Nonlinear Feedback Control of the Inductrack System Based on a Transient Model

2021 ◽  
Author(s):  
Ruiyang Wang ◽  
Bingen (Ben) Yang ◽  
Hao Gao
Keyword(s):  
Feedback Control ◽  
Permanent Magnets ◽  
Control Method ◽  
Control Law ◽  
Operating Speed ◽  
Nonlinear Feedback ◽  
Transient Model ◽  
Mechanical Coupling ◽  
Wide Range ◽  
Halbach Arrays

Abstract As a new strategy for magnetic levitation envisioned in the 1990s, the Inductrack system with Halbach arrays of permanent magnets has been intensively researched. The previous investigations discovered that an uncontrolled Inductrack system may be unstable even if the vehicle travels well below its operating speed and that instability can be persistent near and beyond the operating speed. It is therefore necessary to stabilize the system for safety and reliability. With strong nonlinearities and complicated electro-magneto-mechanical coupling, however, the transient response of such a dynamic system is difficult to predict with fidelity. Because of this, model-based feedback control of Inductrack systems has not been well addressed. In this paper, by taking advantage of a recently available 2-DOF transient model, a new feedback control method for Inductrack systems is proposed. In the control system development, active Halbach arrays are used as an actuator, and a feedback control law, which combines a properly tuned PID controller and a nonlinear force-current mapping function, is created. The proposed control law is validated in numerical examples, where the transient motion of an Inductrack vehicle traveling at constant speed is considered. As shown in the simulation, the control law efficiently stabilizes the Inductrack system in a wide range of the operating speed, and in the meantime, it renders a smooth system output (real-time levitation gap) with fast convergence to any prescribed reference input (desired levitation gap).

Transient Vibration and Feedback Control of an Inductrack Maglev System

2020 ◽  
Author(s):  
Ruiyang Wang ◽  
Bingen Yang ◽  
Hao Gao
Keyword(s):  
Steady State ◽  
Feedback Control ◽  
Dynamic System ◽  
Permanent Magnets ◽  
Preliminary Investigation ◽  
Lookup Table ◽  
Lumped Mass ◽  
Transient Vibration ◽  
Transient Model ◽  
Halbach Arrays

Abstract As a new strategy for magnetic levitation envisioned in 1990s, the Inductrack system with permanent magnets (PMs) aligned in Halbach arrays has been intensively studied and applied in many projects. Due to the nonlinear, time-varying electro-magneto-mechanical coupling in such a system, the dynamic behaviors are complicated with transient responses, which in most cases can hardly be predicted with fidelity by a steady-state Inductrack model. Presented in this paper is a benchmark 2-DOF transient Inductrack model, which is derived from the first laws of nature, without any assumed steady-state quantities. It is shown that the dynamic response of the Inductrack dynamic system is governed by a set of nonlinear integro-differential equations. As demonstrated in numerical simulations with the transient model, unstable vibrations in the levitation direction occur when the traveling speed of the vehicle exceeds a threshold. To resolve this instability issue, feedback control is implemented in the Inductrack system. In the development, an assembly of Halbach arrays and active coils that are wound on the PMs is proposed to achieve a controllable source magnetic field. In this preliminary investigation, the proposed control system design process takes two main steps. First, a PID controller is set and tuned based on a simple lumped-mass dynamic system. Second, the nonlinear force-current correlation is obtained from a lookup table that is pre-calculated by steady-state truncation of the full transient Inductrack model. With the implemented feedback control algorithms, numerical examples display that the motion of the vehicle in levitation direction can be effectively stabilized at different traveling speeds. Although only a 2-DOF transient model is used here, the modeling technique and the controller design approach developed in this work are potentially applicable to more complicated models of Inductrack Maglev systems.

Semi-global output regulation for discrete-time singular linear systems with input saturation via composite nonlinear feedback control

2016 ◽  
Vol 39 (3) ◽  
pp. 352-360 ◽  
Author(s):  
Xiaoyan Lin ◽  
Dongyun Lin ◽  
Weiyao Lan
Keyword(s):  
Feedback Control ◽  
Linear Systems ◽  
Discrete Time ◽  
Input Saturation ◽  
Output Regulation ◽  
Control Law ◽  
Nonlinear Feedback Control ◽  
Nonlinear Feedback ◽  
Composite Nonlinear Feedback ◽  
Singular Linear Systems

The semi-global output regulation problem of multi-variable discrete-time singular linear systems with input saturation is investigated in this paper. A composite nonlinear feedback control law is constructed by using a low gain feedback technique for semi-global stabilisation of discrete-time singular linear systems with input saturation. The sufficient solvability conditions of the semi-global output regulation problem by composite nonlinear feedback control are established. When the composite nonlinear feedback control law is reduced to a linear control law, the solvability conditions are an exact discrete-time counterpart of the semi-global output regulation problem of continuous-time singular linear systems. With the extra control freedom of the nonlinear part in the composite nonlinear feedback control law, the transient performance of the closed-loop system can be improved by carefully choosing the linear feedback gain and the nonlinear feedback gain. The design procedure of the composite nonlinear feedback control law and the improvement of the transient performance are illustrated by a numerical example.

