Modeling and control with neural networks for a magnetic levitation system

MagnetoShield: A Novel Open-Source Magnetic Levitation Benchmark Device for Mechatronics Education and Research

This article presents an open-source device illustrating the well-known magnetic levitation experiment. The uniqueness of this particular device lies in its exceptionally small dimensions, affordability and availability, which makes it a perfect design for take-home experiments for education but it can also serve as a referential design for testing various control algorithms in research. In addition, this paper provides a comprehensive hardware design for reproducibility along with the detailed derivation of the mathematical model, system identification and validation. Moreover, the introduced hardware comes with an easy-to-use open-source application programming interface in C/C++ for the Arduino IDE, Simulink and CircuitPython. REXYGEN, another environment similar to Simulink, had also been used to demonstrate the capabilities of the MagnetoShield.

Design Methodology for a Magnetic Levitation System Based on a New Multi-Objective Optimization Algorithm

Multi-objective (MO) optimization is a developing technique for increasing closed-loop performance and robustness. However, its applications to control engineering mostly concern first or second order approximation models. This article proposes a novel MO algorithm, suitable for the design and control of mechanical systems, which does not require any order reduction techniques. The controller parameters are determined directly from a special type of rapid analysis of simulated transient responses. The case study presented in this article consists of a magnetic levitation system. Certain difficulties such as the nonlinearity identification of the magnetic force and duo magnetic field sensor scheme were addressed. To point out the advantages of using the developed approach, the simulations as well as the experiments performed with the help of the created algorithm were compared to those made with common MO algorithms.

Recurrent neural network based high-precision position compensation control of magnetic levitation system

For improving the dynamic quality and steady-state performance, the hybrid controller based on recurrent neural network (RNN) is designed to implement the position control of the magnetic levitation ball system in this study. This hybrid controller consists of a baseline controller, an RNN identifier, and an RNN controller. In the hybrid controller, the baseline controller based on the control law of proportional-integral-derivative is firstly employed to provide the online learning sample and maintain the system stability at the early control phase. Then, the RNN identifier is trained online to learn the accurate inverse model of the controlled object. Next, the RNN controller shared the same structures and parameters with the RNN identifier is applied to add the precise compensation control quantity in real-time. Finally, the effectiveness and advancement of the proposed hybrid control strategy are comprehensively validated by the simulation and experimental tests of tracking step, square, sinusoidal, and trapezoidal signals. The results indicate that the RNN-based hybrid controller can obtain higher precision and faster adjustment than the comparison controllers and has strong anti-interference ability and robustness.

Development of Magnetically Levitated Rotary Table for Repetitive Trajectory Tracking

The magnetic levitation system has been considered as a promising actuator in micromachining areas of study. In order to improve the tracking performance and disturbance rejection of the magnetically levitated rotary table, an iterative learning PID control strategy with disturbance compensation is proposed. The estimated disturbance compensates for the control signals to enhance the active disturbance rejection ability. The iterative learning control is used as a feed-forward unit to further reduce the trajectory tracking error. The convergence and stability of the iterative learning PID with disturbance compensation are analysed. A series of comparative experiments are carried out on the in-house, custom-made, magnetically levitated rotary table, and the experimental results highlight the superiority of the proposed control strategy. The iterative learning PID with disturbance compensation enables the magnetically levitated rotary table to realize good tracking performance with complex external disturbance. The proposed control strategy strengthens the applicability of magnetically levitated systems in the mechanism manufacturing area.

Neural network compensation control of magnetic levitation ball position based on fuzzy inference

Aiming at the problem of poor transient performance of the control system caused by the control uncertainty of the undertrained neural network, a neural network compensation control method based on fuzzy inference is proposed in this paper. The method includes three control substructures: fuzzy inference block, neural network control block and basic control block. The fuzzy inference block adaptively adjusts the neural network compensation control quantity according to the control error and the error rate of change, and adds a dynamic adjustment factor to ensure the control quality at the initial stage of network learning or at the moment of signal transition. The neural network control block is composed of an identifier and a controller with the same network structure. After the identifier learns the dynamic inverse model of the controlled object online, its training parameters are dynamically copied to the controller for real-time compensation control. The basic control block uses a traditional PID controller to provide online learning samples for the neural network control block. The simulation and experimental results of the position control of the magnetic levitation ball show that the proposed method significantly reduces the overshoot and settling time of the control system without sacrificing the steady-state accuracy of neural network compensation control, and has good transient and steady-state performance and strong robustness simultaneously.

