The Intelligent Drive for Permanent Magnet Ac Motors with the Least Number of Sensors

In this paper, a novel rotor position estimation method for Brushless Permanent Magnet AC motors are described. The algorithm developed here relies on the phase voltages and the currents of the motor drive, which are both reconstructed from the measured DC link current and the switching control signals of the inverter. The paper reports the first phase of the research work, and provides various simulation results to demonstrate the validity and robustness of the method. 1. INTRODUTION Permanent magnet AC (PMAC) motors have a wide range of applications because of their high efficiency, high power density and easy controllability. In order to control such motors, however, their rotor position must be known, and the accuracy of the rotor position data primarily depends upon the type of the motor used. The PMAC motors belong to the family of the synchronous AC machines, and so that the constant torque can be produced only when the winding currents are precisely synchronised with the induced voltages (back emfs), which can be determined from the instantaneous rotor position. The motors are powered via the three-phase inverters that ensure the synchronisation of the current, which generates switching states from the rotor position data. The conventional way of measuring the rotor position data involves some form shaft-mounted sensing devices, such Hall-Effect devices, resolvers, absolute or incremental encoders. However, these mechanical shaft-mounted position sensors have many drawbacks, and therefore, their applications could be restricted. A number of indirect rotor position detection schemes for PMAC motors have been suggested in the recent years. The expected benefits of these indirect techniques are: elimination of the electrical connections of sensors, reduced size, no maintenance, unsusceptible to the environmental factors, increased reliability, and above all these, operating at zero, low and higher speeds. However, most of the indirect position detection techniques have problems when they are used in realtime system, especially at the low and zero speed range. Moreover, in order to extract the rotor position information, the earlier schemes require at least four or more voltage and current sensors in total. The current information in the drive is used to accomplish the current control loop. However, the voltage and current sensors are expensive mainly due the requirements for the isolation. Therefore, employing minimum number of sensors, which also increase the reliability of the system, and reduced cost are desirable in the commercial applications. This paper presents an intelligent control scheme for PMAC motors with the least number of sensors. The scheme includes two principal sections: the rotor position estimation algorithm and the current and voltage reconstruction. In the scheme, only one current sensor is required to measure the DC link current of the inverter. 2. POSITION ESTIMATION In the PMAC motors with trapezoidal back emf, the rotor position information is needed every 60o electrical interval to achieve the current commutation and hence the self-synchronisation. Several rotor position estimation methods for such motors have been proposed in the references [1-4], which are based on the back emf sensing, the third harmonic component sensing or the conducting states of the free-wheeling inverter diodes. However, all of the methods proposed so far ultimately fail at low and zero speed due to the absence of the measurable signal, back emf. In the PMAC motors with sinusoidal back emf however, the continuous rotor position data is required. Furthermore, the continuous rotor position information can be used to eliminate the torque ripple, which occur in the practical motor drives [5]. A number of rotor position elimination techniques have also been reported for such motors. Some of the rotor position estimate techniques are based on the vector control principle of AC motors [6-9]. The state estimation algorithms, such as a state observer or an extended Kalman filter, are also adopted to estimate the rotor position and the speed [10-15]. However, the accuracy of the measured voltages and the currents and the accurate knowledge of the motor parameters are necessary in these algorithms. Moreover, the reported methods suffer at low speeds require extensive computational power. Other rotor position estimation techniques reported in [16,17] are based on the flux linkages, which can be obtained from the stator voltages and the currents of the motors. The flux linkage based methods operate accurately over a wide speed range and can be applied to the PMAC motors with the trapezoidal and the sinusoidal back emfs. However, the performance of the position estimation depends very much on the quality and the accuracy of the estimated flux linkages. The motor parameter variations due to the temperature rise and the saturation also affect the accuracy of the estimated rotor position in these methods. From the mathematical model of the PMAC motor in [21], it can be observed that the back emf or flux linkage varies as a function of the rotor position only. Therefore, if these quantities are measured or estimated, the rotor position information can be determined. However, it is difficult to measure the back emfs , specifically at low operating speeds, or the flux linkages directly because of the integration shift in the calculations. To solve the above problems, instead of direct calculation of the back emfs or the flux linkages, this paper presents an incremental estimation method for the rotor position. From to the mathematical model of the PMAC motor given in [21], the per-phase voltage equation of the star-connected PMAC motor can be given by: e dt di L Ri v + + = (1) Here v is the phase voltage; R is the winding resistance; i is the line current; L is the equivalent winding inductance; and e is the back emf. The back emf, e is a function of the rotor's angular speed and the position, and can be expressed as: dt d p ) ( e . k ) ( e k e e e e e r e θ θ θ ω ⋅ = = (2) Where ke is the back emf constant; ωr is the rotor's angular