Abdelfatah M. Mohamed

Imbalance compensation and automation balancing in magnetic bearing systems using the Q-parameterization theory

The problem caused by imbalance in rotating machinery can be solved using actively controlled magnetic bearing systems. There are two methods to solve this problem using feedback control: 1) compensate for the imbalance forces by generating opposing forces on the bearing surface; and 2) make the rotor rotate around its axis of inertia so no imbalance forces will be generated. The dynamics of the magnetic bearing are described in state-space form using airgap displacement, velocity, and airgap flux as state variables. The system which is unstable in nature is stabilized using the Q-parameterization theory. To compensate for the imbalance disturbance forces, the controller Q-parameter is chosen such that rejection of sinusoidal disturbances is achieved. To achieve automatic balancing, the imbalance is assumed as a sinusoidal noise in the measured signal, and the controller Q-parameter is chosen such that rejection of sinusoidal noise is achieved. Simulation results are presented and show the robustness of the proposed controllers and that the rejection of sinusoidal disturbances is achieved. The rotation of the rotor around its axis of inertia is also achieved. >

Variable structure control of a magnetic levitation system

Presents a variable structure control (VSC) design procedure for robust stabilization and disturbance rejection of a magnetic levitation system. The procedure is based on a method called the reaching law method complemented by a sliding mode equivalence technique. First, the basics of variable structure control system design are reviewed with emphasis on the reaching law method. Second, the dynamics of the magnetic levitation system are described in terms of airgap deviation, airgap flux and the electromagnet voltage. Third, in order to use the VSC to control the airgap deviation using the electromagnet voltage, system dynamics are developed to make the electromagnet input voltage the forced term of the dynamic equation of the airgap deviation. Then the system is described in state variable form and a VS controller is designed for this system using the reaching law method. Finally several simulation results are presented. The results showed that robust stability against parameter variations and disturbance rejection (for any class of disturbance) are achieved using the proposed VS controller.

Modeling and robust control of self-sensing magnetic bearings with unbalance compensation

This paper presents a complete model of four radial DOF self-sensing magnetic bearing systems which includes all interactions between the different degrees of freedom. A method for controlling self-sensing magnetic bearings with unbalance compensation is also presented. The method uses the Q-parameterisation theory. The Q-parameterization controller is an observer-based stabilizing controller with a free parameter Q, which makes it suitable for robust control of self-sensing magnetic bearings. The free parameter and can be chosen through optimization to achieve robustness, noise minimization and to compensate for the unbalance forces. We give a complete four radial DOF mathematical model of the self-sensing magnetic bearing in state space form. We explain the Q-parameterisation controller design of the self-sensing magnetic bearing. Unbalance compensation is achieved by airgap regulation, current regulation and force regulation (automatic balancing), by a suitable choice of Q. The control problem is formulated as an optimization problem in the free parameter and whose constraints are sensor noise, actuator noise and unbalance sinusoidal disturbance rejection. The obtained controllers have 24 states for the current and airgap regulation designs and 20 states for the force regulation design. Finally, several simulations were obtained to evaluate the proposed controller. The results obtained showed that both robust stability and unbalance compensation are achieved.

Q-parameterization control of vibrations in a variable speed magnetic bearing

We propose a controller design methodology using the Q-parameterization theory for a variable speed magnetic bearing in order to achieve elimination of unbalance vibrations. Rotor unbalance usually generates sinusoidal disturbance forces, with frequency equal to the rotational speed. So in order to achieve asymptotic rejection of these disturbance forces, the Q-parameterization controller free parameter Q is chosen such that the controller has j/spl omega/ axis poles at the different speeds of rotation. First, we give a mathematical model for the magnetic bearing in state space form. Second, we explain the proposed Q-parameterization controller design methodology. The controller free parameter Q is assumed to be a proper stable transfer function whose order equals twice the number of operating speeds. Third, we showed that the controller free parameter which satisfies the design objectives can be obtained by simply solving a set of linear equations rather than solving a complicated optimization problem. We also showed that the controller order equals: number of degrees of freedom/spl times/(order of Q+3). Finally, several simulations were obtained to evaluate the proposed controller. The results obtained showed the effectiveness of the proposed controller in eliminating the unbalance vibrations at the different speeds.

Imbalance compensation and automatic balancing in magnetic bearing systems using the Q-parameterization theory

Rotor imbalance leads to sinusoidal disturbance forces which cause undesirable vibration. The problem is addressed using actively controlled magnetic bearing systems. First, the dynamics of the magnetic bearing are described in state space form using airgap displacement. Velocity and airgap flux as state variables. Second, the system, which is unstable in nature, is stabilized using the Q-parameterization theory. In order to compensate for the imbalance disturbance forces, the controller Q-parameter is chosen such that rejection of sinusoidal disturbances is achieved. In order to achieve automatic balancing, the imbalance is assumed as a sinusoidal noise in the measured signal, and the controller 4-parameter is chosen such that rejection of sinusoidal noise is achieved. In both cases the frequency of the sinusoidal disturbance/noise is assumed to be equal to the rotational speed. Simulation results are presented and show the robustness of the proposed controllers and that the rejection of sinusoidal disturbances is achieved. Also rotation of tile rotor around its axis of inertia is achieved.

