IEEE Industry Applications Society Annual Meeting New Orleans, Louisiana, October 5-9, 1997
Maximum Torque Control of a Sensorless Synchronous Reluctance Motor Drive Milutin G. Jovanovi´c∗ and Robert E. Betz† Department of Electrical and Computer Engineering, University of Newcastle, NSW 2308, Australia TEL:∗ +61-49-215963; † +61-49-216091; FAX: +61-49-216993 E-mail : ∗
[email protected]; †
[email protected] WWW: http://www.ee.newcastle.edu.au/staff-info.html Abstract– The algorithmic structure of a vector controller capable of high quality speed control of a synchronous reluctance motor with and without the use of a rotor position sensor is presented in this paper. The controller is based on a conventional saturated machine d-q model. Its main merit is that it can be operated in a sensorless control mode by executing a new, very accurate parameter dependent algorithm for on-line estimation of rotor position and speed. The excellent performance of this scheme under maximum torque per ampere control is demonstrated by simulation and experimental results.
I. INTRODUCTION
S
IGNIFICANT research advances have been recently made and numerous methods developed to control the inverterfed cageless synchronous reluctance machine (Syncrel) without a shaft position sensor [1–6]. Unlike the induction machine, the Syncrel is very suitable for sensorless operation down to zero speed owing to its salient nature and consequent inductance variations with rotor position. It should be noted however that although a sensorless Syncrel drive is more cost-effective and mechanically robust, there is a control performance trade-off compared to the sensed drive. Furthermore, sensorless control is usually complicated to implement in real time and only a few experimental schemes have been reported in the literature [3–6]. All rotor-oriented sensorless control systems rely on various techniques for estimating the rotor position and speed from a knowledge of inverter switching ripples on the current waveforms [2,3,6] or rotational voltages induced in the windings [1]. These two concepts were used in the Kalman filter based algorithm presented in [4] to obtain optimal estimates at low and high speeds respectively. A high performance controller implementing the torque vector control (or direct torque control) principle [7] was proposed in [5]. In contrast to the previously considered schemes, control was flux-oriented and therefore it was rotor position independent. Speed estimates were derived from the flux phasor position and unlike [7] no shaft speed sensor was needed. The final paper of interest [8] describes a versatile sensorless algorithm originally designed for induction machine drives. Its main merit is the potential applicability to all salient ac machines.
The major contribution of the work presented in [3, 5, 8] is the development and practical implementation of robust position estimation techniques independent of machine parameters and loading conditions. The advantage of the control algorithms in [4, 8] is that they allow satisfactory speed control over the whole range, in contrast to those in [3] and [5] whose application is limited to low and high speeds respectively. It should be noted however that the validity of the technique proposed in [8] has been confirmed on induction machine tests, but not as yet on the Syncrel. The limitations of these control algorithms are : (a) relatively modest electrical position estimation accuracy of approximately 10◦ [3, 4]; (b) low estimate update rate and hence poor control performance [1]; (c) the use of special switching procedures to force the inverter into a desired diagnostic state in order to carry out measurements relevant for estimation [1, 4]; (d) applicability restricted to light loading conditions of the machine [4]; (e) closed-loop speed control not achieved [3]; and (f) an injection of special high frequency signals which required substantial filtering and relatively complex controller design to generate position estimates [8]. This paper presents an angular velocity observer based sensorless controller for the Syncrel. Simulation and experimental results for the maximum torque control algorithm are presented for a 5.8-kW axially laminated prototype. A real time software implementation of this novel viable sensorless control scheme was considered in our previous work [6]. The algorithm was confirmed by tests to have several advantages over its counterparts [3–5] the most significant being the substantially higher position estimation accuracy over the entire speed range of the machine including standstill. However in [6] only the high quality control at low speeds was demonstrated. It is the objective of this paper to address some design aspects of a digital controller and experimental system hardware used and to verify the high control performance from zero to rated speed of the machine.
