~~ ~ - ~~~ - SPEED SENSORLESS F'ELD ORENTED CONTROL OF A CS-FED NDUCTON MOTOR BY A TRANSPUTER BASED DGTAL CONTROLLER K J Talbot C E Kleinhans G Diana R G Harley Department of Electrical Engineering, University of Natal, Durban, 4001, South Africa Abdmct- This paper presents a method of speed estimation for a CS-fed induction motor under FOC (Field Oriented Control) which is based on the principle that as the machine is current fed, the rdor speed is proportional to the terminal voltage and the rotor flux linkage. Results of simulations performed using CASED (Computer Analysis and Simulation of Electrical Drives) where the speed estimate is used in the speed feedback loop are presented. Results of the practical implementation on a transputer based controller are also presented showing the practicality of applying Speed Sensorless Field Oriented Control to a CS-fed induction motor (M). speed related harmonics. Because the current waveforms are near sinusoidal in the case of a VS-M, spectral analysis provides harmonics that are clean enough to use. However, in the case of a CS-fed M, blocks of current are fed into the motor, thus introducing unwanted current and voltage harmonics as well as commutation voltage spikes. This noisy voltage waveform would therefore be difficult to analyse for speed related harmonics. A further consideration is the time needed to form the speed estimate. Reference [6] reports a delay of five to ten seconds, rendering this method unsuitable for FOC and in fact for any closed loop controller.. NTRODUCTON CS fed induction motor drives (not to be confused with current regulated VS fed drives) have certain advantages over VS drives, whch become particularly attractive in high power level four quadrant drives. However the dynamic performance of the traditional constant V/f controlled CS drive has not compared favourably to the Vlf VS drive, and most certainly not to that of the Field Oriented Controlled (FOC) VS drive. n many applications the CS drive operates adequately without a tacho if good dynamic performance is not important. More recently, FOC has been applied to CS drives as well, although the tacho again becomes an essential component thereby detracting from the robustness of the CS-fed motor. While fewer CS drives are being installed than VS drives, existing CS drives (traditionally without tachos) could be converted to FOC drives with speed estimators to eliminate the addition of tachos and thereby to benefit from the improved dynamic response of FOC. n VS drives much attention has been paid to applying FOC without a tacho (so-called speed sensorless drives) [ 1-71, but relatively little effort has been directed to developing a sped sensorless FOC controller for a CS drive. The VS speed estimation techniques can be fall mainly into two groups, the Model Reference Adaptive System (MRAS)[ 1-31 and the speed measurement via current harmonics [4-6]. Those techniques that use the current harmonics are based on the principle that rotor slotting and eccentricity give rise to speed dependent harmonics in the current waveform. A notch filter that moves with the supply frequency then filters out the main supply fundamental, thus making it possible to examine the 0-7803-2730-6/95 $4 00 0 1995 EEE 785 The MRAS techniques of speed estimation assume that the motor is under FOC at all times while the transient response is slow in comparison with the required closed loop speed response [7]. Moreover, these techniques also suffer from a significant steady state error. The technique proposed by [7] had not been practically tested for closed loop FOC, and in addition it assumed that the electrical frequency was known, which, in the CS, could be a problem at low speeds. Although other papers exist which do not fall into the above two categories, all are specific to the VS. This paper proposes a simple yet reliable method of estimating the rotor speed from measurements of stator voltages and currents for the CS-fed inverter under FOC. The simulation environment CASED [8] is used to simulate the entire rectifier, inverter, the FOC control circuits, the motor and its load, as well as the speed estimation algorithm. The estimated speed is supplied to the speed controller, in other words, the SPEED ESTMATOR is fast enough to use on line as the actual feedback signal which controls the motor. Many existing speed estimation methods require complex signal processing and might be too slow for insertion into the feedback loop.. THEORY Since the machine is current fed, the voltage can be regarded as an output of the machine. This voltage is dependent on the speed of the machine and the rotor flux linkage. Under FOC, the induction machine can be equated to a separately excited DC machine, which has the following voltage equation - -. -~