CONTROLLING UNCERTAIN VAN DER POL OSCILLATOR VIA ROBUST NONLINEAR FEEDBACK CONTROL

2004 ◽  
Vol 14 (05) ◽  
pp. 1671-1681 ◽  
Author(s):  
MAO-YIN CHEN ◽  
ZHENG-ZHI HAN ◽  
YUN SHANG ◽  
GUANG-DENG ZONG
Keyword(s):  
Feedback Control ◽  
Control Method ◽  
Reference Signal ◽  
Variable Structure ◽  
Van Der Pol Oscillator ◽  
Nonlinear Feedback Control ◽  
Nonlinear Feedback ◽  
Van Der Pol ◽  
Feedback Control Method ◽  
System Uncertainties

Combining the backstepping design and the variable structure control, we propose a robust nonlinear feedback control method to control an uncertain van der Pol oscillator even if there exist system uncertainties and external disturbances in this oscillator. If system uncertainties are estimated and some parameters are chosen suitably, the output of van der Pol osicllator can track arbitrary smooth reference signal. Theoretical analysis and numerical simulations verify the effectiveness of this method.

scholarly journals Wireless Temperature Sensing Using Permanent Magnets for Nonlinear Feedback Control of Exothermic Polymers

2018 ◽  
Vol 18 (19) ◽  
pp. 7970-7979
Author(s):  
Anirban Mazumdar ◽  
Yi Chen ◽  
Bart G. Van Bloemen Waanders ◽  
Carlton F. Brooks ◽  
Michael A. Kuehl ◽  
...  
Keyword(s):  
Feedback Control ◽  
Permanent Magnets ◽  
Temperature Sensing ◽  
Nonlinear Feedback Control ◽  
Nonlinear Feedback

Compound control for autonomous docking to a three-axis tumbling target

2018 ◽  
Vol 41 (4) ◽  
pp. 911-924
Author(s):  
Dong Ye ◽  
Wei Lu ◽  
Zhongcheng Mu
Keyword(s):  
Feedback Control ◽  
Attitude Control ◽  
Sliding Mode ◽  
Control Law ◽  
Nonlinear Feedback Control ◽  
Nonlinear Feedback ◽  
Integral Sliding Mode ◽  
Compound Control ◽  
Tumbling Target ◽  
Autonomous Docking

This paper investigates the coupled position and attitude control problem of an on-orbit servicing spacecraft autonomous docking to a three-axis freely tumbling target in space. A compound control law is presented to guarantee that the docking port of servicing spacecraft is always directing towards the docking port of tumbling target, which is accomplished through the combination of the coupled relative position tracking and relative attitude control. For the purpose of avoiding collision between the two spacecraft, a two-phased approach for the terminal approaching the tumbling target is proposed. Also, the compound control is composed of a nonlinear feedback control law and an integral sliding mode control law. The nonlinear feedback control law is mainly used to track the system command and the integral sliding mode control law is mainly used to deal with the external disturbances and system uncertainties to enhance the robustness of the control system. Furthermore, the control saturation problem is considered. In addition, the characteristic of integral sliding mode under the control constraint and measurement noise is also analyzed. Finally, several numerical simulations are performed to verify the effectiveness and robustness of the compound control law for autonomous docking to a three-axis freely tumbling target.

Nonlinear Control of a Transient Inductrack System Using State Feedback

2021 ◽  
Author(s):  
Ruiyang Wang ◽  
Bingen Yang
Keyword(s):  
Feedback Control ◽  
Nonlinear Control ◽  
Dynamic Modeling ◽  
State Feedback ◽  
Permanent Magnets ◽  
Control Method ◽  
Linear Part ◽  
Control Design ◽  
Nonlinear Part ◽  
Highly Nonlinear