II. SENSORLESS CONTROLLER The vector control system for the Syncrel is shown schematically in Fig. 1. The machine speed can obviously be controlled in both the sensed (using a shaft position encoder) and sensorless mode. This feature is certainly a significant advantage of the controller. It uses a standard saturated machine Park’s d−q model (with the rotor d-axis being adopted as a high permeance axis) for position estimation and control prediction [6].
the state variables (idm , iqm , ωm , θm ) to be stored over each of the switching intervals (usually four per control interval). Note that the sampling in the simulation is simultaneous, but in the real-time case it is not due to hardware limitations. Position Estimator - This is based on a new, parameter dependent estimation technique presented in [6]. It firstly evaluates a value of the rotor electrical angle for each of the inverter leg switching instants corresponding to the previous control interval, using the current samples (iam and ibm ) and the average dc link voltage (Vdc ) as shown in Fig. 2. Of these four estimates, it selects the one (θest ) with the minimum absolute variation from the observer’s last prediction (θref ). The best raw estimate (θest ) is further processed through an angular velocity observer to obtain a resultant filtered value (θ) which is then used in the control procedure in the next control interval. Details of this process and observer tuning rules (clearly a key factor in the controller high performance) were discussed in [6].
Fig. 1. Syncrel Experimental Controller Fig. 2. Sensorless Scheme
The control algorithm is implemented entirely in software using floating point arithmetic as described in [6]. The code was derived from a computer simulation program written in ‘C’ language. The main components of the simulation and the real-time software are similar. Note however that although the control scheme is virtually the same as that simulated, significant structural changes were made to adapt the simulation program for the real time use. These modifications were considered in [6] and will not be repeated here. The functionality of the major control blocks in Fig. 1 (with the control selector in the position “sensorless”) is as follows. The corresponding functions are presented mainly in the order of execution in the real-time control interrupt service routine [6] (which is the main loop of the simulation program). Averager - Once samples of the previous control interval stator currents (iam and ibm ) are available (see Appendix), their average values (ia and ib ) are calculated in order to determine the corresponding dq currents used for control prediction. The dc link voltage samples (Vdcm ) are also averaged to help filter out noise effects. In the simulation, iam and ibm (Vdcm is assumed constant and equal to the value in a real system) are derived from the solutions of the model differential equations obtained by using a conventional 4-th order Runge Kutta algorithm with an adaptive step size [9]. This algorithm is adapted to allow the intermediate values of
Current Calculator - Computes the average dq currents (id and iq ) from the corresponding phase currents (ia and ib ) by applying a Park’s transformation for a machine with no neutral connection : ia √ cos θ sin θ id (1) = iq − sin θ cos θ (ia + 2ib ) / 3 The d-axis position (θ = θref ) used in the above expression is predicted by an observer in the previous control interval. Ld look-up Table - Contains the stored values of the static and incremental d-axis inductances of the machine 0 (Ld and Ld = dLd /did ) derived from the measured saturation curve Ld vs id [6]. The q-axis inductance (Lq ) is assumed constant in the calculations as the q-axis flux path is dominated by air. Torque Estimator - Generates the electromagnetic torque value to be passed into the velocity observer by using a conventional d − q model equation for a 4-pole machine : τ = 3(Ld − Lq )id iq . Velocity Observer - A closed-loop load model based observer algorithm [10] accurately estimates the rotor electrical angular velocity (ω) and predicts the position (θ) in the next interval. The observer is corrected via a feedback loop (Fig. 2) using the most accurate raw position estimate (θest ) and an observed θ from the previous control interval (θref ).
