Index: switching power amplifier, PWM, active magnetic bearing. I. INTRODUCTION ..... actual current in the coil is measured with Hall effect transducers in the ...
A PWM Based Switching Power Amplifier for Active Magnetic Bearings∗ Zhu Changsheng, Mao Zhiwei Department of Electrical Engineering, College of Electrical Engineering Zhejiang University, Hangzhou 310027, China
Abstract—A two-level PWM based switching power amplifier for active magnetic bearings with current-loop, which can be used in either voltage-controlled mode or current-controlled mode, was proposed, designed and debugged in this paper. The characteristics of the switching power amplifier with the maximum output current 8 A, such as the static input-output characteristic, frequency response characteristics and current harmonic distortion, were measured. The power amplifier was successfully used to suspend a rotor system. It is shown the proposed two-level PWM switching power amplifier can meet the requirements of the amplifiers of industrial active magnetic bearings. Index: switching power amplifier, PWM, active magnetic bearing.
I. INTRODUCTION Active magnetic bearings(AMB), which use the controllable attractive force of electromagnets to maintain a rotating ferromagnetic body contact-free in its nominal position, have seriously developed in the rotating machinery, provide numerous advantages compared with the conventional bearings, such as: no contact, no wear, no lubrication, long life and controllable dynamic characteristics etc. However, the AMB system is inherently unstable, a position control loop is necessary to stabilize this system in which the position controller gets the information of the actual rotor position from the transducers and controls the coil current of the magnets by means of power amplifier. The power amplifier, a bridge between the control signal and the applied current in the coil, is one of the main components of an AMB system and has a great effect on the dynamic characteristics of the AMB-rotor system. According to its operating principles, the power amplifiers are classified into linear analog power amplifier and switching power amplifier. The linear power amplifier was used in the early development of AMBs of a small power AMBs, because it can be easily realized and controlled. It has some advantages against the switching power amplifier, for example, less current ripple and noise, greater bandwidth. The main disadvantage of the linear power amplifier is the large power losses or very inefficient, especially at a large power rating. In the switching power amplifier, high voltage and high current is present in the power transistors only during the short periodic. The power loss is greatly reduced. Though the current harmonic distortion
is bigger than the linear power amplifier, it can be reduced by properly using of the pulse modulation technique. The switching power amplifiers are widely using in all AMB systems. A two-level PWM based switching power amplifier with current-loop, which can be used in either voltagecontrolled mode or current-controlled mode was proposed, designed and debugged in this paper. The characteristics of the switching power amplifier, such as the static inputoutput characteristic, dynamic frequency response characteristics, and current harmonic distortion, were measured, and the effects of some parameters on the dynamic characteristics were dealt with. The effectiveness of the switching power amplifier in the AMB system was shown in a rotor system. II. TWO-LEVEL PWM SWITCHING POWER AMPLIFIER In generally, the simple switching power amplifier is composed of drive circuit and power main circuit. The switching power amplifier with inner feedback loop is composed of inner controller, drive circuit, power main circuit, and feedback circuit, as shown in Figure 1. The main purpose of adding the inner feedback loop is to improve the characteristics of the power amplifier.
(a) simple switching power amplifier
(b) switching power amplifier with inner feedback loop Fig 1. Basic structure of a switching power amplifier The drive circuit, including the pulse modulator and signal amplifier is to produce pulse signal with variable duty-cycle according to the control signal from the inner controller and the position controller, and to amplify the pulse signal to a certain voltage to drive the transistor switches in the power main circuit. The power main circuit realizes the amplification function of the power. The feedback circuit, including the transducers and related measurement circuit, is used to get the feedback information that may be voltage, current or flux in the
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This project is supported by the Nature Science Foundation of Zhejiang Province (R104129), Key Project of Education Department of Zhejiang Province and National Science Foundation of China (10332030), respectively. 1563
bearing. The function the inner controller is to produce the inner control signal to adjust the amplifier’s characteristics according to the inner feedback information. The pulse modulator, power main circuit and feedback circuit are key components in the switching power amplifier. A. Main Circuit There are two basic power main circuits of the switching power amplifiers: the monopole(or semi-bridge type) and dipole(or full-bridge type). The full-bridge type has small current ripple than the semi-bridge type, and can change the direction of the output current, but more expensive and larger size than the semi-bridge type. Since a standard AMB magnet requires only two quadrants control, i.e., the output voltage of the power amplifier should be modulable between a negative and positive limit and the current between zero and the maximum. Negative currents are undesirable. It means that it is not necessary to change the current direction in the coil of the AMB. The semi-bridge type is enough for the AMB power amplifier. This may greatly simplify the structure of the power amplifier and reduce the cost, which is very appropriate for the application of the AMB system.
