Dynamics Analysis and Control of the Malkus-Lorenz Waterwheel with Parametric Errors

  • Angelo M. TussetEmail author
  • Jose M. Balthazar
  • Mauricio A. Ribeiro
  • Wagner B. Lenz
  • Thiago C. L. Marsola
  • Mateus F. V. Pereira
Conference paper
Part of the Springer Proceedings in Physics book series (SPPHY, volume 228)


This work presents a dynamical analysis for the Malkus-Lorenz waterwheel, a physical system that behaves following the Lorenz equations. With this, two types of controllers were designed to control the system presenting chaotic behavior. The first controller is the time-delay feedback control (TDFC), and the second one is the State-Dependent Riccati Equation control (SDRE). The control strategy for the SDRE control involves the application of two signals: a nonlinear feedforward signal to maintain the controlled system in a periodic orbit, and a feedback signal, to take the system trajectory into the desired periodic orbit. Numerical simulations demonstrated the effectiveness of the control strategy in taking the system presenting chaotic behavior into a desired periodic orbit. In addition, the SDRE control robustness is investigated analyzing parametric errors in control loop.


Time delay feedback control SDRE control Malkus-Lorenz waterwheel 


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Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.Federal University of Technology—ParanáPonta GrossaBrazil

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