scholarly journals Design of a PID Controller for a Linearized Magnetic Bearing

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
Theodore K. Psonis ◽  
Pantelis G. Nikolakopoulos ◽  
Epaminondas Mitronikas
Keyword(s):  
Pid Controller ◽  
Closed Loop ◽  
Laboratory Data ◽  
Magnetic Bearing ◽  
Magnetic Bearings ◽  
Controller Performance ◽  
The Stability ◽  
Linearized Model ◽  
And Control ◽  
Linear Controllers

This paper presents the study of magnetic bearings regarding a linear model. Initially, the advantages of magnetic bearings are referenced, in relation to the existing technology. Subsequently, the linearized model of the system is presented and the need for closed loop and control of the system is clarified. This need leads to further analysis of linear controllers like P, I, D, PI, PD, and PID. For each of them, the stability of closed loop system is studied, using the characteristic equation of the system and the Routh-Hurwitz criterion. To this end, the boundary conditions for the existence of the stability of each of them are found and presented. After finding the controllers’ characteristic parameters which could provide stability to the system, simulation tests with existence of white noise follow. Finally, the proposed PID controller performance is examined, based on existing laboratory data, and results concerning the stability of this controller are presented.

On the Influence of Controller Parameters on the Performance of Rotating System With Magnetic Bearings

2013 ◽  
Author(s):  
Ying He ◽  
Zhe Sun ◽  
Jingjing Zhao ◽  
Zhengang Shi ◽  
Lei Shi ◽  
...  
Keyword(s):  
Pid Controller ◽  
Closed Loop ◽  
Magnetic Bearing ◽  
Design Criterion ◽  
Magnetic Bearings ◽  
Flexible Rotor ◽  
Quantitative Investigation ◽  
Rotating System ◽  
Locus Method ◽  
The Relationship

Rotating machineries, in High Temperature Gas-cooled Reactor (HTGR), are usually supported by magnetic bearings. In the paper, we provide a research on the relationship between the performance of machinery and the controller parameters. More specifically, this paper concentrates on the modified Proportion-Integral-Differential (PID) controller, which is characterized by five parameters: two poles, two zeros and the gain. The system performance is evaluated by the closed-loop poles. To perform quantitative investigation, a flexible-rotor-magnetic-bearing system model is established. Based on this model, the Bode plot and root locus method are applied to analyze the effect of controller’s parameters (locations of zeros and poles along with gain) on the closed-loop performance (stability, damping ratios of closed-loop poles). The results of this paper can offer some design criterion of such controllers and help the users of rotating machinery with magnetic bearings to understand the relationship between the performance of machinery and the controller parameters.

scholarly journals Design and Control of a Piezoelectric-Driven Microgripper Perceiving Displacement and Gripping Force

Micromachines ◽  
2020 ◽  
Vol 11 (2) ◽  
pp. 121 ◽  
Author(s):  
Yanru Zhao ◽  
Xiaojie Huang ◽  
Yong Liu ◽  
Geng Wang ◽  
Kunpeng Hong
Keyword(s):  
Pid Controller ◽  
Closed Loop ◽  
Tracking Error ◽  
Closed Loop Control ◽  
Structure Parameters ◽  
Loop Control ◽  
Amplification Ratio ◽  
Gripping Force ◽  
And Control ◽  
Tip Displacement

A piezoelectric-driven microgripper with three-stage amplification was designed, which is able to perceive the tip displacement and gripping force. The key structure parameters of the microgripper were determined by finite element optimization and its theoretical amplification ratio was derived. The tracking experiments of the tip displacement and gripping force were conducted with a PID controller. It is shown that the standard deviation of tracking error of the tip displacement is less than 0.2 μm and the gripping force is 0.35 mN under a closed-loop control. It would provide some references for realizing high-precision microassembly tasks with the designed microgripper which can control the displacement and gripping force accurately.

Dynamic Analysis and Control of High Speed and High Precision Active Magnetic Bearings

1992 ◽  
Vol 114 (4) ◽  
pp. 623-633 ◽  
Author(s):  
K. Youcef-Toumi ◽  
S. Reddy
Keyword(s):  
Time Delay ◽  
High Speed ◽  
Dynamic Stiffness ◽  
Magnetic Bearing ◽  
Magnetic Bearings ◽  
Successful Operation ◽  
Highly Nonlinear ◽  
Wide Range ◽  
And Control ◽  
Digital Time

The successful operation of actively controlled magnetic bearings depends greatly on the electromechanical design and control system design. The function of the controller is to maintain bearing performance in the face of system dynamic variations and unpredictable disturbances. The plant considered here is the rotor and magnetic bearing assembly of a test apparatus. The plant dynamics consisting of actuator dynamics, rigid rotor dynamics and flexibility effects are described. Various components of the system are identified and their corresponding linearized theoretical models are validated experimentally. Tests are also run to identify the coupling effects and flexibility modes. The highly nonlinear behavior of the magnetic bearings in addition to the inherent instability of such a system makes the controller design complex. A digital Time Delay Controller is designed and its effectiveness evaluated using several simulations based on linear and nonlinear models for the bearing including bending mode effects. This controller is implemented as an alternative to an existing linear analog compensator. Several experiments are conducted with each controller for spinning and nonspinning conditions. These include time responses, closed loop frequency responses and disturbance rejection responses. The experimental results and comparisons between those of a digital Time Delay Controller and an analog compensator indicate that the Time Delay Controller has impressive static and dynamic stiffness characteristics for the prototype considered. The Time Delay Controller also maintains almost the same dynamic behavior over a significantly wide range of rotor speeds.

