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THE MINISTRY OF EDUCATION AND TRAINING THAI NGUYEN UNIVERSITY NGUYEN THI THANH BINH Title: IMPROVING THE CONTROL QUALITY OF MAGNETIC BEARINGS Speciality: Control Engineeering and Automation Research code: 62.52.02.16 DOCTORAL DISSERTATION ABSTRACT Supervisors Prof Dr Do Khac Duc Assoc.Prof Dr Nguyen Nhu Hien Thai Nguyen - 2013 Training Institution: Thai Nguyen University of technology – Thai Nguyen University Supervisors Prof Dr Do Khac Duc Assoc.Prof Dr Nguyen Nhu Hien Phản biện 1: PGS TS Bùi Quốc Khánh Phản biện 2: PGS TS Phạm Ngọc Tiệp The dissertation will be defended in front of council in Univeristy Level at: Trường Đại học Kỹ thuật Công nghiệp Thái Nguyên - Đại học Cai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anh DOCTORAL DISSERTATION ABSTRACT Introduction Overview There is no direct contact between the stationary and moving parts, so the magnetic bearings has important applications and efficiency for the rotating machines with high speeds (from 5000 r/ to 10,000 r/min), requiring great precision, working in environments not using lubricants (temperature, pressure very high or very low) Currently, research is focusing on the following four directions: 1.1 Research and apply in industrial and biomedical devices 1.2 Research to reduce the size of the magnetic bearing 1.3 Research to work in special environments such as vacuum, temperature, pressure very high or very low 1.4 Research to apply modern controllers Dissertation’s content will research following the 4th trend Motivation of topic Unlike mechanical bearings, magnetic bearings have no contact between the stationary and moving elements Thus, magnetic bearings used in electric motors are considered as an advanced and environmentally friendly technology They strongly contribute in raising the rotational speed to the engine and help the engine be applied in the special environment that common engine with ball mechanical bearing can not work or work with very high maintainance cost The studies about magnetic bearings typically are in the developed countries such as Japan, America, France, Germany and Switzerland Currently, the applicability of electric motor using magnetic bearings is necessary in many areas; the study of manufacturing electric motors using magnetic bearings and applications is also being promoted in developing countries such as China, Korea, Brazil Cai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anh Cai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anh Magnetic bearings used in electric motors currently classify as the high-tech products containing many levels of intelligence and also the new green technology products, although there are limitations in the use of wide available due to the large size and high cost but in the near future when the researchers succeed in reducing the cost, the replacement of electric motor using magnetic bearings in the field of clean technology, medical equipment, defense equipment and industrial space, will be inevitable The important part of the magnetic bearings is the controller Currently the controller for the magnetic bearings is low quality as maladaptive, unsustainable, control signals are not limited This fact is due to the dynamics of the magnetic bearing is highly nonlinear, and the method of designing the controller for nonlinear systems (including magnetic bearings) under the effect of external disturbance and containing changing parameters during operation have not been studied and developed completely in order to the apply to design the controller to ensure that the magnetic bearing is capable of performing well in any mode working So study to design the controller in order to improve the quality of magnetic bearing is necessary Objects and scope of research - Controlling radial magnetic bearing DOFs, in the drive system using synchronous electric motors, stimulating by permanent magnet and blocking motion along axis, working with high speed - The research of this dissertation limits in building mathematical description having the impact of disturbance and uncertainty parameters to synthesize nonlinear control system under the equation Euler - Largrange (EL) with enough structure - nonlinear channel separation, to improve the control quality compared with classical linear control system Cai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anh Cai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anh Research Methodology - Based on the mechanical, electrical and magnetic laws to calculate dynamics for a radial magnetic bearing DOFs - The mathematical description of the radial magnetic bearings 4DOFs in the form of EL - Design the controller of nonlinear channel separation for the magnetic bearings - Research magnetic bearing by simulation - Empirical study on the magnetic bearing The content and scope of the problem will be studied in depth, resolution and prospects for achieving results - Develop mathematical description of magnetic bearing DOFs, under the radial force - Design to control nonlinear channel separation for system under the effects of