Nonlinear control design method based on state-dependent Riccati equation (SDRE) via quasi-Newton method

2004 ◽  
Author(s):  
J. Imae ◽  
H. Sagami ◽  
T. Kobayashi ◽  
Guisheng Zhai
Keyword(s):  
Nonlinear Control ◽  
Riccati Equation ◽  
Newton Method ◽  
Design Method ◽  
Control Design ◽  
State Dependent ◽  
Quasi Newton

State Dependent Riccati Equation (SDRE) Control Method Applied in Cancellation of a Parametric Resonance in a Magnetically Levitated Body

2011 ◽  
Author(s):  
Fa´bio Roberto Chavarette ◽  
Jose´ Manoel Balthazar ◽  
Ce´lia Aparecida dos Reis ◽  
Nelson Jose´ Peruzzi
Keyword(s):  
Riccati Equation ◽  
Control Method ◽  
Equations Of Motion ◽  
Control Design ◽  
Inertial Force ◽  
The Body ◽  
State Dependent ◽  
Oscillatory Movement ◽  
Magnetically Levitated ◽  
Static Equilibrium State

Here, a simplified dynamical model of a magnetically levitated body is considered. The origin of an inertial Cartesian reference frame is set at the pivot point of the pendulum on the levitated body in its static equilibrium state (ie, the gap between the magnet on the base and the magnet on the body, in this state). The governing equations of motion has been derived and the characteristic feature of the strategy is the exploitation of the nonlinear effect of the inertial force associated, with the motion of a pendulum-type vibration absorber driven, by an appropriate control torque [4]. In the present paper, we analyzed the nonlinear dynamics of problem, discussed the energy transfer between the main system and the pendulum in time, and developed State Dependent Riccati Equation (SDRE) control design to reducing the unstable oscillatory movement of the magnetically levitated body to a stable fixed point. The simulations results showed the effectiveness of the (SDRE) control design.

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