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.

Observer-based robust control for flexible-joint robot manipulators: A state-dependent Riccati equation-based approach

2020 ◽  
Vol 42 (16) ◽  
pp. 3135-3155
Author(s):  
Neda Nasiri ◽  
Ahmad Fakharian ◽  
Mohammad Bagher Menhaj
Keyword(s):  
Robust Control ◽  
Control Problem ◽  
Riccati Equation ◽  
Power Transmission ◽  
Control Method ◽  
Main Idea ◽  
Robotic Systems ◽  
Flexible Joint ◽  
State Dependent ◽  
Highly Nonlinear

In this paper, the robust control problem is tackled by employing the state-dependent Riccati equation (SDRE) for uncertain systems with unmeasurable states subject to mismatched time-varying disturbances. The proposed observer-based robust (OBR) controller is applied to two highly nonlinear, coupled and large robotic systems: namely a manipulator presenting joint flexibility due to deformation of the power transmission elements between the actuator and the robot known as flexible-joint robot (FJR) and also an FJR incorporating geared permanent magnet DC motor dynamics in its dynamic model called electrical flexible-joint robot (EFJR). A novel state-dependent coefficient (SDC) form is introduced for uncertain EFJRs. Rather than coping with the OBR control problem for such complex uncertain robotic systems, the main idea is to solve an equivalent nonlinear optimal control problem where the uncertainty and disturbance bounds are incorporated in the performance index. The stability proof is presented. Solving the complicated robust control problem for FJRs and EFJRs subject to uncertainty and disturbances via a simple and flexible nonlinear optimal approach and no need of state measurement are the main advantages of the proposed control method. Finally, simulation results are included to verify the efficiency and superiority of the control scheme.

Nonlinear Active Cancellation of the Parametric Resonance in a Magnetically Levitated Body

2004 ◽  
Vol 126 (3) ◽  
pp. 433-442 ◽  
Author(s):  
Hiroshi Yabuno ◽  
Ryo Kanda ◽  
Walter Lacarbonara ◽  
Nobuharu Aoshima
Keyword(s):  
Parametric Resonance ◽  
Degrees Of Freedom ◽  
Control Method ◽  
Inertial Force ◽  
Phase Lock Loop ◽  
Vibration Absorber ◽  
Control Input ◽  
Main System ◽  
Magnetically Levitated ◽  
Active Control Strategy

An active control strategy for the stabilization of parametric resonance in a magnetically levitated body is proposed. 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. As a distinguished feature, the proposed control method does not rely on the effective autoparametric energy transfer between the main system and the absorber. Because the main system is not linearly coupled with the absorber, the drawback inherent in the increase of the system degrees of freedom (i.e., the increase of the linear vibrational mode for the main system due to the attachment of the absorber) is overcome. The effective frequency and amplitude of the pure-tone control input—the torque driving the vibration absorber—are designed so that the nonlinear action of the pendulum on the main system counteracts the effect of the resonant parametric excitation. The effectiveness of the theoretically proposed control method is experimentally validated using an apparatus that comprises a phase-lock loop system.

FINITE DURATION TREATMENT OF CANCER BY USING VACCINE THERAPY AND OPTIMAL CHEMOTHERAPY: STATE-DEPENDENT RICCATI EQUATION CONTROL AND EXTENDED KALMAN FILTER

2015 ◽  
Vol 23 (01) ◽  
pp. 1-29 ◽  
Author(s):  
MOSTAFA NAZARI ◽  
ALI GHAFFARI ◽  
FARHAD ARAB
Keyword(s):  
Kalman Filter ◽  
Riccati Equation ◽  
Extended Kalman Filter ◽  
Control Method ◽  
Domain Of Attraction ◽  
Treatment Method ◽  
Drug Dosage ◽  
Vaccine Therapy ◽  
Finite Duration ◽  
State Dependent

The main purpose of this paper is to propose an optimal finite duration treatment method for preventing tumor growth. The obtained results show that changing the dynamics of the cancer model is essential for a finite duration treatment. Therefore, vaccine therapy is used for changing the parameters of the system and chemotherapy is applied for pushing the system to the domain of attraction of the healthy state. The state-dependent Riccati equation (SDRE)-based optimal control method is used for optimal chemotherapy. In this method, the special conditions of the patients could be considered by choosing suitable weighting matrices in the cost function and restricting the drug dosage. Also, there are infinite ways to choose these state-dependent matrices. In this paper, these interesting features of this method are used for each patient. Since measuring the states of the system is impossible at each time for states feedback; an extended Kalman filter (EKF) is designed as an observer in the nonlinear system. So, the SDRE method is employed just by measuring the population of normal cells. Numerical simulations show the flexibility and effectiveness of this treatment method.

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