties of simple strategies for swinging up an inverted pendulum are discussed. It is shown that the behavior critically depends on the ratio of the maximum acceleration of the pivot to the acceleration of gravity. A comparison of energy based strategies with minimum time strategy gives interesting insights into the robustness of minimum time solutions.

Generally the inverted pendulum is unstable, because the pendulum will fall downward due to the gravitational force acting on mass of the pendulum. Keeping the pendulum at vertically inverted position, the position of DC motor shaft needs to be controlled using closed loop analysis. For closed loop analysis, feedback or input device such as encoder is used. To control and set the pendulum at de...

The inverted pendulum is a canonical problem in both Nonlinear Dynamics and Control Theory. In this article, the phenomenon of dynamic stabilization of the vertically driven inverted pendulum is investigated experimentally and numerically. We resolve the first stabilizing boundary in driving parameter space, as well as investigate the effects of frictional damping on the dynamics of the pendulu...

The purpose of this paper is to present the design of a complete control strategy for the classical and rotary single inverted pendulum system. The design, which involves swing-up and stabilization of both systems, is based on function blocks and GUI tools from the Inverted Pendula Modeling and Control, a Simulink block library developed by the author of the paper. Keywords—classical single inv...

This paper presents the control of an inverted pendulum system using intelligent algorithms, such as fuzzy logic and neural networks, for advanced control education. The swing up balancing control of the inverted pendulum system was performed using fuzzy logic. Because the switching time from swing to standing motion is important for successful balancing, the fuzzy control method was employed t...

Unstable wheel inverted pendulum is modelled and controlled deploying Kane’s method and optimal partial-state PID control scheme. A correct derivation of nonlinear mathematical model of a wheel inverted pendulum is obtained using a proper definition of the geometric context of active and inertia forces. Then the model is decoupled to two linear subsystems namely balancing and heading subsystems...

Backstepping control technique is a Lyapunov based nonlinear robust technique which is applicable to only strict feedback system. Backstepping technique has been applied on linear inverted pendulum which is under actuated system. Inverted pendulum is swung from its pendant position and stabilized at its upright position. Swing up is achieved by nonlinear backstepping controller but the linear i...

X–Z inverted pendulum is a new kind of inverted pendulum and it can move with the combination of the vertical and horizontal forces. In this paper, the control problem of X-Z inverted pendulum with system uncertainties is addressed, and a pair of decoupled adaptive fuzzy sliding mode control method is proposed. The fuzzy logic system is employed to approximate the system uncertainties as well a...

We investigate the dynamics of an inverted pendulum subjected to Jacobi elliptic forcing both numerically and experimentally. In so doing, we hope to provide a coherent picture on stability of an inverted pendulum subjected to forcing that ranges from harmonic to nonharmonic in nature. We are able to determine the regions of stability of a sinusoidally forced inverted pendulum, with results sim...

Double Inverted Pendulum is a nonlinear system, unstable and fast reaction system. Double Inverted Pendulum is stable when its two pendulums allocated in vertically position and have no oscillation and movement and also inserting force should be zero. The aim of the paper is to design and performance analysis of the double inverted pendulum and simulation of Linear Quadratic Regulator (LQR) con...