where E is the magnitude of the voltage, 0 is the flux linkage of the machine, w is the rotational speed and K is a machine constant. using eqn (5) for positive speed, the synchronous reference frame will be aligned correctly, thereby greatly improving stability. For the induction motor, With eqn (5) providing the appropriate value of electrical angle to eosure FOC, the speed estimate is only required for the speed control. Therefore under FOC, the slip frequency can be calculated from On rearranging eqn (2), the induction machine equations in the d q reference frame are as shown in eqn (3), where the numerator is the induced emf providing the similarity with eqn (1). where U, R is the electrical speed, is the magnitude of the stator voltage vector, is the stator resistance P is the magnitude of the stator current vector, is the differential operator, is the magnitude of the stator flux linkage vector and L 'm a-1-- (4) 41 L22 An important variable in maintaining FOC is the electrical angle de, which determines the position of the synchronous d- q reference axes. The speed estimate could be considered to calculate this electrical angle, but the speed estimate would have to be extremely accurate otherwise any error would be integrated thereby causing an unstable situation where FOC would be lost. Because of the excessive noise on the voltage of the CS-fad M, this accuracy is not easily obtainable, thus yielding incorrect positioning of the very synchronous reference frame on which the speed estimation was based in the first place. To avoid this situation, this paper proposes that the electrical angle is calculated (via the use of the alphabeta voltages) independently of the speed estimate. This calculation is based on the converse of the fact that under FOC, if the rotor flux linkage is aligned with the d-axis, the stator emf is aligned with the positive q-axis for positive speed, and the negative q-axis for negative speed. Hence, by (3) and thus the estimated instantaneous rotor speed is then calculated at every sampling instant by subtracting this value of sw, from the value of we found in eqn (3). The rotor flux linkage is positioned on the d-axis, resulting in zero q-axis rotor flux linkage as defined by the conditions of FOC, and is calculated as (7) As a measure of whether or not the controller is holding FOC, the q-axis rotor flux linkage can be calculated from the stator quantities as follows and this flux linkage should be zero, but due to parameter variation and an incorrect speed estimate, a build up in this flux linkage is possible. With the use of eqn (9), this build up of flux linkage can be taken into account and incorporated into the calculation of the d-axis rotor flux linkage as follows The final variable needed in order to calculate the electrical frequency in eqn (3) is the stator flux linkage whose components are calculated as follows (9) 786
Lm, - al,i, + +* Ln Once the emf's in the a,@ reference frame have been found and filtered, eqn (5) is used to calculate the electrical angle 0, which forces the drive to be under FOC. 0, is then used in the Park Transform and in the calculation of the demanded current vector angle calculation. B. Park Transform and Emag Calculator The equations preseoted above are then used in the controller as shown in Figs. 1 through 3 which are discussed in the following section. 111. SPEED SENSORLESS CS SYSTEM A block diagram of the speed sensorless CS-fed M appears in Fig 1. This system samples the M stator voltages and currents, computes the necessary firing signals for the rectifier and inverter and outputs these firing signals to the relevant thyristors. The control algorithm outside the dotted line area in Fig. 1 has been presented previously [8], (but then a tacho speed signal was used in the flux and angle calculator and in the speed controller) and is not discussed in this paper. This paper is concerned with the parts inside the dotted line area in Fig. 1 and these are described in more detail in the following subsections. A. lhetae Calculator The block labelled ThetaE Calculator in Fig 1 is expanded in Fig. 2 to illustrate the steps followed during each sampling period. Two line voltages and two line currents are sampled, converted to their equivalent a and p values and then via the use of the numerator in eqn (3), the a,@ emf s are calculated. t is difficult to compute the derivative-of-current term in eqn (3) without incurring a delay and this introduces an error whenever there is a rapid change in the current as in the case when a commutation spike appears in the terminal voltage. This spike should not appear in the emf's, but due to the above error, a small amount of the commutation spike