Abstract The concept of Inductrack refers to the magnetic levitation technology achieved by Halbach arrays of permanent magnets. In an Inductrack system, the dynamic behaviors involved with transient responses are difficult to capture due to the highly nonlinear, time-varying, electromagnetic-mechanical couplings. In the literature, dynamic modeling of Inductrack systems that aims to analyze the transient behaviors has been widely addressed. However, one common issue with the previous investigations is that most of the dynamic models either partly or completely adopted certain steady-state and ideal case assumptions. These assumptions are extremely difficult to maintain in a transient scenario, if not impossible. Therefore, while providing good understanding of Inductrack systems, the previous results in dynamic modeling have a limited utility in providing guidance for feedback control of Inductrack systems. Recently, a benchmark transient Inductrack model was created for characterizing the transient time response of the system with fidelity, which enables model-based feedback control design. In this work, based on the transient model, a new control method for the Inductrack dynamic system is developed. The proposed control method consists of a linear part and a nonlinear part. The linear part is devised based on a state feedback configuration; the nonlinear part is accomplished by fitting a nonlinear “force-current” mapping function. With this nonlinear feedback controller, the levitation gap of the Inductrack vehicle can be effectively stabilized at both constant and time-dependent traveling speed. The proposed control law is demonstrated in numerical examples. The nonlinear control design is potentially extensible to more complicated Inductrack systems with higher degrees of freedom.

Continuous time-varying feedback control of a robotic manipulator with base vibration and load uncertainty

2020 ◽  
pp. 107754632092759
Author(s):  
Xi Wang ◽  
Baolin Hou
Keyword(s):  
Feedback Control ◽  
Lyapunov Function ◽  
Continuous Time ◽  
Position Control ◽  
Control Method ◽  
Robotic Manipulator ◽  
Control Law ◽  
Time Varying ◽  
Load Uncertainty ◽  
Feedback Control Method

To solve precise and fast position control of a robotic manipulator with base vibration and load uncertainty, a continuous time-varying feedback control method based on the implicit Lyapunov function is studied. This method is proportional–derivative-like in the form of control law, but its proportional and differential coefficients depend on the system Lyapunov function, which are differentiable functions of system error variables. In the motion process of the robotic manipulator, the system performance is influenced by three main nonlinear factors: system friction, balance torque, and base vibration. As the former two factors are available to be modeled and identified through experiments, compensation of the two terms is added to the proposed control law to reduce the effects of system nonlinearities to a certain extent. Experimental results show that the proposed control strategy is robust to base vibration and load uncertainty. Besides, the compensation of system friction and balance torque can shorten the positioning time by 27.3%, from 1.32 s to 0.96 s. Meanwhile, the positioning precision is guaranteed, which verifies the effectiveness of the proposed control scheme.

Compound Control of Attitude Synchronization for Autonomous Docking to a Tumbling Satellite

2013 ◽  
Vol 394 ◽  
pp. 470-476 ◽  
Author(s):  
Xue Yan An ◽  
Wei Lu ◽  
Zhang Ren
Keyword(s):  
Feedback Control ◽  
Control Law ◽  
Nonlinear Feedback Control ◽  
Nonlinear Feedback ◽  
External Disturbances ◽  
Compound Control ◽  
Bounded Disturbances ◽  
System Uncertainties ◽  
Attitude Synchronization ◽  
Autonomous Docking

In order to solve the attitude synchronization control problem for an on-orbit servicing spacecraft autonomous docking to a tumbling satellite in the presence of unknown bounded disturbances and system uncertainties, a compound control law is presented in this paper. The compound control law is composed of a nonlinear feedback control law and a compensate control law. The nonlinear feedback control law is mainly used to track the system command and the compensate control law is mainly used to deal with the external disturbances and system uncertainties to enhance the robustness of the control system. Simulation results verified the effectiveness of the designed compound control law, and the robustness to the unknown bounded disturbances, system uncertainties is also demonstrated.

Active Compressor Surge Control Using Piston Actuation

2011 ◽  
Author(s):  
Nur Uddin ◽  
Jan Tommy Gravdahl
Keyword(s):  
Feedback Control ◽  
Closed Loop ◽  
Linear Feedback ◽  
Control Law ◽  
Asymptotically Stable ◽  
Nonlinear Feedback Control ◽  
Nonlinear Feedback ◽  
Closed Loop System ◽  
Linear Feedback Control ◽  
Surge Control

A novel approach to active surge control in compressors using piston actuation is presented. Two control laws are compared in order to evaluate the feasibility of implementing the concept. The first control law is a nonlinear feedback control derived by using backstepping and the second one is a linear feedback control derived by analyzing the eigenvalues of the linearized system around the operating point. The nonlinear feedback control law makes the closed loop system globally asymptotically stable (GAS) and uses full states feedback. The linear feedback control is only using feedback from plenum pressure and piston velocity and the removal of the mass flow feedback is advantageous for implementation. The closed loop system with the linear feedback control is locally asymptotically stable around the operating point. Simulations show that both controllers are capable of stabilizing surge.

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