The paper offers evolving Takagi–Sugeno (T–S) fuzzy models for a nonlinear benchmark represented by the pendulum-crane system and focused on the dynamics of pendulum angular position behavior. The rule bases and parameters of T–S fuzzy models are continuously evolved by an online identification algorithm in terms of computing the potentials of new data points. Accepting the pendulum angle as mo...

The balancing of an inverted pendulum by moving a cart along a horizontal track is a classic problem in the area of control. This paper will describe two methods to swing a pendulum attached to a cart from an initial downwards position to an upright position and maintain that state. A nonlinear heuristic controller and an energy controller have been implemented in order to swing the pendulum to...

In this paper, we describe the conceptual design for the suspension system for the test masses for Advanced LIGO, the planned upgrade to LIGO, the US laser interferometric gravitational-wave observatory. The design is based on the triple pendulum design developed for GEO 600—the German/UK interferometric gravitational wave detector. The GEO design incorporates fused silica fibres of circular cr...

Inverted pendulum system is a complicated, unstable and multivariable nonlinear system. In order to control the angle and displacement of inverted pendulum system effectively, a novel double-loop digital PID control strategy is presented in this paper. Based on impulse transfer function, the model of the single linear inverted pendulum system is divided into two parts according to the controlle...

In this paper, we will propose a nonlinear passivity based controller fur a double inverted pendulum system, consisting of a two-link pendulum mounted on a pad which is moved by a linear induction motor so that the double pendulum points straight-up The proposed controller nut only can drive the double pendulum from its “natural stable hanging position” tu its “unstable upright inverted positio...

The objective of this paper is to compare the time specification performance between conventional controller PID and modern controller SMC for an inverted pendulum system. The goal is to determine which control strategy delivers better performance with respect to pendulum’s angle and cart’s position. The inverted pendulum represents a challenging control problem, which continually moves toward ...

The hybrid solution to the pendulum swinging-up and stabilizing problem introduced by Åström and Furuta is based in two steps: an energy injection and a linear stabilization around the desired inverted position. However the energy injection stage only considers the pendulum, and not the motion of the pivot. Furthermore, for the stabilization stage linear law, only a very small basin of attracti...

This paper describes the method for trajectory tracking and balancing the Self Erecting Single Inverted Pendulum (SESIP) using Linear Quadratic Regulator (LQR). A robust LQR controller for stabilizing the SESIP is proposed in this paper. The first part of the controller is a Position Velocity (PV) controller to swing up the pendulum from its hanging position by moving the pendulum left and righ...

The rotary inverted pendulum system was a highly nonlinear model, multivariable and absolutely unstable dynamic system. This paper presents hybrid control method for swing up and LQR control method for the stabilization. The flexibility of the hybrid control method based on the selection of heuristic swing up controller and energy swing up controller at the different positions of pendulum. The ...

This paper considers the problem of damping the oscillation of a plane pendulum by moving the pivot in the vertical plane and the weight along the rod of the pendulum, with limited amplitudes. Conditions for stability of the motion of the pendulum are derived using energybased methods, and based on them energy-based controls satisfying the amplitude constraints are developed, which move the piv...