noise and uncertainty parameter - Simulations and experiments on the control system in laboratory equipment The theoretical and practical meaning of topics - This is a new problem to be studied in Vietnam and is one of the first scientific studies of the magnetic bearings announcing in Viet Nam and is a new research direction having highly promising application in scientific research… - The results of the research will be the reference to students and graduate students From the results of the research will serve as a basis for many subsequent studies, in order to widespread application of the electric magnetic bearing to drive system in Vietnam, especially in systems with special requirements (speed high, high or low temperature, vacuum, not lubrication, ) Layout of the dissertation The dissertation consists of chapters, 97 pages (including references), 61 references, 64 figures and graphs Cai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anh Cai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anh Chapter 1: Overview of the magnetic bearing 1.1 The concept of the shaft and drive shaft bearing - Presentation of the basic concepts of bearing and magnetic bearings - Classification of magnetic bearings and identifying the research object is active magnetic bearings (AMB) Displacement sensor Controller Power amplifier b) a) Figure 1.6: a) Shape and b) the basic elements of magnetic bearing Electromagnetic actuator - Trình bày nguyên lý nâng dùng lực từ Power amplifier Electromagnetics (Stator) Rotor Rotor Magnetic force fm Controller Rotor weight mg Sensor Figure 1.7: Structure of AMB DOF Cai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anh Cai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anh 1.2 Theory, research-orientation of topics 1.2.1 Overview of research in Viet Nam and in the world 1.2.2 Research in the Viet Nam In Vietnam today only at Hanoi University of Technology and Thai Nguyen University of Technology are now studying 1.2.3 Research in the world Presenting some of the results of research works from around the world in recent years from 2003 to 2009 1.3 Conclusion of Chapter Chapter has solved some problems: - Introducing the most generalized definitions of bearing and magnetic bearing - Select the type of active magnetic bearings to research - Orientation of research is to apply modern control methods to control the magnetic bearings in the drive systems - Propose the control method PD to compensate gravity, nonlinear channel separation based on EL description for the enough structure system to design controller for the magnetic bearing system On the basis of preliminary studies on the magnetic bearing, chapter will study in depth the dynamics of magnetic bearing under radial force to describe mathematically the drive system using magnetic bearings DOFs Chapter 2: The mathematical description of the active magnetic bearing 2.1 Introduction Principles of magnetic bearing are a electric magnet instead of creating shaft torque, it generates displacement forces in the x and y axis, these forces are automatically adjusted to maintain the gap between stator and rotor around the nominal value Cai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anh Cai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anh 2.2 Mathematical basis of magnetic levitating system - According to [1] magnetic levitating system was studied on the basis of approximations based on assumptions such as: flux is closed completely in the ferromagnetic core, not consider at the saturation mode etc - The calculation is based on the average length of the path of magnetic field and the length of the air gap to the nominal value x0 2.2.1 Magnetic flux density of the magnetic circuit With these assumptions have not leakage flux, we have: Ni 2x lC l I 0 r 0 r Sa 0SaNi 2x lC lI r r (2.6) 2.2.2 Reluctance R and the inductance L of the magnetic circuit The components of magnetomotive force, flux, relectance and the invariable magnetic circuit are considered as components corresponding to the voltage, current, resistance and power (DC) in the circuit The main difference is that reluctance is an energy storage component rather than dissipating energy component Source "DC" – Ni performs for the magnetomotive force due to the currents on the coil generated 2.2.3 Electromagnetic force including the magnetic saturation of core of steel Electromagnetic force including the magnetic saturation of core of steel is determined [1]: Wa 0 Sa N i 0 Sa N i (2.16) F 2 x l l l l 2x0 C I 2x0 C I r r r r 2.2.4 Electromagnetic force not including the magnetic saturation of core of steel Cai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anh Cai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anh Electromagnetic force not including the magnetic saturation of core of steel is determined [1]: Ni i2 i2 F 0 Sa N S K ; K 0 N Sa (2.17) a 2 2x x0 x0 2.2.5 The relationship between electromagnetic forces and currents in the AMB When changing the current i compared to the nominal polarized current i0, it will alter the electromagnetic force and after transforming, we have the basic