Magnetic Levitation Ball System Research Articles

Deep Learning based Model Predictive Controller on a Magnetic Levitation Ball System

The magnetic levitation (maglev) ball system is a prototypical Single-Input-Single-Output (SISO) system, characterized by its pronounced nonlinearity, rapid response, and open-loop instability. It serves as the basis for many industrial devices. For describing the dynamics of the maglev ball system precisely in the pseudo linear model, the long short-term memory (LSTM) based auto-regressive model with exogenous input variables (LSTM-ARX) is proposed. Firstly, the LSTM network is modified by incorporating the auto-regressive structure with respect to sequence input, allowing it to deduce a locally linearized model without the need for Taylor expansion. Then, the LSTM-ARX model is transformed into a linear parameter varying (LPV) state space model, and upon this foundation, a model predictive controller (MPC) is proposed. Specifically, when deducing the MPC, the deep learning-based model is linearized by fixing its state input at the current state, so that the nonlinear, non-convex optimization problem can be converted to a finite-horizon quadratic programming problem, thereby deriving the explicit form of MPC. To further enhance the efficiency of the controller in real-time control tasks, a predictive functional controller (PFC) is proposed. It employs multiple nonlinear functions to fit the control sequence, thereby reducing the number of decision variables of the on-line optimization problem in MPC. The proposed controller was successfully applied to the real-time control of the maglev ball system. Simulation and real-time control experiments have validated the improvement in transient performance and efficiency of the LSTM-ARX model-based PFC (LSTM-ARX-PFC).

Performance recovery of uncertain nonaffine systems by active disturbance rejection control

This paper studies performance recovery problem of a class of uncertain nonaffine strict-feedback systems with mismatched uncertainties. First, the strict-feedback nonaffine system with mismatched system dynamics is transformed into an integrator-chain nonaffine system by a diffeomorphism. Second, the transformed system is converted to an affine one by constructing an auxiliary control input term, and dynamical uncertainties and external disturbances are viewed as total disturbance of the affine system. Then, a two-time-scale active disturbance rejection controller (ADRC) is designed for the transformed affine system. Under some mild assumptions, it can be proved that the proposed ADRC-based closed-loop system can achieve performance recovery and weak performance recovery in different cases of mismatched system dynamics, respectively. Experimental results on a magnetic levitation ball system demonstrate the effectiveness of the proposed control scheme.

Evolution of Controllers Under a Generalized Structure Encoding/Decoding Scheme With Application to Magnetic Levitation System

Evolutionary search has been widely implemented for the adjustment of controllers’ parameters. Nevertheless, the structure of controllers, which has a more important role in control systems, has been seldom studied. To this end, an evolutionary design method of controllers is proposed to optimize both structures and parameters simultaneously in this article. A controller is made up of a combination of some basic controller components and relevant parameters. The design of controllers can be transformed into an optimization problem involving the structure (represented by discrete vectors) and parameters (represented by real numbers). A generalized structure encoding/decoding scheme is developed. Guided by the performance indicators, intelligent algorithms for both combinatorial and numerical optimization are employed to iteratively and cooperatively evolve the controller structure and parameters, respectively. In order to effectively reduce some redundant or infeasible solutions, a set of generation rules for the controller structure are put forward, which also ensures the feasibility of the structure. Furthermore, this method is applied to a magnetic levitation ball system with nonlinear dynamics and external disturbance. Both simulation and experiment results demonstrate the effectiveness and practicability of the proposed method.

Wavelet CMAC for MIMO uncertain nonlinear systems using a modified social ski‐driver algorithm

AbstractThis study uses a Mexican hat wavelet membership function for a cerebellar model articulation controller (CMAC) to develop a more efficient adaptive controller for multiple input multiple output (MIMO) uncertain nonlinear systems. The main controller is called the adaptive Mexican hat wavelet CMAC (MWCMAC), and an auxiliary controller is used to remove the residual error. For the MWCMAC, the online learning laws are derived from the gradient descent method. In addition, the learning rate values are very important and have a great impact on the performance of the control system; however, they are difficult to choose accurately. Therefore, a modified social ski driver (SSD) algorithm is proposed to find optimal learning rates for the control parameters. Finally, a magnetic ball levitation system and a nine‐link biped robot are used to illustrate the effectiveness of the proposed SSD‐based MWCMAC control system. The comparisons with other existing control algorithms have shown the superiority of the proposed control system.

