Multivariable control of a magnetic levitation system using closed loop identification and H/sub ∞/ control theory

2002 ◽  
Author(s):  
K. Nakashima ◽  
T. Tsujino ◽  
T. Fujii
Keyword(s):  
Control Theory ◽  
Closed Loop ◽  
Magnetic Levitation ◽  
Multivariable Control ◽  
Levitation System ◽  
Closed Loop Identification ◽  
Magnetic Levitation System

Backstepping Based Adaptive Control of Magnetic Levitation System

2013 ◽  
Vol 341-342 ◽  
pp. 945-948 ◽  
Author(s):  
Wei Zhou ◽  
Bao Bin Liu
Keyword(s):  
Parameter Uncertainty ◽  
Closed Loop ◽  
Controller Design ◽  
Magnetic Levitation ◽  
Adaptive Controller ◽  
Closed Loop System ◽  
Actual System ◽  
Levitation System ◽  
Magnetic Levitation System ◽  
Control Accuracy

In view of parameter uncertainty in the magnetic levitation system, the adaptive controller design problem is investigated for the system. Nonlinear adaptive controller based on backstepping is proposed for the design of the actual system with parameter uncertainty. The controller can estimate the uncertainty parameter online so as to improve control accuracy. Theoretical analysis shows that the closed-loop system is stable regardless of parameter uncertainty. Simulation results demonstrate the effectiveness of the presented method.

scholarly journals Stabilization of the Magnetic Levitation System

2021 ◽  
Vol 11 (21) ◽  
pp. 10369
Author(s):  
Štefan Chamraz ◽  
Mikuláš Huba ◽  
Katarína Žáková
Keyword(s):  
Closed Loop ◽  
Magnetic Levitation ◽  
Internal Model Control ◽  
Pass Filter ◽  
Low Pass Filter ◽  
First Order ◽  
Model Based ◽  
Model Control ◽  
Levitation System ◽  
Magnetic Levitation System

This paper contributes toward research on the control of the magnetic levitation plant, representing a typical nonlinear unstable system that can be controlled by various methods. This paper shows two various approaches to the solution of the controller design based on different closed loop requirements. Starting from a known unstable linear plant model—the first method is based on the two-step procedure. In the first step, the transfer function of the controlled system is modified to get a stable non-oscillatory system. In the next step, the required first-order dynamic is defined and a model-based PI controller is proposed. The closed loop time constant of this first-order model-based approach can then be used as a tuning parameter. The second set of methods is based on a simplified ultra-local linear approximation of the plant dynamics by the double-integrator plus dead-time (DIPDT) model. Similar to the first method, one possible solution is to stabilize the system by a PD controller combined with a low-pass filter. To eliminate the offset, the stabilized system is supplemented by a simple static feedforward, or by a controller proposed by means of an internal model control (IMC). Another possible approach is to apply for the DIPDT model directly a stabilizing PID controller. The considered solutions are compared to the magnetic levitation system, controlled via the MATLAB/Simulink environment. It is shown that, all three controllers, with integral action, yield much slower dynamics than the stabilizing PD control, which gives one motivation to look for alternative ways of steady-state error compensation, guaranteeing faster setpoint step responses.

Control of magnetic levitation system using recurrent neural network-based adaptive optimal backstepping strategy

2020 ◽  
Vol 42 (13) ◽  
pp. 2382-2395
Author(s):  
Armita Fatemimoghadam ◽  
Hamid Toshani ◽  
Mohammad Manthouri
Keyword(s):  
Neural Network ◽  
Recurrent Neural Network ◽  
Optimization Problem ◽  
Closed Loop ◽  
Magnetic Levitation ◽  
Backstepping Control ◽  
Loop System ◽  
Closed Loop System ◽  
Levitation System ◽  
Magnetic Levitation System

In this paper, a novel approach is proposed for adjusting the position of a magnetic levitation system using projection recurrent neural network-based adaptive backstepping control (PRNN-ABC). The principles of designing magnetic levitation systems have widespread applications in the industry, including in the production of magnetic bearings and in maglev trains. Levitating a ball in space is carried out via the surrounding attracting or repelling magnetic forces. In such systems, the permissible range of the actuator is significant, especially in practical applications. In the proposed scheme, the procedure of designing the backstepping control laws based on the nonlinear state-space model is carried out first. Then, a constrained optimization problem is formed by defining a performance index and taking into account the control limits. To formulate the recurrent neural network (RNN), the optimization problem is first converted into a constrained quadratic programming (QP). Then, the dynamic model of the RNN is derived based on the Karush-Kuhn-Tucker (KKT) optimization conditions and the variational inequality theory. The convergence analysis of the neural network and the stability analysis of the closed-loop system are performed using the Lyapunov stability theory. The performance of the closed-loop system is assessed with respect to tracking error and control feasibility.

Multivariable Control of a Magnetic Levitation System with a Y Shape Iron Plate

1994 ◽  
Vol 27 (9) ◽  
pp. 25-28
Author(s):  
T. Fujii ◽  
T. Tsujino ◽  
K. Suematu ◽  
K. Sasaki ◽  
Y. Murata
Keyword(s):  
Magnetic Levitation ◽  
Multivariable Control ◽  
Iron Plate ◽  
Levitation System ◽  
Magnetic Levitation System

Control Theory in Practice: Magnetic Levitation

2010 ◽  
Author(s):  
John Rogers ◽  
Robert Rabb
Keyword(s):  
Control Theory ◽  
Magnetic Levitation ◽  
The United States ◽  
Steel Ball ◽  
System Control ◽  
Development Effort ◽  
Sensors And Actuators ◽  
Hands On ◽  
Levitation System ◽  
Magnetic Levitation System

A device that levitates a steel ball beneath an electromagnet is used for educational purposes at the United States Military Academy, West Point, New York. Students in the course “Mechatronics” engage in a set of laboratory exercises with the device to reinforce classroom learning. Mechatronics is a senior-level course that introduces the interdisciplinary design of smart systems. Students in the electrical engineering and mechanical engineering programs take the course together, and the material is taught by a team of instructors from both academic departments. The Magnetic Levitation experiments are the primary means of teaching the classical analog control portion of the course. Other aspects of the course involve interfacing microcontrollers with sensors and actuators, and digital control. The magnetic levitation device fits easily on a two-person workbench and requires a power supply and oscilloscope. An infra-red emitter / detector pair is used to sense ball position for a feedback compensator. Students first learn classical control theory in a co-requisite course, “Dynamic Modeling and Control.” Modeling principles are introduced in the context of the magnetic levitation system as an unstable plant to be controlled. The system can be simulated by models ranging from simply linear to more complex to teach the trade-off between model fidelity and model development effort. The students derive the nonlinear governing equations and then linearize the equations and develop the transfer function of the plant. Students design a compensator and simulate the resulting stabilized system with Matlab and Simulink software. Students build their compensator on a solderless project board to levitate the steel ball. A proven lead-type compensator using two resistors and a capacitor is readily provided to students that struggle with their own compensator design so that all teams may enjoy the fruit of a successful experiment. As a laboratory aid, the magnetic levitation system allows for basic and advanced approaches to both theoretical study and practical investigation of a nonlinear, unstable system control. The comparison of measured results to predicted behavior leads to insight about how the physical system is modeled by mathematics. Students write a case study describing the system in detail including characterization of the sensors and actuators. Instructors report that the hands-on nature motivates students to excel. Surveyed students cite the hands-on activities as relevant applications that help develop deeper understanding and greater appreciation for the concepts learned in the classroom. The students are motivated to learn by the fascination of defying gravity.

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