iqp = iq +
ud −Rid +ωLq iq ∆ 0 Ld (id )+Ld (id )id uq −Riq −ωLd id ∆ Lq
) (2)
where ∆ ≡ time of one control interval and the dq voltages (ud and uq ) are the outputs of the feedforward current controllers (to be discussed in the following) evaluated in the previous control interval. Angular Velocity and Current Control Loops - These are conventional PI algorithms with anti-windup on the integrators. A speed regulator calculates the desired electromagnetic torque of the machine (τd ) in the following control interval. The torque limit at rated current is set to a value precomputed using Matlabr. The current controller (one for each rotor axis) calculates the dq voltages (ud and uq ) to be applied to the machine terminals to generate τd . It uses circular voltage limiting which allows a maximum volt√ age magnitude of Vdc / 3. Current Reference Generator - Identifies the minimum dq currents (idd and iqd ) required for the machine to develop τd . These are fed as reference inputs to the corresponding current regulators. The saturated d − q model optimal idd vs τd characteristic was obtained using Matlabr and stored in a look-up table. State Feedback - Allows decoupling of the current regulators from the machine rotational voltages by generating and adding the countervoltages udsf = −ωLq iqp and uqsf = ωLd (idp )idp = ωLdp idp to the regulators unconstrained output [11]. In a real control system, the effectiveness of this block is obviously subject to the model quality and the accuracy of both the machine parameter knowledge and speed (position) estimates. The resultant voltages from the current controller (ud and uq ) are fed to a PWM generator in order to determine the appropriate switching pattern and switching times of inverter legs. PWM Generator - Implements a conventional space vector based PWM algorithm with double edged modulation [12] and inverter dead-time compensation [13] (this is set to zero in the simulation). The appropriate timers on the control signal generation board (see Appendix) are programmed to produce the required PWM waveform. The generated control signals are then transferred to the inverter hardware as shown in the Appendix.
MACHINE SPEED 1500 dashed - speed reference solid - speed 1000
Speed [rpm]
idp = id +
pling rate of 38-kHz and a dc link voltage of 600-V (rectified 415-V, 50-Hz mains voltage) were assumed. Fig. 3 shows the observed speed of the machine and the corresponding estimation errors. The latter represent the absolute variations from the correct numerical solutions of the model equations. It can be seen that the speed characteristic is very smooth with no ripples, and more importantly it exactly follows the desired trajectory. The speed reversal occurs in approximately 1.4-s with no overshoot. This time can also be predicted from the load model equation considering that the machine is developing the maximum torque in this period. The excellent observer performance and high estimation accuracy are clearly demonstrated in the bottom plot. The maximum error during transients is only about 2-rpm and less than 1.5-rpm in steady speed.
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Current Predictor - Predicts the machine control currents (idp and iqp ) using a simple Euler’s approximation of the current differentials in the model voltage equations :-
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III. SIMULATION ANALYSIS This section presents computer simulation results for the maximum torque per ampere strategy applied to an unloaded (inertially loaded) Syncrel whose specifications are given in Appendix. In order to emulate the situation in a real system (see Appendix), a control frequency of 2-kHz, current sam-
Fig. 3. Estimated speed and estimation errors from simulation
The average torque produced by the machine when changing the speed between ±1000-rpm is plotted in Fig. 4. The actual torque accurately tracks the reference values. Slight
at the speed reference change instants. This phenomenon is also visible in the experimental curves (Figs. 8 and 9) and results from maximum voltage being applied to the machine. D-AXIS CURRENT 14 solid - controlled dashed - desired 12
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d-axis current [A]
deviations under transient conditions when the machine is fully fluxed are due to control current prediction inaccuracies and consequent errors in the machine applied voltages. The prediction errors and torque ripple (resulting from inverter switching) are larger at higher speeds and currents (hardly visible in the figure due to scaling) because of the increased influence of rotational voltages. In steady-state, on the other hand, the actual torque characteristic is fairly smooth and the quality of control is much better despite the high speed. This can be explained by the more accurate control prediction as there is no flux and therefore no induced voltages in the unloaded machine (it should be noted here that windage and bearing friction are ignored in the simulation).