equation to describe the motion of an object is levitated by the electromagnetic force in a fixed direction (2.24) mx Kai K n x [23]: The model built for magnetic bearing from the above will be generalized for magnetic bearings 4DOFs 2.3 Building a mathematical model of magnetic levitating system using poles 2.3.1 The structural form of the current magnetic bearing and researching trend 4-pole active magnetic bearing is actively promoted to research [5, 6], [14, 15] and is attracting the attention of many manufacturers (Synchrony, Mutecs) This is the trend that author will research Figure 2.3 Some of the typical structure of the active magnetic bearing 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Cai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anh 2.3.2 Structure of the magnetic levitating system degrees of freedom Radial active magnetic bearing Radial active magnetic bearing Actuator and Sensor Control System (Hardware and Software) Control System Interface 2.3.3 Building the mathematical model This part studies to build mathematical model of the magnetic bearing DOFs based on the analysis of the equivalent circuit diagram of the motion x, y After analyzing and transformation, we have a mathematical model describing the magnetic bearing: The total flow of flux: H p (x x ) Nix x 1 xc bx 0S x 2 (x x x ) S Nix H p (x x ) xc bx x 1 x (2x x 12 x 2 ) (2.30) Ni H x x ( ) p x 2 xc bx 0S x 2 x (2x x x ) Ni H p (x x ) x xc bx 0S 2 x 2 x (2x x x ) Cai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anh Cai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anh 11 Fxr, Fyr: The tilt force of the rotor in the x and y direction : The distance between the two center of rotor AMB system rm : Angular velocity J and J : Jumping component when levitating shaft rm k x rm k y Transforming the equations to matrix form: u M(q)q+C(q,q)q+g(q) (2.50) Then, prove that M q M T q (*) and M q C q C T q (**) Derive equations describing magnetic bearing degrees of freedom to satisfy the Euler Largrange.system 2.7 Conclusion of Chapter (1) Building a general mathematical model of the magnetic bearing, having the phenomenon of inter-channel effects and instability (2) From the mathematical model built generally performs the process of levitating shaft of magnetic bearings, the model also includes dissipating inductance Lse (new contributions in the dissertation) (3) Building the control model of active magnetic bearing four degrees of freedom (2:50), in accordance with the design to control in the next chapter Chapter Building control system for proactive drive from degrees of freedom 3.1 Problem Magnetic bearing is a heavily nonlinear element, moreover it works with the electromechanical system, there is the appearance of some phenomenons as follows: 3.1.1 Hysteresis 3.1.2 The misalignment of centripetal force Cai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anh Cai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anh 12 3.1.3 The vibrations caused by unbalanced mechanical properties in a rotating system 3.2 Building control systems using linearization methods around working point From the linearized model transforming to the center of the rotor shaft (2.34), building control systems with PID controllers with structure as Figure 3.1 AMB Model Controller Figure 3.1: Model PID controller for the linearized model around the operating point of the magnetic bearing With controlling in the x, y directions in magnetic bearings, we need to have controllers corresponding to control channels x1, x2, y1, y2 Each channel has two control loops: the inner control loop is the current control loop (enhanced load carrying capacity of the magnetic bearing) and outer control loop is position control loop From the above analysis, the control structure diagram of x1 channel is in Figure 3.2 Position Controller Current Controller Power electronics amplifier Figure 3.2: The control structure in the x1 direction Cai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anh Cai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anh 13 And to control a magnetic bearing, we need to control in the directions x, y so that the control structure diagrams of magnetic bearing at x1 and y1 as shown in Figure 3.3 Figure 3.3: Structure diagram of control system of magnetic bearing Due to the capacity variation with time constant is very small, the PID controller of current control loop (inner loop) is set according to optimal modularity standard [50] But the position control loop is designed according to the symmetrical standard [50] 3.2.2 Simulation of system in Matlab-Simulink - Simulation Data: The number of turns in a coil 200 turns Resistance of coil 3.1 Ω Inductance of coil 12.61 mH Polarization flux 0.058 T Rotor mass Kg Inertial moment in z direction 0.00241 kgm2 Inertial moment in x and y direction 0.00298 kgm2 The gap between the stator and rotor in equilibrium point x0 1mm Cai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anh Cai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anh 14 Cross section of the magnetic poles 525 mm2 The distance between magnetic bearings 125mm