It is shown that both the hysteresis and the samplehold have significant shortcomings in application. The hysteresis amplifier suffers from short-pulse susceptibility leading to low efficiency or output device failure. The sample-hold one provides excellent short-pulse immunity but produces fairly severe harmonic distortion and deadband, especially at low signal amplitudes. The minimum pulse width combines the advantages of both the hysteresis and the sample-hold, but the control signals are much complex. The PWM is most common as the PWM technique has been thoroughly studied and widely implemented successfully in power electronic systems. The PWM of the semi-bridge power amplifier may be based on two-level or three-level scheme. For the twolevel scheme, the output voltage of the power amplifier is either positive DC-link voltage or negative one. The main drawback is that the current harmonic distortions are related with DC-link voltage. By varying the duty-cycle between both levels, the average output current is controlled. The two-level PWM scheme can be easily realized. It is shown that the two-level semi-bridge amplifier is enough for the AMB application. For the three-level scheme, the output voltage of the power amplifier is not only positive and negative DC-link voltage, but also zero voltage. The main advantages over the two-level scheme are large bandwidth and small current harmonic distortion. Figure 3(a) shows a conventional two-level PWM scheme. In this PWM scheme, the duty-cycle between positive and negative pulses determined by the crossing points between the command voltage U r and the triangle reference voltage is proportional to the voltage U r . The switching frequency of the power switchers is constant, and equal to the frequency of the triangle reference voltage.
Fig.2 Principle schematic of a semi-bridge power main circuit of switching power amplifier Figure 2 shows the principle schematic of a semibridge power main circuit of switching power amplifier working in two-guadrant PWM mode. Most industrial AMB amplifiers are built based on this configuration. It consists of two transistor switches(T1 and T2), such as MOSFET, IGBT etc, a capacitor and two free-wheel diodes(D1 and D2), which form the H bridge structure. The two transistors form one circuit that allows the coil current to be increased. The two free-wheel passive diodes form the other circuit that allows the coil current to be decreased when the transistors are in the “off” state. Only the two transistor switches have to be controlled by the drive circuit. This guarantees the current direction in the bearing’s coil. B. PWM Modulation There are a number of the modulation techniques in the switching power amplifier: such as pulse width modulation (PWM), current hysteresis, sample-hold, and minimum pulse width[1-4].
Fig.3 Schematic of a two-level PWM scheme In this paper, we are focus on the two-level semibridge PWM switching power amplifier. The operation states of the two-level semi-bridge PWM switching power amplifier are divided into charge state and discharge state. (a) Charge state When the control voltage from the controller makes the switches T1 and T2 close, as shown in Figure 4(a), a positive voltage with the amplitude of Vdc is applied to the bearing coil and the coil current increases. The coil current after the switches T1 and T2 close is
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i (t ) = −
t t − − Vdc − 2VD (1 − e τ ) + I L 0 e τ R
(1)
where Vdc is the DC supply voltage of the power amplifier, VD is the voltage on the switches when the switches are close, τ = L / R is a time constant of the circuit, L and R are the inductance and the resistance of the coil, respectively. I L 0 is the initiation current in the coil at closing the switchers. As τ is much larger than the switching period, i (t ) can be simplified as a linear function and its slope is (Vdc − 2VT ) / L − I L 0 τ .
(a) charge state
Figure 5 shows the power main circuit of the twolevel PWM switching power amplifier based on the MOSFET. It has two P mode MOSFETs and one N mode MOSFET, shearing the same driver circuit, which simplifies the structure of the power amplifier and improves its reliability. The power main circuit can also be used in the three-level scheme. C. Drive Circuit The drive circuit, especially the PWM modulator, is an important part of the switching power amplifier. Different PWM modulators, such as the two-level or three-level scheme, will result in different amplifier’s characteristics, The PWM modulator can be realized in two ways: hardware method and software method. The hardware method, which is based on the special PWM module, such as TL494, to generate PWM wave, as shown in Figure 6(a), can be integrated with the inner controller, inner feedback loop, power main circuit etc as an independent switching power amplifier. This kind of switching power amplifier done not use the computer and has more widely application, but it is difficult to adjust the PWM scheme.
