We develop a method for the stabilization of mechanical systems with symmetry based on the technique of controlled Lagrangians. The procedure involves making structured modifications to the Lagrangian for the uncontrolled system, thereby constructing the controlled Lagrangian. The Euler–Lagrange equations derived from the controlled Lagrangian describe the closed-loop system, where new terms in...

This study presents a Linear Quadratic Optimal (LQR) controller design for an inverted pendulum on a cart using the Artificial Bee Colony (ABC) algorithm. Main design parameters of the linear quadratic regulator are the weighting matrices. Generally, selecting weighting matrices is managed by trial and error since there exists no apparent connection between these weights and time domain require...

This paper describes a procedure for incorporating artificial gyroscopic forces in the method of controlled Lagrangians. These energy-conserving forces provide additional freedom to expand the basin of stability and tune closed-loop system performance. We also study the effect of physical dissipation on the closed-loop dynamics and discuss conditions for stability in the presence of natural dam...

This paper presents the application of discrete-time variable structure control with sliding mode based on the ‘reaching law’ method for robust control of a ‘simple inverted pendulum on moving cart’ a standard nonlinear benchmark system. The controllers designed using the above techniques are completely insensitive to parametric uncertainty and external disturbance. The controller design is car...

The challenge in the swing-up problem of double inverted pendulum on a cart (DIPC) is to design a controller that bring all DIPC's states, especially the joint angles of the two links, into the region of attraction of the desired equilibrium. This paper proposes a new method to swing-up DIPC based on a series of restto-rest maneuvers of the first link about its vertically upright configuration ...

This paper presents a possible way to control the a very fast nonlinear systems. The system of the inverted pendulum was chosen as an exemplar process. This is an example of the nonlinear single-input multi-output process with a sampling period in order of milliseconds. The state-space predictive control was chosen as a control method and the system is described by CARIMA model. The whole proce...

Copyright © 2016 Frontiers of Current Trends in Engineering and Technology, ACET 21 Abstract: The Cart-Inverted Pendulum System (CIPS) is a classical benchmark control problem. The control of this system is challenging as it is highly unstable, highly non-linear, non-minimum phase system and under actuated. The basic control objective of the inverted pendulum is to maintain the unstable equili...

In this paper, the decoupled neural network reference compensation technique (DRCT) is applied to the control of a two degrees-of-freedom inverted pendulum mounted on an x-y table. Neural networks are used as auxiliary controllers for both the x axis and y axis of the PD controlled inverted pendulum. The DRCT method known to compensate for uncertainties at the trajectory level is used to contro...

The “inverted pendulum problem” is perhaps the most widely used benchmarking study to assess the effectiveness of emerging control design techniques. In this paper the “Backpropagation Through Time” learning method is used to train a multilayer perceptron neural network to control an actual physical system, consisting in a pendulum free to pivot on a cart, which is moved by a DC motor within a ...