The distance between sensors 169mm - Simulating result + Without disturbance Figure 3.5ab: Displacement response of magnetic bearing in (y,x) Figure 3.6a,b: Displacement response of magnetic bearing in (y,x) + With disturbance Cai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anh Cai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anh 15 Figure 3.9ab: Displacement response of magnetic bearing in (y,x) Figure 3.10ab: Displacement response of magnetic bearing in (y,x) + Considering the impact of cross coupling between the x and y in the magnetic bearing: Figure 3.11: Displacement response in directions x, y with the impact of channel alternating with PID controller: a) Magnetic bearing 1; b) Magnetic bearing 3.3 Improving the control quality of active magnetic bearings (AMB) by feedback linearization v Controller (3.12) u EL basedplant (3.11) Figure 3.12: Control structure PD to compensate gravity Cai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anh q Cai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anh 16 The EL full system is a system class having the model as follows: M (q )q C (q, q)q g (q ) u (3.11) Using the controller introduced in references [50, 53]: u M (q )v C (q, q)q g (q ) (3.12) Becomes linear system (Figure 3.12) and the linear form of the second order integral (unstable): M (q )q C (q, q)q g(q ) u M (q )v C (q, q)q g(q ) q v (3.13) To stabilize by designing additional PD controller in the outer loop: v qref K1e K 2e (3.14) qref e - Outer controller (3.14) v Controller (3.12) u EL –based plant (3.11) q Figure 3.13: PD controller to compensate gravity for magnetic bearing d2qre + ∑ + u v ∑ M(q) + + AMB DOF + q dq K2 K1 C(q,dq)+g(q) dqref + q + e ∑ de ∑ - Figure 3.14: Control structure PD to compensate gravity (3.15) With K1 and K2 are symmetrical matrices of positive definition Cai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anh Cai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anh 17 k p K 0 k p2 k d 0 ; K 0 k p n 0 kd k dn I have two inner loop controllers (3.13) and outer loop (3.14), we will write as: (3.15) u M (q ) qref K1e K 2e C (q, q)q g(q ) made the state trajectory q(t ) , q(t ) of system (3.11) asymptotically stable tracking on the desired set trajectory qref t , qref t From above, we have detailed diagram of control method as figure 3.14 3.3.1 Building control system According to expression (3.15), we have accurately linearized controller - channel separation for DOF AMB system is represented as follows: 2K u y d x d y d x d Jy a h a 2 c o s y J 2K a ha x c o s x y k x y x 0 k2 0 k2 0 y d x d y d k x d 0 m 2K 0 0 a m 2K a y y d x x d y y d x x2 d J i sin y rmJ kcosy y y2 h h a 2K acos3y a cosx K a rmJ kcosy J i sin xK n x x h a cosx K a 2K ncos x 0 0 K 0 a K n y1 x 0 y x 0 0 k 0 Ka Kn 0 Ka Kn 0 0 k1 0 k1 y1 x y x K a K n 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Cai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anh 18 3.3.2 Simulation of ABM control system - Simulation result + Without disturbance Figure 3.21: Displacement response in directions x anf y of magnetic bearing Figure 3.22: Displacement response in directions x anf y of magnetic bearing + With disturbance Figure 3.24: Displacement Figure 3.25: Displacement response in directions x and y of response in directions x and y of magnetic bearing magnetic bearing Cai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anh Cai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anh 19 + Checking channel separation’s capacity (Eliminating the cross coupling) Figure 3.26a: The Impact of channel alternating of magnetic bearing in the x and y directions is avoided Figure 3.26b: The Impact of channel alternating of magnetic bearing in the x and y directions is avoided 3.4 Quality assessment of PID controller and nonlinear controller by squared error integral standard To assess the quality of the controllers for control system of magnetic bearings four degrees of freedom, we use the squared error integral standard 3.5 Conclusion of Chapter This nonlinear control method has solved the fundamental problem of the DOF AMB system: (1) Stable tracking control for system with the change of the input signal with high precision, according th the squared error integral standard, the error is smaller when the system works with accurately linearized controller This demonstrates the quality of the system has been enhanced (2) Ensuring the channel separation for control system Cai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anh Cai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anh 20 (3) The controller is designed in this chapter will be empirically tested in the next chapter Chapter Experimental test bench and Experimental results 4.1 Introduction of Experimental test bench The experimental test bench is illustrated in figure 4.1: Figure 2.4: Diagram of the general structure of magnetic bearings To connect DSP1104 to PC, some steps are implemented as follows: - Initiating Matlab/Simulink - Calling out necessary blocks in Simulink to build the system - Starting up Control Desk program - Connecting - After connecting to Simulink