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.

An Improved Equivalent-Input-Disturbance Method for Uncertain Networked Control Systems with Packet Losses and Exogenous Disturbances

In a networked control system (NCS), time delays, uncertainties, packet losses, and exogenous disturbances seriously affect the control performance. To solve these problems, a modified disturbance suppression configuration of NCS was built. In the configuration, a proportional–integral observer (PIO) reproduces the state of a plant and reduces the observation error; an equivalent input disturbance (EID) estimator estimates and compensates for the disturbance in the control input channel. The stability conditions of the NCS are given by using a linear matrix inequality, and the gains of the PIO and state feedback controller are obtained. Numerical simulation results and an application of a magnetic levitation ball system verifies the effectiveness of the presented method. Comparison with the conventional PIO and EID methods shows that the presented method reduced the tracking error to about one-fifth and two-thirds of their original values, respectively. This demonstrates the validity and superiority of the presented method.

Particle Swarm Sliding Mode-Fuzzy PID Control Based on Maglev System

The magnetic levitation system is a typical open-loop unstable system. To weaken the chattering phenomenon of sliding mode control (SMC), a hybrid control strategy of particle swarm sliding mode-fuzzy PID control was designed. This strategy uses particle swarm optimization (PSO) to optimize the SMC using the method of exponential approach law, so as to obtain the best sliding mode surface parameters and exponential approach rate coefficients, thus shortening the time required to approach the stable region when the nonlinear system is far from the stable point; a state supervision controller was designed by analyzing the stable conditions of sliding mode. When the system approaches the stable region, it smoothly transitions to fuzzy PID control, thereby weakening the chattering phenomenon of SMC. To verify the dynamic performance of the designed algorithm, a magnetic levitation ball system was selected as the controlled object. Through simulation and experiment, it was verified that the controller had strong robustness and strong anti-interference performance. It effectively weakened the chattering and had good adaptability to external disturbance and state variable crossing.

Position Control of Magnetic Levitation Ball Based on an Improved Adagrad Algorithm and Deep Neural Network Feedforward Compensation Control

To control the position of the magnetic levitation ball more accurately, this paper proposes a deep neural network feedforward compensation controller based on an improved Adagrad optimization algorithm. The control structure of the controller consists of a deep neural network identifier, a deep neural network feedforward compensator, and a PID controller. First, the dynamic inverse model of the magnetic levitation ball is established by the deep neural network identifier which is trained online based on the improved Adagrad algorithm, and the trained network parameters are dynamically copied to the deep neural network feedforward compensator. Then, the position control of the magnetic levitation ball system is realized by the output of the feedforward compensator and the PID controller. Simulations and experiments illustrate that the accuracy of the deep network feedforward compensation control based on an improved Adagrad algorithm is higher, and its control system shows good dynamic and static performance and robustness to some extent.

Design of a MAGLEV System with PID Based Fuzzy Control Using CS Algorithm

Abstract The main aim of this study consists of proposing a simple but effective and robust approach for PID type fuzzy controller (Fuzzy-PID) in order to improve the dynamics and stability of a magnetic ball levitation system. The design parameters of the proposed controller are optimally determined based on Cuckoo Search (CS) algorithm. During the optimization, a time domain objective function is used for minimizing the values of common step response characteristics for the optimal selection of the controller parameters. Robustness tests are performed to evaluate the performance of the proposed controller through extensive simulations under load disturbance, parametric variation and changes in references. Moreover, to show the advantage and compare the performance of the proposed controller, the PID and Fractional Order PID (FOPID) controllers tuned with CS are designed. The simulation results and comparisons with the CS based PID and FOPID controllers demonstrate that the CS based Fuzzy-PID controller has superior performance depending on small overshoot, short settling time, fast rise time and minimum steady state error. Compared with the PID and FOPID controller tuned with CS, the simulation results show that the proposed Fuzzy-PID controller tuned with CS outperforms in terms of the accuracy, robustness and the least control effort.