(b) discharge state Fig. 4 The operation states of the two-level switching power amplifier (b) Discharge state When the control voltage from the controller makes the switches T1 and T2 open, as shown in Figure 3(c), the circuit output negative voltage to decrease the coil current. The coil current after the switches T1 and T2 open is i (t ) = −
t t − − Vdc + 2VD (1 − e τ ) + I L 0 e τ R
(a) independent switching power amplifier
(2)
where VD is the voltage on the diodes. Similarly, i (t ) also can be treat as a linear function with a slope of − (Vdc + 2V D ) / L − I L 0 τ . By change the duration of charge state and discharge state in every period, the average current can be controlled.
Fig. 5 Main circuit of proposed power amplifier
(b) DSP based switching power amplifier Fig. 6 The basic structure of the PWM module In the software method, which is based on the computer with PWM outputs, such as DSP, as shown in Figure 6(b), the PWM wave is produced by numerical method. In this way, it is easy to adjust the PWM scheme and the structure of the power amplifier is great simplified, but the inner feedback information, the inner controller and the position controller should be properly designed in the computer, which increases the complexity of the AMB’s control system. Since the software method takes the computer CPU time, it is based on the high-speed DSP. In this paper we adopt the hardware method.
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D. Inner Feedback Loop in the Power Amplifier Corresponding to the controlled variables, the power amplifier may be classified into current-controlled mode, voltage-controlled mode and flux-controlled mode. The input variable of the power amplifier in three modes is the voltage, but the output variable is voltage for the voltagecontrolled mode, current for the current-controlled mode and magnetic flux density in the air-gap for the fluxcontrolled mode. Because the magnetic force is directly related with the magnetic flux density in the air-gap between the magnets and the rotor, it is expected that the flux-controlled mode is able to reach the best performance of the AMB, if the magnetic flux densities in the air-gap can be directly controlled. But actually it is hard to precisely measure and control the magnetic flux densities between the magnets and the rotor, such type of AMB is rarely applied in practice. The voltage-controlled mode and the current-controlled mode indirectly control the magnetic force, but it is easy to measure the voltage or the current in the coil. In the voltage-controlled mode, the control variable is the coil voltage, this voltage produces the coil current which then generates magnetic force. The basic behaviors of the voltage-controlled mode are more accurate modeling of the plant, therefore higher robustness, weaker open-loop instability, easier to realize than the current-controlled mode, but very low stiffness and higher order controller. In the current-controlled mode, the control variable is the coil current, which directly generates the magnetic force. The basic behaviors of the current-controlled mode are simple control plant description, and simple controller. The voltage-controlled mode is often used for large or very large systems. For most AMB system, the current-controlled mode with a high stiffness is satisfactory, especially when the peak output voltage of the power amplifiers may be the multiple of the operating point current. This permits neglecting the dynamics of the inner current loop in the power amplifiers. The inner feedback loop of the switching power amplifier proposed is based on the current feedback. The actual current in the coil is measured with Hall effect transducers in the output side of the switching power amplifier. The measured current is input to the current inner controller and compared with the reference current suspending the rotor that it is obtained from the position controller. The new control signal is formed and applied to the power main circuit.
switching power amplifier developed here can also work in the voltage-controlled mode by selecting the input signal to the inner controller. As shown in Figure 7, in the current-controlled mode, the current signal is feedback from the current of the magnetic coil, and in the voltagecontrolled mode the voltage signal may feedback from the output of the power amplifier. With an inner current/voltage negative feedback loop can greatly improves the dynamic and linear characteristic of the switching power amplifier. The different feedback signals, the inner controller will produce different output signal to generate PWM wave. III. RESULTS AND ANALYSES The specifications of the two-level switching power amplifier in design per channel are shown in Table I. TABLE I The specifications of the power amplifier per channel
maximum current voltage rating bandwidth frequency rating control mode
8A 80 V >1.20 kHz 78 kHz current-controlled mode or voltagecontrolled mode
A. Static Transfer Characteristic of the Power Amplifier Since the maximum current of the experimental rig of the AMB system used is about 4 A, the maximum current of the power amplifier is set to 4 A. The range of the input DC voltage to the amplifier is from 0-10V. The variation of the output current of the amplifier with the input voltage is shown in Figure 8 for the different control resistances in the circuit. The control resistances for curves 1, 2 and 3 are 5.6 k Ω , 2 k Ω , and 150 Ω , respectively. It is shown that the static transfer characteristic of the power amplifier can be modified by change the control resistance. By choosing properly the control resistance, a very good linearity relation between the input voltage and the output current can be obtained.
