The Robust Control of Magnetic Bearings for Rotating Machinery

The fast progress in the applications of active magnetic suspension systems needs to apply the modern control theory. This paper deals with H∞ and H2 control of rigid rotor movement, which is supported in magnetic bearings. The robust control of magnetic bearings is investigated analytically. The nominal model of active magnetic suspension of rotor and the uncertainty model were derived. The standard PID control and robust control are compared and performance of nominal feedback configuration with weights is presented. We propose a robust control with a multi-objective controller to achieve good robust stability when the model of a plant is uncertain. The behavior of multiplicative uncertainty of magnetic suspension system is shown. The aim of optimal robust control is to improve the magnetic suspension taking into account the energy limitation (i.e., to avoid the saturation of actuators). The H2 performance and H∞ performance depend on a proper selection of weighting functions. So a very important step in the controller design process is to choose the appropriate weight functions: We, Wu, Wd. The influence of noise is limited by weight functions. We also put limits on input and output signals. The stability of a system with disturbance interaction is discussed. The simulations of a well-posed and internally stable magnetic system are presented. The success of the robust control is demonstrated through results of numerical simulations.

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Robust vibration control of flexible panel: modeling and simulation

World Journal of Engineering ◽

10.1108/wje-10-2016-0102 ◽

2017 ◽

Vol 14 (5) ◽

pp. 433-442

Author(s):

Aalya Banu ◽

Asan G.A. Muthalif

Keyword(s):

Robust Control ◽

Vibration Control ◽

Controller Design ◽

Control Strategies ◽

Active Vibration Control ◽

Flexible Structures ◽

Parametric Uncertainty ◽

Design Algorithm ◽

Content Type ◽

And Performance

Purpose This paper aims to develop a robust controller to control vibration of a thin plate attached with two piezoelectric patches in the presence of uncertainties in the mass of the plate. The main goal of this study is to tackle dynamic perturbation that could lead to modelling error in flexible structures. The controller is designed to suppress first and second modal vibrations. Design/methodology/approach Out of various robust control strategies, μ-synthesis controller design algorithm has been used for active vibration control of a simply supported thin place excited and actuated using two piezoelectric patches. Parametric uncertainty in the system is taken into account so that the robust system will be achieved by maximizing the complex stability radius of the closed-loop system. Effectiveness of the designed controller is validated through robust stability and performance analysis. Findings Results obtained from numerical simulation indicate that implementation of the designed controller can effectively suppress the vibration of the system at the first and second modal frequencies by 98.5 and 88.4 per cent, respectively, despite the presence of structural uncertainties. The designed controller has also shown satisfactory results in terms of robustness and performance. Originality/value Although vibration control in designing any structural system has been an active topic for decades, Ordinary fixed controllers designed based on nominal parameters do not take into account the uncertainties present in and around the system and hence lose their effectiveness when subjected to uncertainties. This paper fulfills an identified need to design a robust control system that accommodates uncertainties.

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An adaptive robust control scheme for robot manipulators with unknown backlash nonlinearity in gears

Transactions of the Institute of Measurement and Control ◽

10.1177/0142331218810773 ◽

2018 ◽

Vol 41 (10) ◽

pp. 2789-2802 ◽

Cited By ~ 4

Author(s):

Soheil Ahangarian Abhari ◽

Farzad Hashemzadeh ◽

Mahdi Baradarannia ◽

Hamed Kharrati

Keyword(s):

Robust Control ◽

Controller Design ◽

Robot Manipulators ◽

Dead Zone ◽

Main Idea ◽

Adaptive Robust Control ◽

Zone Model ◽

Robot Trajectory ◽

Zone Parameter ◽

The Stability

This paper presents an adaptive robust control algorithm for the nonlinear dynamics of robot manipulators with unknown backlash in gears. The basic nonlinear model of a serial manipulator robot is used for the controller design, and this is combined with the nonlinear proposed dead zone model, based on the input and output torque. The main idea of providing this model is to achieve a dynamic model of the system considering the backlash of the robot joint gears, and having less complexity such that the developed controller does not need the inverse backlash model. The adaptive robust controller is developed, without using the inverse backlash model. The proposed controller is designed based on an unknown dead zone parameter and it guarantees the stability and path tracking of the robot trajectory with unknown dead zone parameter in the desired range. Numerical simulations are conducted to show the effectiveness of the proposed controller. Finally, the efficiency and capability of the proposed controller in dealing with the unknown backlash nonlinearities in gears of the manipulator are demonstrated by experimental results with a five-bar manipulator.