Research on hardware-in-the-loop simulation of single point suspension system based on fuzzy PID

The stability control of maglev trains is one of the core problems in the research of maglev train technology and the realisation of this goal is of the great scientific value in the field of magnetic levitation. Based on this, the research on the suspension control strategy of single point maglev system is founded and the control strategy is verified by experiments on Magnetic Levitation Ball System (MLBS). Aiming at the structure of multi-group independent control system of maglev train suspension frame, in order to improve the overall stability control ability of the suspension frame, the coupling relationship between the subsystems is established by introducing the suspension response deviation compensator. Finally, the effect of single point suspension control system is discussed and the cooperative control of suspension frame is carried out on MATLAB. Simulation and analysis show that each subsystem has good anti-jamming ability and the suspension system realises the balanced and stable control under different interference signals, which provides a certain reference value for further study of maglev train suspension control.

Design and Real-Time Implementation of Takagi–Sugeno Fuzzy Controller for Magnetic Levitation Ball System

An integral state feedback control method based on T-S fuzzy model is proposed for nonlinear and unstable magnetic levitation ball system in this paper. Firstly, the fuzzy model of the magnetic levitation ball is derived from the nonlinear dynamic model by using the sector nonlinearity, and the local controller is designed by using the integral state feedback control. The global controller is constructed by a parallel distributed compensation (PDC) method, and the feedback gain is obtained using a linear matrix inequality (LMI). Finally, the integrated state feedback controller is applied to the position control of the magnetic levitation ball system, and a dSPACE real-time control platform is established for experimental research. The simulation and experiment are performed to prove that the designed controller can levitate the ball stably, and has better control performance.

Research on hardware-in-the-loop simulation of single point suspension system based on fuzzy PID

The stability control of maglev trains is one of the core problems in the research of maglev train technology and the realisation of this goal is of the great scientific value in the field of magnetic levitation. Based on this, the research on the suspension control strategy of single point maglev system is founded and the control strategy is verified by experiments on Magnetic Levitation Ball System (MLBS). Aiming at the structure of multi-group independent control system of maglev train suspension frame, in order to improve the overall stability control ability of the suspension frame, the coupling relationship between the subsystems is established by introducing the suspension response deviation compensator. Finally, the effect of single point suspension control system is discussed and the cooperative control of suspension frame is carried out on MATLAB. Simulation and analysis show that each subsystem has good anti-jamming ability and the suspension system realises the balanced and stable control under different interference signals, which provides a certain reference value for further study of maglev train suspension control.

On disturbance rejection in magnetic levitation

Magnetic levitation systems belong to an important and challenging class of control engineering problems with nonlinear uncertain dynamics, multiple disturbances and large sensor noise. To obtain a simple and practical solution that does not depends on the exact model information, a time-varying active disturbance rejection solution is proposed and validated in both numerical and experimental results. The proposed method is confirmed with rigorous analysis of transient performance and noise attenuation. Moreover, the proposed solution is tested in a magnetic levitation ball system with disturbances and measurement noise. The results show that the proposed solution is effective and practical.

CDM Based Servo State Feedback Controller with Feedback Linearization for Magnetic Levitation Ball System

This paper explains the design of Servo State Feedback Controller and Feedback Linearization for Magnetic Levitation Ball System (MLBS). The system uses feedback linearization to change the nonlinear model of magnetic levitation ball system to the linear system. Servo state feedback controller controls the position of the ball. An integrator eliminates the steady state error in servo state feedback controller. The parameter of integral gain and state feedback gains is achieved from the concept of Coefficient Diagram Method (CDM). The CDM requires the controllable canonical form, because of that Matrix Transformation is needed. Hence, feedback linearization is applied first to the MLBS then converted to a controllable form by a transformation matrix. The simulation shows the system can follow the desired position and robust from the position disturbance. The uncertainty parameter of mass, inductance, and resistance of MLBS also being investigated in the simulation. Comparing CDM with another method such as Linear Quadratic Regulator (LQR) and Pole Placement, CDM can give better response, that is no overshoot but a quite fast response. The main advantage of CDM is it has a standard parameter to obtain controller’s parameter hence it can avoid trial and error.

Adaptive TOPSIS fuzzy CMAC back-stepping control system design for nonlinear systems

This paper aims to propose a more efficient control algorithm for nonlinear systems. A novel adaptive Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) fuzzy cerebellar model articulation controller (FCMAC) back-stepping control system is developed. The proposed adaptive TOPSIS FCMAC (ATFCMAC) incorporates a multi-criteria decision analysis with a fuzzy CMAC structure to determine the optimal threshold values for selecting suitable firing nodes, improving the computational efficiency, reducing the number of firing rules, and achieving good performance for nonlinear systems. A back-stepping technique is employed for the control system design. The proposed control system comprises an ATFCMAC and a robust compensator; the ATFCMAC is used to approximate an ideal controller and the robust compensator is used to reduce the influence of residual approximation error between the ideal controller and the ATFCMAC. The parameters of the proposed ATFCMAC are tuned online using the adaptation laws that are derived from a Lyapunov stability theorem, so that the stability of the control system is guaranteed. The simulation and experimental results for a Duffing–Holmes chaotic system and a magnetic ball levitation system are used to verify the effectiveness of the proposed control scheme.