Stability and constrained control for positive two-dimensional systems with delays in the second FM model

2018 ◽  
Vol 36 (2) ◽  
pp. 515-536
Author(s):  
Jian Shen ◽  
Weiqun Wang
Keyword(s):  
Closed Loop ◽  
Sufficient Conditions ◽  
Multiple Delays ◽  
Two Dimensional ◽  
Bounded Control ◽  
Delayed Systems ◽  
Closed Loop Systems ◽  
The Stability ◽  
And Control ◽  
Time Systems

Abstract This paper addresses the stability and control problem of linear positive two-dimensional discrete-time systems with multiple delays in the second Fornasini–Marchesini model. The contribution lies in three aspects. First, a novel proof is provided to establish necessary and sufficient conditions of asymptotic stability for positive two-dimensional delayed systems. Then, a state-feedback controller is designed to ensure the non-negativity and stability of the closed-loop systems. Finally, a sufficient condition for the existence of constrained controllers is developed under the additional constraint of bounded control, which means that the control inputs and the states of the closed-loop systems are bounded. Two examples are given to validate the proposed methods.

scholarly journals Magnetic Bearing Control of Flexible Shaft Vibrations Based on Multiaccess Velocity-Displacement Feedback

1993 ◽  
Author(s):  
G. Petela ◽  
K. K. Botros
Keyword(s):  
Closed Loop ◽  
Dynamic Behaviour ◽  
Magnetic Bearing ◽  
Reduced Order ◽  
Flexible Mode ◽  
Non Linear ◽  
Bearing Design ◽  
The Stability ◽  
Multi Access ◽  
Stability Limits

A model of the forced vibrations of a flexible, asymmetric and unbalanced shaft, supported by two magnetic bearings is derived to simulate the effect of different schemes of active control on shaft dynamic behaviour. Simulation results were compared for several cases of single and multi-access bearing controls, rigid-body-mode only and rigid with flexible mode control, and linear and non-linear bearing responses. It is shown that the multi-access bearing response calculated from the known equation of the stable ROCL (Reduced Order Closed Loop) and based on the direct velocity-displacement feedback, provided the most precise shift in critical frequencies and also reasonable suppression of shaft vibration amplitudes. The non-linear bearing design was also briefly discussed. The stability analysis showed that stability limits were influenced by more parameters in this case, but no particular advantages were observed in suppression of the vibration amplitudes as compared to the linear case.

scholarly journals Pid Controller Design for Multiple Time Delays System

2021 ◽  
Vol 15 ◽  
pp. 121-127
Author(s):  
Asma Karoui ◽  
Rihem Farkh ◽  
Moufida Ksouri
Keyword(s):  
Pid Controller ◽  
Time Delays ◽  
Controller Design ◽  
Multiple Time ◽  
Multiple Time Delays ◽  
Pid Controller Design ◽  
The Stability ◽  
And Control ◽  
Time Invariant

This paper presents an approach of stabilization and control of time invariant linear system of an arbitrary order that include several time delays. In this work, the stability is ensured by PI, PD and PID controller. The method is analytical and needs the knowledge of transfer function parameters of the plant. It permits to find stability region by the determination of p K , i K and d K gains.

Chilled Water Temperature Control of HVAC System Using GPC Based Controller

2012 ◽  
Vol 151 ◽  
pp. 626-631
Author(s):  
Qiang Ma ◽  
Jian Gang Lu ◽  
Qin Min Yang ◽  
Jin Shui Chen ◽  
You Xian Sun
Keyword(s):  
Predictive Control ◽  
Pid Controller ◽  
Closed Loop ◽  
Controller Design ◽  
Simulation Environment ◽  
Closed Loop System ◽  
Satisfactory Performance ◽  
Chilled Water ◽  
The Stability ◽  
Theoretical Results

This work proposes a generalized predictive control (GPC) based controller for the temperature of HVAC chilled water supply. In this paper, several models of evaporator are firstly introduced, wherein an identified black-box model is selected for the purpose of controller design. Based on this model, a GPC based controller is employed to obtain a satisfactory performance even with the presence of disturbance. The theoretical results show the stability of the closed-loop system and the performance of this scheme is compared with that of traditional PID controller under simulation environment.

Adaptive Compensation of Sensor Runout for Magnetic Bearings With Uncertain Parameters: Theory and Experiments

1999 ◽  
Vol 123 (2) ◽  
pp. 211-218 ◽  
Author(s):  
Joga D. Setiawan ◽  
Ranjan Mukherjee ◽  
Eric H. Maslen
Keyword(s):  
Magnetic Bearing ◽  
Magnetic Bearings ◽  
Parameter Uncertainties ◽  
Persistent Excitation ◽  
Electrical And Magnetic Properties ◽  
Periodic Disturbances ◽  
Mass Unbalance ◽  
On Line ◽  
The Stability ◽  
Rotor Balancing

The problem of sensor runout in magnetic bearing systems has been largely overlooked due to similarities with mass unbalance in creating periodic disturbances. While the effect of mass unbalance can be significantly reduced, if not eliminated, through rotor balancing, sensor runout disturbance is unavoidable since it originates from physical nonconcentricity between rotor and stator. Sensor runout is also caused by nonuniform electrical and magnetic properties around the sensing surface. To improve performance of magnetic bearings, we present an adaptive algorithm for sensor runout compensation. It guarantees asymptotic stability of the rotor geometric center and on-line feedforward cancellation of runout disturbances using persistent excitation. Some of the advantages of our algorithm include simplicity of design and implementation, stability, and robustness to plant parameter uncertainties. The stability and robustness properties are derived from passivity of the closed-loop system. Numerical simulations are presented to demonstrate efficacy of the algorithm and experimental results confirm stability and robustness for large variation in plant parameters.

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