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The Robust Control of Magnetic Suspension with Rapidly Changing of Rotor Speed

Solid State Phenomena ◽

10.4028/www.scientific.net/ssp.147-149.302 ◽

2009 ◽

Vol 147-149 ◽

pp. 302-307 ◽

Cited By ~ 1

Author(s):

Arkadiusz Mystkowski ◽

Zdzisław Gosiewski

Keyword(s):

Control System ◽

Robust Control ◽

High Speed ◽

Controller Design ◽

Angular Speed ◽

Magnetic Bearing ◽

Magnetic Suspension ◽

Experimental Results ◽

Active Magnetic Bearing ◽

Robust Controller

An optimal robust vibration control of a rotor supported magnetically over a wide angular speed range is presented in the paper. The laboratory stand with the high speed rotor (max. 24000 rpm) was designed. The wide bandwidth controller with required gain, which is necessary to stabilize the structurally unstable and active magnetic bearing system was computed. For controller design, the weighting functions putted on the input and output signals were chosen. For control design, the dynamics of the rotor and uncertain parameters were considered. The optimized control system by minimization of the H norm putted on transient process of the system was presented. The robust controller was designed with considered asymmetrically magnetic bearings, signal limits and power amplifiers dynamic. The success of the robust control is demonstrated through computer simulations and experimental results. Matlab-Simulink was used for the numerical simulation. The experimental results show the effectiveness of the control system as good vibrations reducing and robustness of the designed controller in all dynamic states.

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LQG-Based Robustifying Flight Control System

Dynamic Systems and Control, Volumes 1 and 2 ◽

10.1115/imece2003-43596 ◽

2003 ◽

Author(s):

D. Griffin ◽

A. G. Kelkar

Keyword(s):

Control System ◽

Flight Control ◽

Controller Design ◽

Second Step ◽

Flight Control System ◽

Robust Controller ◽

Fighter Aircraft ◽

Stability Robustness ◽

Uncertainty Model ◽

The Stability

This paper presents a robust controller design for an automatic flight control system (AFCS) for a fighter aircraft model with eight inputs and seven outputs. The controller is designed based on McFarlane-Glover robustifying technique using a simple baseline LQG design. Controllers designed purely based on traditional LQG techniques are known to have no guaranteed robustness margins. The McFarlane-Glover technique can be used to enhance the stability robustness of the baseline LQG design using a two-step design process. In the first step, an LQG controller is designed which is optimized only for performance without any consideration to robustness. In the second step, the performance optimized LQG design is rendered robust using McFarlane-Glover procedure. The robustifying procedure uses a coprime factor uncertainty model and H∞ optimization. An important advantage of this procedure is that no problem dependent uncertainty modelling or weight selection is required in the second step of the process. The robustifying procedure also yields the quantitative estimate of the robustness.

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Vibration Control of a Turbo Molecular Pump Suspended by Active Magnetic Bearings

Volume 3: Controls, Diagnostics and Instrumentation; Education; Electric Power; Microturbines and Small Turbomachinery; Solar Brayton and Rankine Cycle ◽

10.1115/gt2011-45785 ◽

2011 ◽

Cited By ~ 3

Author(s):

Kai Zhang ◽

Jinping Dong ◽

Xingjian Dai ◽

Xiaozhang Zhang

Keyword(s):

Controller Design ◽

Magnetic Bearings ◽

Control Algorithms ◽

Active Magnetic Bearings ◽

Bending Mode ◽

High Rotation Speed ◽

Structure Vibration ◽

The Stability ◽

Bending Modes ◽

Gyroscopic Effects

In a turbo molecular pump suspended by active magnetic bearings (AMBs), vibration caused by the rotor’s bending modes, gyroscopic effects and structure vibration modes influenced the pump performance and even cause instability. Different methods were used to deal with these problems. A Cross Feedback method was effective in restraining the nutation and precession of the rotor. A Phase Shaping method provided sufficient damping for the 1st bending mode of the rotor. The structure vibration instability was avoided by adjusting the joint strength between two parts of the pump housing. The gyroscopic effects also destroyed the stability of unbalance control algorithms for the AMBs at a high rotation speed. It was shown that, to ensure the stability of the controller when the unbalance control algorithms were applied, the 1st bending frequency of the rotor should be increased. Experiment results concerning the problems discussed above were provided. With a suitable controller design and an appropriate consideration of the dynamic problems, the rotor was successfully accelerated to 27 000 rpm.