Fuzzy PID Control of the Magnetic Levitation Ball System

The magnetic levitation ball system has nonlinear and open loop instability. The traditional PID control system has good stability. But when the system is disturbed by the outside factor, the control performance of the system is limited because of the fixed PID parameters. In this paper, a fuzzy PID controller which could adjust the PID parameters on-line to enhance the robustness of the system was designed. The experimental study was carried out on the dSPACE platform. The experimental results show that the proposed control strategy exhibits better control character than that of the traditional PID control. The fuzzy PID control can reduce the overshoot of the system and has better anti-interference capability.

Robust output tracking of a class of non-affine systems

ABSTRACTThis paper considers the robust output tracking problem for a class of uncertain non-affine systems. The state-space equations of these systems have a non-affine quadratic polynomial structure. In order to design the output tracking controller, first the error dynamical equations are constructed. Then, a novel sliding mode controller is designed for robust stabilization of the error dynamical equations. For this purpose, a proper sliding manifold which is a function of error vector is suggested. According to upper and lower bounds of uncertainties, two quadratic polynomials are built and with respect to the location of the roots of the given polynomials, the new sliding mode control law is obtained. The proposed controller can conquer the uncertainties and guarantees the asymptotic convergence of the system output toward the wanted time-varying reference signal. Finally, in order to verify the theoretical results, the proposed method is applied to the magnetic ball levitation system. Computer simulations demonstrate the efficiency of the proposed method.

Enhanced Proportional Integral Derivative control strategy for Magnetic Ball Levitation System

Enhanced Proportional Integral Derivative control strategy for Magnetic Ball Levitation System

Adaptive Intelligent Inverse Control Of Nonlinear Systems With Regard To Sensor Noise And Parameter Uncertainty (Magnetic Ball Levitation System Case Study)

Abstract Type-2 Fuzzy Neural Networks have tremendous capability in identification and control of nonlinear, time-varying and uncertain systems. In this paper the procedure of designing inverse adaptive type-2 fuzzy neural controller for online control of nonlinear dynamical systems will be presented. At first the structure of a novel class of Interval Type-2 Nonlinear Takagi-Sugeno-Keng Fuzzy Neural Networks (IT2-NTSK-FNN) will be presented. There is a class of nonlinear function of inputs in the consequent part of fuzzy rules. This IT2-NTSK-FNN comprises seven layers and the fuzzification is done in two first layers including type-2 fuzzy neurons with uncertainties in the mean of Gaussian membership functions. Third layer is rule layer and model reduction occurs in fourth layer via adaptive nodes. Fifth, sixth and seventh layers are consequent layer, centroid rules’ calculation layer and output layer respectively. For training the network backpropagation (steepest descend) method with adaptive training rate is used. Finally, three methods including online adaptive inverse controller based on IT2-NTSK-FNN, IT2-TSK-FNN (linear consequent part) and Adaptive Neuro-Fuzzy Inference System (ANFIS) are employed to control of a magnetic ball levitation system. External disturbances and uncertainty in parameters are considered in the model of magnetic ball levitation system. Simulation results show the efficacy of the proposed method

A Nonlinear Neural Controller Design for the Single Axis Magnetic Ball Levitation System Based on Slice Genetic Algorithm

This paper presents a ball position tracking control tuning algorithm for single axis magnetic levitation system using slice genetic optimization technique based nonlinear neural controller. As simple and fast tuning technique, slice genetic optimization algorithm is used to tune the nonlinear neural controller's parameters in order to get the best control action for the magnetic levitation system through the tracking of pre-defined location of the steel ball. Pollywog wavelet activation function is used in the structure of the nonlinear neural controller. The obtained results (using MATLAB program) show that the effectiveness of the proposed controller in minimizing the tracking error to zero value and also, in the softness of the control action with the lowest amount of fitness evaluation number.