speed; e(θe) is the back emf function that varies with rotor position; θe is the electrical rotor position; and p is the number of pole pairs in the motor. Substituting Eq.2 into Eq.1, the increment of the rotor position within each time step can be calculated by p ) ( . ) ( ⋅ ∆ − ∆ − = ∆ e e e e . k i L t Ri V θ θ (3) Hence, the rotor position can be estimated by an incremental algorithm as given below. e e e ) k ( ) k ( θ θ θ ∆ + − = 1 (4) If the parameters p, R, L and ke and the function e(θe) are known, the rotor position θe can be calculated by using the data of the voltage and the current of the motor. As will be demonstrated later, the simulation studies carried out in this paper illustrate that the new rotor position estimation method has several advantages. Firstly, due to the less mathematical computations, the algorithm is simple and easy to implement in realtime. Secondly, the method can operate at very low operating speeds and even at zero speed. Thirdly, if the initial value of the rotor position has in error, it can be corrected within a short time and an accurate rotor position information can be obtained. Finally, the method does not dependent upon the shape of the back emfs and hence can be applied to the any types of PMAC motors. 3. THE VOLTAGE AND THE CURRENT RECONSTRUCTION IN THE DRIVE In order to control the PMAC motor, it is necessary to know all of the three line currents for the current control and/or the rotor position estimation. The conventional method of obtaining the line currents in the practical drive is to measure them directly. Depending upon the winding connections of the motor, at least two current sensors are needed, as in the star connected motor. However, the current sensors are usually expensive due to the requirements of the high frequency bandwidths and the electrical isolation. The number of current sensors can be reduced to one by measuring only the DC link current of the inverter and reconstructing the three-phase line currents from the measurement. Two current reconstruction methods have already been reported in the literature. The method in [18] uses the inverter switching states, and then determines the corresponding conduction interval of the winding current in the DC link. If the Pulse Width Modulation (PWM) frequency is high enough, the phase current will only vary slightly over one or two PWM periods. Hence, the three line currents can be reconstructed by observing the DC link current. However, there are time intervals within the line current conduction cycle that the winding current circulates in the inverter bridge (through the free wheeling diodes) without flowing through the DC link. Therefore, this method lacks to reconstruct the winding currents accurately within the free wheeling periods. The second method [19] uses an observer that is based on the models of the motor and the inverter. In the state observer, the error between actual and the estimated DC link current is used to update the estimated winding currents. However, because of the poor reconstruction method of the estimated DC link current, the winding currents are unobservable if all of the windings conduct the current at the same time [20]. This means that such current observer works only in the rectangular current excited motors, such as the PMAC motors with trapezoidal back emfs. The current and the voltage reconstruction method proposed in this paper is also a state observer that is based on the model of the PMAC motor drive. The switching control signals, the rotor position and the speed of the motor are used in the state observer that estimates not only the three-phase currents but also the three-phase voltages of the motor. The output of the observer is the estimated DC link current, which is reconstructed from the switching control signals and the estimated three-phase currents. The estimated DC link current and the measured DC link current are subtracted to generate an error term that can be used to correct the estimated voltages and the currents. In comparison with the observers in [19,20], the observer in this paper has two improvements: • A three-phase inverter consisting six switching devices and six diodes can create seventy-two possible switching states. The observer proposed here can reconstruct the DC link current under all of the seventy-two states. • The error between the measured DC link current and the reconstructed DC link current is used to compensate the DC link voltage. Hence the observer can not only estimate the voltages and the currents accurately at any operation condition but also compensate the parameter variations in the motor. 4. THE COMPLETE INTELLIGENT DRIVE SYSTEM The complete motor drive consists of the rotor position estimator and the current/voltage reconstruction sections. Figure 1 shows the block diagram of the drive system. If the DC link voltage of the inverter is constant, the drive requires only one current sensor that is used to measure the DC link current. As explained above, the state observer estimates the phase voltages and the phase currents of the motor from the switching control signals, the rotor position and the speed. The estimated three-phase currents reconstruct the DC link current by using the switching control signals. Then the error between the reconstructed DC link current and the measured DC link current is used to correct the estimated voltages and the currents in the drive. Figure 1: The complete block diagram of the intelligent motor drive system Using these estimated voltages and currents, the rotor position and the speed can be predicted from Eqns.14. The predicted rotor position and the speed data are fed back to the state observer for the conventional control purposes, which are utilised in the speed controller, in the reference current generator and in the current controller (hysteresis or PWM). 4.1 LabVIEW Based Simulator In order to demonstrate the validity of the method, a complete drive simulation is implemented. The simulation software is written in LabVIEW [21]. The Fig. 2 shows the programming block diagram of the simulator. Figure 2: The block diagram of the simulation virtual instrument (VI) of the simulation. t o r q u e