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.

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.

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.

scholarly journals Fractional PIλD Controller Design for a Magnetic Levitation System

Electronics ◽  
2020 ◽  
Vol 9 (12) ◽  
pp. 2135
Author(s):  
Waldemar Bauer ◽  
Jerzy Baranowski
Keyword(s):  
Performance Indicators ◽  
Parametric Optimization ◽  
Controller Design ◽  
Magnetic Levitation ◽  
Stability Margins ◽  
Integer Order ◽  
Levitation System ◽  
Nyquist Stability ◽  
Magnetic Levitation System

Currently, there are no formalized methods for tuning non-integer order controllers. This is due to the fact that implementing these systems requires using an approximation of the non-integer order terms. The Oustaloup approximation method of the sα fractional derivative is intuitive and widely adopted in the design of fractional-order PIλD controllers. It requires special considerations for real-time implementations as it is prone to numerical instability. In this paper, for design and tuning of fractional regulators, we propose two methods.The first method relies on Nyquist stability criterion and stability margins. We base the second on parametric optimization via Simulated Annealing of multiple performance indicators. We illustrate our methods with a case study of the PIλD controller for the Magnetic Levitation System. We illustrate our methods’ efficiency with both simulations and experimental verification in both nominal and disturbed operation.

Sign in / Sign up

Export Citation Format

Share Document