Fig. 7 Feedback mode of the switching power amplifier In order to make the switching power amplifier more flexible and combine the advantages of the voltagecontrolled mode and the current-controlled mode, the
Fig. 8 The variation of the output current of the amplifier with the input voltage B. Frequency Response of the Power Amplifier
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Figure 9 shows the output current waveform of the power amplifier when the input signal of the power amplifier is a sine wave with amplitude of 4.8 V and frequency of 500 Hz and 1000 Hz. It is shown the output current can follow the input wave and the phase lag between the input and the output wave increases with an increasing on the frequency of the input signal. In order to understand the dynamic characteristics of the power amplifier, the frequency response curves of the power amplifier with different output currents are measured. Figure 10 shows the frequency response curve of the power amplifier with an output current of 2 A. It is shown the –3 dB bandwidth of the power amplifier is about 1.6 kHz, therefore the maximum rotational speed in which the power amplifier can be used is over 60,000 r/min.
C. Current Harmonic Distortion of the Power Amplifier In a two-level PWM switching power amplifier, the current harmonic distortion is related with the DC-link voltage and the frequency of the switches. The higher the voltage is, the greater the harmonic distortion will be. But the relationship between the frequency and the distortion is on the contrast, the higher the frequency is, the lower the distortion will be. But the high frequency will produce large power loss. When the switching power amplifier is supplied with a DC-link voltage of Vdc , the relative current harmonic distortion is: Iw Vdc = I 4 3LfI
(3)
where L and R are the induction and the resistance of the coil, respectively, f is the frequency of the switches, I is the output current of the switching power amplifier. For the switching power amplifier, when Vdc =50 V, L=18 mH, R=0.5 Ω , f=78 kHz, and I=1 A, the relative current harmonic distortion is 2.06 %. Figure 11 shows the current harmonic distortion of the switching power amplifier in the case, the spike noises are produced by switching disturbances and the stray capacitor in the cable of the power amplifier. The relative current harmonic distortion measured is about 4.17 %, which is larger than the analysis one. In order to reduce the current harmonic distortion of the two-level switching power amplifier, the three-level switching power amplifier is being studied as it has the same power main circuit as two-level switching power amplifier.
(a) at a frequency of 500 Hz
(b) at a frequency of 1000 Hz Fig. 9 The output current waveform in the sine input of the power amplifier Fig. 11 Current waveform of the switching power (0.1V/grid) The switching power amplifier was used to successfully suspend a rotor with weight of 3.5 kg. The results about the rotor supported on the active magnetic bearings will report in further. IV. CONCLUSIONS
Fig. 10 Frequency response curve of the power amplifier with an output current of 2A
A two-level PWM based switching power amplifier with current-loop, which can be used in either voltagecontrolled mode or current-controlled mode was developed. It is shown that the two-level PWM switching power amplifier presented has good static and dynamic
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characteristics. The proposed PWM based switching power amplifier with maximum output current 8 A and maximum output voltage 80 V was used to successfully suspend a rotor. It is shown that the two-level voltage power amplifier can meet the requirements of industrial AMB switching power amplifiers in rotational speed of up to 60,000 r/m. REFERENCES [1] G. Schweitzer, H. Bleuler, Bearings, ETH, 1994
[2] Zhang Jing, Power amplifier for magnetic bearings, Swiss Federal Institute of Technology, 1995 [3] F.J. Keith, et al., Switching amplifier design for magnetic bearings. Proc. of 2nd Inter. Symposium on Magnetic Bearings, July 12-14, 1990, Tokyo, Japan, pp:211-218. [4] T. Bardas, et al., Problems, solutions and application in the development of a wide band power amplifier for magnetic bearings. Proc. of 2nd Inter. Symposium on Magnetic Bearings, July 12-14, 1990, Tokyo, Japan, pp:219-227. [5] Yu Lie, Controllable Magnetic Bearing Systems, Science Press, 2003 (in Chinese)
and A. Traxler, Active Magnetic
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