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

*Authors: Thiago César Marsola, Mateus Pereira, Mauricio Ribeirao, Wagner Lenz, Angelo Tusset, and José Manoel Balthazar*

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.

a Displacement in time x1 . b Displacement in time x2 . c Displacement in time x3 . d Phase Diagram ( x1 vs. x2 vs. x3 ).