does in fact appear in the emf's, but this is removed by a filter. Different types of filters were considered with the first being the moving average filter but this filter cannot sufficiently reduce the noise levels without introducing large time delays. Synchronous sampling was also considered but at low speeds when the drive is in PWM, very few acceptable samples can be taken. A first order low pass filter was therefore selected it gives sufficient noise attenuation without creating delays in the pass band which would limit the dynamic control. The filter time constants were chosen so as to ensure that all relationships held, even after filtering had taken place. Because at low speeds the noise to signal ratio is high, filters with a lower cut off frequency were used at the high speeds, when the signal varied at a faster rate. Because the speed estimation is calculated in the synchronous referme Erame, the ubc voltages and currents are converted by the Park Transform to their equivalent d and q variables. The d and q voltages and currents are then passed into the Emag Calculator where the numerator of eqn (3) is used in the calculation of the emf's in the synchronous reference frame. The emf's are passed through a first order low pass filter and into the Speed Estimator. C. lhe Speed Estimator The block labelled the Speed Estimator in Fig. 1 is expanded in Fig. 3 to again illustrate the various calculations in more detail. The Speed Estimator is the most complex of these blocks as the slip frequency, the electrical frequency, the q- axis rotor flux linkage, the magnitude of the stator flux linkage and the rotor speed are all calculated internally inside this block. The external inputs to the block are the d and q axis currents, the OL and p emf s and the rotor flux linkage calculated in the previous sampling period. The electrical frequency calculated (by eqn (3)) in the previous sample is also used in the calculations of this block, but it is calculated internally and is not regarded as an external input to the block. The slip frequency is calculated using eqn (6), filtered, and then subtracted from the electrical frequency, to form the estimated rotor speed. The q-axis rotor flux linkage is then calculated using eqn (8) and exported to the Flux Model along with the slip frequency. D. lhe F lu Model The Flux Model uses eqn (9) along with the relevant inputs to calculate the d-axis rotor flux linkage. Because the CS-fed M is held under FOC via the method used to calculate the electrical angle, the q-axis rotor flux is relatively small, as will be shown later, but in the regions of large slip, if the compensation for q-axis flux build up is not taken into account, a steady state error is found to exist in the speed estimate. V. SMULATON The software package CASED [8] was used to simulate the entire CS drive of Fig. 1 under FOC with the speed estimate used in the speed feedback loop. The motor parameter values appear in the appendix. A step speed 787
-' 3 Y 3- i,! t j! Fig.. Block diagram of the speed sensorless Field Oriented Controlled CS-fed induction motor 788
~ reference of 100 radts is applied to the drive, with the estimated speed in the feedback loop, and the simulated response appears in Figs. 4 through 6. Figure 4 shows the simulated estimated speed against the simulated tacho speed and the tacho signal is the smoother of the two curves. Figure 5 presents the d-axis rotor flux linkage that is present in the machine; the lower of the two curves during runup is the d-axis rotor flux linkage (eqn (7)) when the q-axis rotor flux Wge is assumed to be zero, and the upper curve is the d-axis rotor flux linkage when the small q-axis rotor flux linkage is taken into account (eqn (9)). Allowing for the small q-axis rotor flux linkage yields an improved speed estimation in the regions of large slip. The actual value of the q-axis rotor flux linkage, (calculated as per eqn. (8)), is shown in Fig. 6 (smooth curve due to filtering) and is compared with the q-axis rotor flux linkage that is calculated in the simulation model of the machine. The relatively small nature of these q-axis flux linkages indicates that the machine is in FOC. The FOC controller and speed estimator is written in C in the CASED simulation and is compiled using the NMOS C toolset for the transputer controller; this eliminates the need to write new code when going from the simulation to the implementation. V. HARDWARE AND PRACTCAL RESULTS Two T800 transputers were used in order to execute the control and speed estimation algorithm of Fig. 1 and to output the control signals to the PWM ASC and thyristors of a 7.5 kw drive. The motor currents were sampled at 4 khz, the voltages at 2 khz and the entire control algorithm ran at 1 