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RESEARCH PAPERS

# Nonlinear Dynamics and Control of an Ideal/Nonideal Load Transportation System With Periodic Coefficients

[+] Author and Article Information
N. J. Peruzzi

Department of Exact Science, State University of São Paulo, Jaboticabal, SP, Brazil 134884-900, Jaboticabal, SP, Brazilperuzzi@fcav.unesp.br

J. M. Balthazar

Department of Statistics, Applied Mathematics and Computation, State University of São Paulo Rio Claro, SP, Brazil, P.O. Box 178, 13500-230 Rio Claro, SP, Brazilimbaltha@rc.unesp.br

B. R. Pontes

Department of Mechanical Engineering, State University of São Paulo Bauru, SP, Brazilbrpontes@feb.unesp.br

R. M. L. R. F. Brasil

Department of Structural and Foundations Engineering, University of São Paulo, Brazilrmlrdfbr@usp.br

J. Comput. Nonlinear Dynam 2(1), 32-39 (Sep 26, 2006) (8 pages) doi:10.1115/1.2389040 History: Received January 31, 2006; Revised September 26, 2006

## Abstract

In this paper, a loads transportation system in platforms or suspended by cables is considered. It is a monorail device and is modeled as an inverted pendulum built on a car driven by a dc motor. The governing equations of motion were derived via Lagrange’s equations. In the mathematical model we consider the interaction between the dc motor and the dynamical system, that is, we have a so called nonideal periodic problem. The problem is analyzed, qualitatively, through the comparison of the stability diagrams, numerically obtained, for several motor torque constants. Furthermore, we also analyze the problem quantitatively using the Floquet multipliers technique. Finally, we devise a control for the studied nonideal problem. The method that was used for analysis and control of this nonideal periodic system is based on the Chebyshev polynomial expansion, the Picard iterative method, and the Lyapunov-Floquet transformation (L-F transformation). We call it Sinha’s theory.

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## Figures

Figure 1

Nonideal physical system

Figure 2

Subsystem details

Figure 3

Stability diagram of the ideal dynamic system

Figure 4

Stability diagram for ς=6.0

Figure 5

Stability diagram for ς=4.0

Figure 6

Zoom of the stability diagram for ς=0.1

Figure 7

Stability diagram for Δ=0.33

Figure 8

Noncontrolled system time history

Figure 9

Controlled system time history

Figure 10

Organization chart with a summary of the technique used in this work

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