Elimination of imbalance vibrations in magnetic bearing systems using discrete-time gain-scheduled Q-parametrization controllers

We propose a method to eliminate the imbalance vibrations in magnetic bearing systems using discrete-time gain-scheduled Q-parametrization controllers. Imbalance in rotating machines generates variable frequencies sinusoidal disturbance forces that cause the vibrations. Since the frequency of vibrations equals the rotational speed, the free parameter Q of the Q-parametrization controllers is scheduled as a function of the rotational speed to achieve rejection of the imbalance sinusoidal disturbance forces at all operating speeds. First, we present a mathematical model for the magnetic bearing in state space from which includes the effect of imbalance. Next, we explain the discrete-time Q-parametrization controller design for the magnetic bearing to achieve robust stability mid rejection of the variable frequencies sinusoidal disturbance forces. Finally, several simulation results are presented. The results showed that elimination of the imbalance vibrations are achieved at all operating speeds, and moreover robust stability is also achieved.

A Comparison between Current and Flux Control in Magnetic Bearing Systems

A comparison between current and flux control in magnetic bearing systems is made. The system dynamics were modeled in two different forms. In the first form, the magnetic force and electric circuit equations were expressed in terms of airgap flux and gap displacement. In the second form both equations were expressed in terms of coil current and gap displacement. A controller was designed using the Q-parameterization theory and CONSOLE [14] (an optimization software developed at the University of Maryland) to stabilize the system which without control is unstable in nature. The time and frequency responses for both models were compared. The comparison is based on the same values of the respective controller Q-parameters. The results show that magnetic bearing systems can have better performance if they are modeled using airgap flux.

Real-Time Implementation of a Robust H∞ Controller for a 2-DOF Magnetic Micro-Levitation Positioner

Robust H∞ optimal control theory has proven to be one of the best techniques in linear control system design. The achievable robust stability and performance are high, but the resulting controllers are very complex and difficult to implement. As a result, few practical implementations of H∞ control can be found in the literature. This paper presents a robust H∞ controller for a two-degree-of-freedom magnetic micro-levitation positioner and its real time experimental implementation. The experimental device used in this study is designed for use in semiconductor manufacturing and consists of two U-shaped electromagnets and a manipulator. First, we describe the system dynamics in state space form. Second, the system which is unstable in nature is stabilized using the H∞ synthesis. The H∞ control design problem is described and formulated in the standard form with emphasis on the selection of weighting transfer functions that reflect robustness and performance goals. The interactive computing environment MATLAB is used to calculate the controller. Third, the controller is implemented digitally using a digital signal processor with 16 bit A/D and 12 bit D/A converters. Finally, some simulation and experimental results are presented. The results obtained show that robust stability against model uncertainties is achieved and the performance goals are satisfied.

Q-parametrization//spl mu/-control of an electromagnetic suspension system

This paper presents a new controller design methodology for an electromagnetic suspension system using the Q-parametrization theory and /spl mu/-analysis, in order to achieve both robust stability and robust performance. The set of all stabilizing controllers of the plant is characterized by a free parameter Q. This free parameter is chosen through optimization such that both robust stability and robust performance are achieved. We describe the experimental setup and give a mathematical model for the electromagnetic suspension system (ESS) used in this research. We explain the Q-parametrization control with /spl mu/-analysis of a given plant, formulate the control problem as an optimization problem in the free parameter and with robust stability and nominal performance as constraints, and assess robust performance with /spl mu/. The proposed controller design methodology is applied to a simple SISO ESS employed in this research and a fifth order controller which achieves both robust stability and robust performance is obtained. Finally, several simulation and experimental results are presented.

Dynamic Analysis of a Parallel Manipulator-Based Multi-function Mobility Assistive Device for Elderly

Dynamic simulation of manipulators interacting directly with human is crucial for predicating their performance before the actual use. This paper describes the dynamic analysis and simulation of a novel multi-function mobility assistive device for elderly. The device is designed to help patients who suffer from degradation of the lower limbs muscular strength. Rather than one function device, the proposed device is intended to assist in different lower limb activities, namely, sit to stand and walking activities as well as transfer paralyzed patients from bed to wheelchair and help them stand in upright position to improve blood circulation. The device is based on a non-conventional structure of a 3-RPR planer parallel manipulator which has high rigidity due to the parallel structure. It has some interesting kinematic advantages that facilitate structure and control design. Dynamic model for the assistive manipulator is derived using the first type of Lagranges equations. A PD-computed torque controller is tuned using genetic algorithm. Simulation results prove high performance of the proposed device in terms of the low tracking error and the proper actuator force.