khz, corresponding to 40 calculations per shaft revolution at rated speed. Code scheduling and execution times are thus of importance and are implemented well within the hard real-time constraints. The results of two tests are presented, with the first test result in Fig. 7 showing the estimated and actual measured speed of the induction motor with a 100 rad/s step in the speed reference confirming the accuracy of the estimation technique; in Fig. 8 the corresponding rotor flux linkages indicate the presence of FOC as the q-axis rotor flux linkage is nearly zero. The deviation of this flux linkage from zero is primarily due to pamneter variation and the lack of online parameter identification while the different runup times are due to different current limits imposed on the system. n the second test, Fig. 9 shows the actual and the estimated speeds when a ramped reversal in speed is commanded from +SO to -50 rad/s. The estimated speed follows the actual speed relatively closely except for a small difference around zero speed, which is probably caused by small voltages giving rise to small signal-to-noise ratios. Even with this small difference the estimated speed is still sufficiently accurate to maintain closed loop stability during the zero speed crossover. V. CONCLUSON Operating a CS-fed induction motor under FOC gives a better dynamic performance than a traditional constant Vlf controlled CS drive, but needs an accurate speed signal although the tacho detracts from the robustness and cost advantages of induction motors. A reliable speed estimator eliminates the need for the tacho. This paper has therefore described the development and implementation of an alldigital controller for a CS-fed FOC induction machine drive, using a relatively simple speed estimator and an innovative technique of angle estimation. Simulated and measured results have been presented to show that the angle estimator ensures that the drive remains under FOC at all times, while the estimated speed is sufficiently accurate to maintain good speed tracking and closed loop stability during rapid speed transients including zero speed crossovers. ACKNOWLEDGMENTS The authors greatfully acknowledge the assistance of M Randelhoff in determining the transputer execution times, and the Foundation for Research Development and the University of Natal for financial support. APPENDX: MOTOR PARAMETERS R, = 0.4079 ohm; R, = 0.3515 ohm; L,, = L'22 = 141.9 mh; J = 0.59 kg-m2; 11 121 131 141 151 REFERENCES L,,, = 135 mh; Stiction = 1.09 N-m; Tamai S., Sugimoto H. and Yano M. : "Speed Sensor-less Vector Control Of nduction Motor With Model Reference Adaptive System ", EEE Transactions, 1987, pp. 189-195. Schauder C. : "Adaptive Speed dentification For Vector Control Of nduction Motors Without Rotational Transducers", EEE Transactions, 1989, pp. 493-499. Tajima H. and Hori Y. : "Speed Sensorless Field Orientation Control of the nduction Machine", EEE Transactions, 1991, pp. 385-391. Owner R.M., Lorenz R.D. and Novotny D.W. : "Apllication of Non-Linear Observers for Rotor Position Detection on an nduction Motor Using Machine Voltages and Currents", EEE Transactions, 1990. pp. 416-421. Green T.C.. Williams B.W. and Schramm D.S. : "Non- 789
nvasive Speed Measurement of nve-r Driven nduction Moton', EEE Transactions, 1990, pp. 395-398. 161 Hurrt K D, Habetler T G, "Sensorlerr Speed Measurement Using Cumnt Harmonic Spectral Fstimtion in nduction [81 Mach &U", PESC'94, Taiwan, 20-25 June, 1994. pp. 1CL 15. 171 Rubin N.P., Harley R.G. and Dians G. : 'Evaluation of Various Slip Estimation Techniques for an nduction Motor Operating Under Field Onentation Control Conditions', EEE Transactions on ndustry Applicationti, Vol. 28, No. 6, November December 1992. CE Kleinhans, G.Dum, RG Harley, MD McCulloch, M Randclhoff, DR Woodward, "Analysing a CS-Fed Field Oriented Controlled nduction Motor using a New Simulation Package CASED", Conference Proceedinpa of the EEE ndustrial Electronics Society, ECON, 1994, Bolognc, taly, paper ref. No. EPZ37P102. hdroq eqn(6) Fig. 2. A block diagram of the ThetaE Calculator. -jml* Flux Model Fig. 3. A block diagram of the speed estimator. 790
Fig. 4 O f 2 Time (s) Simulated tech0 and estimated speed response with the estimated speed in the feedback loop. Fig. 7 0 0 a 4 e e Time (s) Practical tach0 and speed estimate with estimate in the feedback loop. J 1 1 1 8 1 Fig. 5 d-axis rotor flux linkage with and without q-axis flux linkage Compensation. Fig. 8 d-q Rotor flux linkages for a 100 radls step in reference speed..2 \ v) f 2 go L g-.a D E 4-4 -.e 0 ' Time (s) a Time (s) Fig. 6 Calculated and actual q-axis rotor flux linkage. Fig. 9. Practical ramped speed reversal with the speed estimate in the speed feedback loop. 79 1