model, Matlab will convert the Simulink model to the form of file.sdf (file describes the system) and save it into the processor of DS1104 Cai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anh Cai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anh 21 AMB Stator of motor Rotor of motor AMB Figure 4.7: Test bench configuration - Motor in the middle and 02 AMBs at both ends of the shaft 4.2 Experimental results - System responses: - Decoupling action in x and y axes: Hình 4.14 Đáp ứng độ dịch chuyển trạng thái bắt đầu nâng Cai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anh Cai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anh 22 Figure 4.15: Position displacement of rotor shaft in x and y axes compared to the balanced position of bearings and Remarks: This experiment is implemented at rotating speed of 5.000 RPM of rotor shaft Obtained experimental results indicate the similarity to those of aforementioned simulation 4.3 Conclusion According to the simulation and experimental results, it can be seen that: - Control performance of the magnetic bearings is considerably improved on nonlinear decoupling control regime compared to the performance of linearization at the operating point control regime (position error and vibration are reduced) - However, as working at steady-state, AMB system is still affected by disturbances This indicates that the difference between simulation results and experimental results is partly caused by the imperfectness of mathematical model of the system Cai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anh Cai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anh 23 CONCLUSION AND FUTURE WORKS Conclusion: Automated electric drive systems applied magnetic bearings to replace conventional mechanical bearings have offered preeminent advantages including: very high-speed drive systems, negligibility of lubricant requirements and working well in very high or low temperature and pressure environment… However, applicability of AMB is not popular due to the cumbersome size and expensiveness Recent researches concentrate on size and cost reduction and working robustness for magnetic bearings Therefore, AMB are used for not only special applications but also for industrial applications The content of this research work concentrates mainly on studying the applicability of modern controllers for AMB systems in order to enhance control performance and robustness for AMB drive systems Until now, researching thoroughly in AMB is still not popular in Vietnam Therefore, reference materials in this area are quite rare With the great effort of the author, some significances have been achieved through the research work which include: - Basing on fundamental relations among parameters (flux, reluctance, inductance, magnetic force, stored magnetic energy,…) of a magnetic suspension system, dynamic representations of system with four degrees of freedom are described in this dissertation From these representations, the generalized nonlinear mathematical model for DOF AMB is formulated under the form of Euler – Lagrange (EL) representation - As can be seen from the equations of motion, AMB is a nonlinear and coupled system Moreover, AMB’s dynamic behavior is inherently unstable The dissertation has designed successfully PD Cai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anh Cai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anh 24 controller which can implement directly to decoupling As a result, control performance can be improved considerably when it is compared to other PID controllers - Working under the experience deficiency in terms of test bench designing and making, the author has tried to build a completed experimental test bench to testify the proposed PD control method Experimental results obtained satisfy the requirements This experimental test bench can work well at high speed of rotation (5000 RPM or even higher) Future Works: Although this research work has contributed some significances in studying of AMB, it has modestly mentioned some issues related to controlling AMB in particular, and using AMB in industry in general For the only controlling aspect of AMB, some problems should be further investigated: - Effects of mutual magnetic flux amongst electromagnetic coils in a bearing; - Effects of flux saturation to the performance of the control system - AMB has been applied successfully to artificial hearts, air compressors, liquid-helium pumps…However, in heavy- or pulseload systems, whether or not the robustness of these systems is satisfied? Other problems what have been mentioned at the beginning of Chapter 3, such as lag phenomena, inclination of radial forces and vibrations caused by mechanical unbalance when rotating,…Those are interesting issues needed to further researches in future Cai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anh Cai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anh Cai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anhCai.thien.chat.luong.dieu.khien.cac.o.do.tu.ban.tom.tat.luan.an.tieng.anh
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