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Vibration and Control of a Flexible Rotor in Magnetic Bearings Using Hybrid Method and H∞ Control Theory

Volume 5: Manufacturing Materials and Metallurgy; Ceramics; Structures and Dynamics; Controls, Diagnostics and Instrumentation; Education; General ◽

10.1115/94-gt-057 ◽

1994 ◽

Author(s):

Ting Nung Shiau ◽

Geeng Jen Sheu ◽

Clann Dong Yang

Keyword(s):

Control Theory ◽

Hybrid Method ◽

Controller Design ◽

Control Design ◽

Expansion Method ◽

Rotor System ◽

Magnetic Bearings ◽

Experimental Simulation ◽

Flexible Rotor ◽

H2 Control

The vibration and active control of a flexible rotor system with magnetic bearings is investigated using Hybrid Method (HM) and H∞ control theory with consideration of gyroscopic effect. The hybrid method which combines the merits of finite element method (FEM) and generalized ploynomial expansion method (GPEM) is employed to model the flexible rotor system with small order of plant. The mixed sensitivity problem of H∞ control theory is applied to design the control of system vibration with spillover phenomena for the reduced order plant. The H2 control design is also employed for the comparison to the H∞ design. The experimental simulation is used to illustrate the effects of control design. It is shown that the H∞ controller design can be very effective to suppress spillover phenomena. In addition, HM control design has robustness to the variation of the parameters of the model. The application of hybrid method (HM) together with H∞ control design is highly recommended for the vibration control of flexible rotor system with magnetic bearings.

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Nonlinear Robust Control of Vehicle Lateral Dynamics Considering Driver’s Dynamics

Volume 12: Transportation Systems ◽

10.1115/imece2014-39311 ◽

2014 ◽

Author(s):

Saeid Khosravani ◽

Iman Fadakar ◽

Amir Khajepour ◽

Baris Fidan ◽

Bakhtiar Litkouhi ◽

...

Keyword(s):

Robust Control ◽

Controller Design ◽

Control Level ◽

Stability Margin ◽

Nonlinear Damping ◽

Change Scenario ◽

Loop Control ◽

Yaw Rate ◽

The Stability ◽

Bounded Uncertainties

Guaranteeing stability of a vehicle without considering the driver in the control loop is difficult. In this paper, a driver-in-the-loop control strategy is proposed to improve the lateral vehicle behavior and extend the stability margin. The driver is modeled as a delayed linear controller with the aim of tracking the desired path. The main aim of the controller design is to track the desired yaw rate of the vehicle considering the driver effects. To make an implementable approach, it is assumed that the desired road information and the exact values of longitudinal and lateral forces are not available for the control level and the controller treats them as bounded uncertainties. The nonlinear damping technique is adopted to stabilize the yaw rate error. For two different robust designs, we have shown that the yaw rate error will confine inside a certain neighborhood even in the presence of uncertainty. The size of this neighborhood is directly proportionate to the gain of the robust control terms and the driver characteristics. A standard harsh double lane change scenario is simulated as the desired path for the driver. The results demonstrate that the design process improves the overall behavior of the driver-vehicle system in the presence of bounded uncertainties.

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Adaptive Robust Control for Driving and Regenerative Braking of Electric Vehicle

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.441.887 ◽

2013 ◽

Vol 441 ◽

pp. 887-891

Author(s):

Long Xu ◽

Jun Ping Wang ◽

Yuan Bai ◽

Gai Ling Hu

Keyword(s):

Robust Control ◽

Electric Vehicle ◽

Adaptive Robust Control ◽

Disturbance Attenuation ◽

Regenerative Braking ◽

Stability Robustness ◽

Recovery System ◽

And Performance ◽

The Stability ◽

Braking Energy Recovery

The driving and braking energy recovery system of electric vehicle faces a lot of uncertainties, including the system parameters and the running environment uncertainties. An adaptive robust control (ARC) is presented in this paper to treat the problems including disturbance and parameter variation in the design of driving and regenerative braking controller. It can enhance the stability robustness and performance robustness. A model of the driving and regenerative braking system is constructed and then the ARC controller is designed. The experiment results show that the controller based on ARC theory has better performance of stability, robustness, and disturbance attenuation than traditional PID controller.

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Tracking Control of Robot Manipulator Using Sliding Mode Controller With Performance Robustness

Journal of Dynamic Systems Measurement and Control ◽

10.1115/1.2802443 ◽

1999 ◽

Vol 121 (1) ◽

pp. 64-70 ◽

Cited By ~ 20

Author(s):

Chieh-Li Chen ◽

Rui-Lin Xu

Keyword(s):

Tracking Control ◽

Feedback Linearization ◽

Controller Design ◽

Sliding Mode ◽

Robot Manipulator ◽

Design Procedure ◽

Sliding Mode Controller ◽

Systematic Design ◽

And Performance ◽

The Stability

The tracking control problem of robot manipulator is considered in this paper. A sliding mode controller design with global invariance is proposed using the concept of extended system and feedback linearization. The sliding surface is assigned such that the sliding mode motion will occur while the proposed control law is applied. This results in a system with global invariance. The stability and performance of the resulting system can be guaranteed by the proposed systematic design procedure.

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