Interpretable PID parameter tuning for control engineering using general dynamic neural networks: An extensive comparison

Modern automation systems largely rely on closed loop control, wherein a controller interacts with a controlled process via actions, based on observations. These systems are increasingly complex, yet most deployed controllers are linear Proportional-Integral-Derivative (PID) controllers. PID controllers perform well on linear and near-linear systems but their simplicity is at odds with the robustness required to reliably control complex processes. Modern machine learning techniques offer a way to extend PID controllers beyond their linear control capabilities by using neural networks. However, such an extension comes at the cost of losing stability guarantees and controller interpretability. In this paper, we examine the utility of extending PID controllers with recurrent neural networks—–namely, General Dynamic Neural Networks (GDNN); we show that GDNN (neural) PID controllers perform well on a range of complex control systems and highlight how they can be a scalable and interpretable option for modern control systems. To do so, we provide an extensive study using four benchmark systems that represent the most common control engineering benchmarks. All control environments are evaluated with and without noise as well as with and without disturbances. The neural PID controller performs better than standard PID control in 15 of 16 tasks and better than model-based control in 13 of 16 tasks. As a second contribution, we address the lack of interpretability that prevents neural networks from being used in real-world control processes. We use bounded-input bounded-output stability analysis to evaluate the parameters suggested by the neural network, making them understandable for engineers. This combination of rigorous evaluation paired with better interpretability is an important step towards the acceptance of neural-network-based control approaches for real-world systems. It is furthermore an important step towards interpretable and safely applied artificial intelligence.

Robust switched control of an air levitation system with minimum sensing

This work studies the control problem of an air levitation system with limited sensing capabilities. We propose a simple but considerably robust switched controller. We prove that the output of the system is globally uniformly ultimately bounded with a bound as small as we desire and we show through simulations and real experiments the robustness of the controller in the presence of disturbances, model uncertainties and parameter tuning.

Research on one-dimensional motion control system and method of a magnetic levitation ball

Research on the multi-degree-of-freedom and large-displacement motion control of the levitated object makes a contribution to broadening the application field of the Maglev technology. A one-dimensional motion control system and method of the Maglev ball are investigated in this paper. The Maglev ball motion control system is required to have a large operating range. In order to meet this requirement, a novel Maglev system based on double linear hall sensors is designed and implemented. The step-by-step control based on the Proportional-Integral-Derivative (PID) controller is proposed as one method to realize the large step response of the levitated object. The controlled object responds to the successive small step input rather than the large step input. Then, the mathematical model of the system is set up based on the electromagnetic force equation and controller parameters are tuned by following the mathematical model of the Maglev system at different positions. The experimental data show that the position accuracy of the Maglev control system using the PID controller reaches ±0.02 mm. Moreover, step-by-step control can not only safely realize large-displacement motion of the levitated object but also effectively reduce the overshoot of the step response and make the step response process smoother.

Fisher Information Matrix of Unipolar Activation Function-Based Multilayer Perceptrons

The multilayer perceptrons (MLPs) are widely used in many fields, however, singularities in the parameter space may seriously influence the learning dynamics of MLPs and cause strange learning behaviors. Given that the singularities are the subspaces of the parameter space where the Fisher information matrix (FIM) degenerates, the FIM plays a key role in the study of the singular learning dynamics of the MLPs. In this paper, we obtain the analytical form of the FIM for unipolar activation function-based MLPs where the input subjects to the Gaussian distribution with general covariance matrix and the unipolar error function is chosen as the activation function. Then three simulation experiments are taken to verify the validity of the obtained results.