me2001_1_03 - PERIODICA POLYTECHNICA SER. MECH. ENG. VOL....

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PERIODICA POLYTECHNICA SER. MECH. ENG. VOL. 45, NO. 1, PP. 17– 24 (2001) DEVELOPMENT OF A CONTROL CIRCUIT FOR A RADIAL ACTIVE MAGNETIC BEARING János HALAS Department of Precision Engineering and Optics Technical University of Budapest H-1111 Budapest, Egry J. u. 1, Hungary Phone: (+36) 1 463 2604, Fax: (+36) 1 463 3787 E-mail: halas@antares.fot.bme.hu Received: April 5, 2000 Abstract The electromagnetic bearings are the result of the modern control technique. Utilizing this princi- ple frictionless bearing is reachable, but an appropriate control circuit is needed. In this report a development of an analogue PID controller will be demonstrated. Keywords: active magnetic bearing, PID controller, electromagnet, displacement sensor. 1. The Operating Principle The schematic figure of the analyzed construction can be seen in Fig. 1 . The oper- ating principle is based on the force effect in a magnetic field; the magnetic flux lines strive for energy minimum. The rotor (1) is made of a magnetically passive material, for example aluminium. The flux conducting ferromagnetic ring (2) is fixed on the rotor. The actuators are electromagnets, which consist of two parts, the coil (4) and the ferromagnetic body (3). 1.1. Calculating of the Arising Forces Each of the electromagnets can be independently analyzed, because the distance be- tween them is large enough. The arising force can be calculated from the derivative of the energy of the magnetic field with respect to the displacement: F = W m x = A ∂δ x Z B d H = 8 2 2 µ 0 A = µ 0 AH 2 . (1) where A is the surface, δ is the air gap, µ 0 is the permeability of the free air, B is the magnetic induction and H is the strength of the magnetic field. The strength of the magnetic field can be determined from the field excitation law. Ignoring the magnetoresistance of the iron parts the strength of the magnetic
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18 J. HALAS field becomes: H = NI δ , (2) where N is the turn of the coil and I is the current. According to the above the acting force by the two electromagnets to the rotor can be written: F = µ 0 A ( NI 1 ) 2 + x ) 2 ( NI 2 ) 2 x ) 2 ! . (3) It is obvious that the force is proportional to the second power of the current and the reciprocal value of the change of the air gap. 2. Dynamical Analysis of the System According to Eq. (3) it is obvious that the system is highly non-linear. To design an analogue control circuit it is needed to linearize the system near the operating point. For the linearization the following equation can be used as a starting point: 1 F = F i 1 i + F x 1 x . (4) There are two ways for the linearization of the system. The first is when permanent magnets are applied to produce a constant equilibrium magnetic field, like in Fig. 2 The resultant magnetic flux is the sum of the flux from the electric current (8 el ) and the flux of the permanent magnet (8 m ) . The magnetic field, which is Fig. 1 . Schematic figure
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me2001_1_03 - PERIODICA POLYTECHNICA SER. MECH. ENG. VOL....

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