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Fig. 4. Simulated Torque Performance -10
Fig. 5 plots the machine dq currents corresponding to the speed and torque operating characteristics presented previously. Note the close similarity between the q-axis current and torque waveforms. This is expected as the current in the low permeance q-axis has a faster response compared to the d-axis current and as such determines the machine dynamics. The d-axis current, on the other hand, essentially serves to set up the flux in the air-gap and unlike the q-axis current is always positive regardless of the torque sign. The excellent torque performance is verified by the results shown in Fig. 5. There is obviously a good agreement between the controlled and desired currents. The effects of control prediction errors are clearly visible during transients at high speed as in Fig.4. The variations of both the reference and actual current waveforms from zero values (the ripples are higher in the q-axis currents due to the lower inductance) at constant speed are due to slight drifting of the machine speed from 1000-rpm and consequent fluctuations of the torque command output from the PI regulator (refer to Fig. 4). These minor control inaccuracies are mainly caused by the noisy speed feedback estimates (see Fig. 3). Also, one can notice spikes in the actual current and torque waveforms
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Fig. 5. Machine dq currents - simulation results
IV. EXPERIMENTAL RESULTS The following plots are experimental results obtained for an inertially loaded Syncrel prototype using the maximum torque per ampere sensorless control algorithm shown in Fig. 1. In order to verify the controller performance, an additional observer algorithm (not shown in Fig. 1) identical to that used for the sensorless control is executed. Its only function was to predict the actual machine angular velocity using a 10bit absolute encoder output as its input. This observer had nothing to do with the sensorless control procedure in any other way. It should be also mentioned that the machine torque transient response could not be recorded on the oscilloscope for the reasons discussed in Appendix. However, the steady-
SPEED REVERSAL WITH INTER-PERIOD AT STANDSTILL 1500
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state torque predictions from the saturated dq model were fairly accurate as the test Syncrel had small iron losses. This is illustrated by the plots in Fig. 6 generated for a fully loaded Syncrel being controlled in a sensor control mode without speed feedback (Fig 1). The machine current magnitude was maintained at its rated value whilst the current angles were varied on-line. The speed was adjusted by changing the torque of a DC load machine (refer to Appendix). Fig. 6 shows a good agreement between the measured and estimated torque characteristics around the optimal current angle of approximately 60◦ (≈ 58◦ predicted). Therefore, it is reasonable to assume that these curves will also correspond well under transient conditions as the machine is mainly operated at the maximum current. Note from the same figure that the torque reduction at 1500-rpm, which results from torque control without iron loss compensation [14], is not significantly different from that at 300-rpm.
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Fig. 7. Experimental Controller Performance Fig. 6. Torque performance of fully loaded Syncrel
The high performance of the sensorless controller over a wide speed range including standstill is demonstrated in Fig. 7. At higher speeds the observer and speed controller PI gains can be increased as the accuracy of position estimates is better (for more detail refer to [6]). This allows rapid convergence of the control algorithm and much faster transient response compared to that obtainable at low speeds [6]. In addition, the quality of control is improved as there is no overshoot at all. It can be seen that the machine reaches a speed of 1000-rpm in about 1-s which is somewhat slower than predicted from the simulation studies (≈0.7-s). Another important observation about Fig. 7 is the smooth and stable machine operation down to zero speed. The controller effectiveness is also evident from the machine dq current and estimated torque waveforms shown in Figs. 8 and 9. These correspond to a changing speed reference between ±1000-rpm and zero (Fig. 7). Notice that the measured currents in Fig. 8 represent the actual values
and not the sensorless control variables. In contrast to this, the torque characteristics in Fig. 9 were not measured (as mentioned earlier) but were derived from measurements of rotor position and phase currents using a conventional torque expression of the machine model. Two immediately obvious observations about Figs. 8 and 9 are (1) the very noisy waveforms obtained at rest and (2) the non-zero current (torque) values at 1000-rpm. The noise is expected as the position estimation accuracy and observer performance deteriorate at low speed [6]. The control algorithm however is still sufficiently accurate to allow the machine speed to be effectively controlled even at standstill (see Fig. 7). It can be seen from Figs. 8 and 9 that despite the ripples, the average value of the q-axis current and torque are close to zero at rest as expected. Slight variations still exist (d-axis currents are a few amps in an average sense) and are mainly due to minor speed control inaccuracies. The resulting torque reference value from the PI controller is however insufficient to overcome the bearing friction and move
DESIRED d-axis current
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Fig. 8. Machine dq currents while varying the speed between ±1000-rpm and zero
the rotor. It should be noted that the effects of noisy estimates are also present in the simulation. However, in the real time implementation one has additional influences such as noise and quantization error in the measurements coupled with temperature drift in the Hall-effect transducers (see Appendix). At high speeds the sensorless algorithm performance is less sensitive to current measurement noise, and the position estimates are more accurate and the quality of control is substantially better [6]. The current and torque pulsations at 1000-rpm are consequently much less compared to those at standstill as illustrated in Figs. 8 and 9. Also, it can be seen from Fig. 8 that the average dq currents are approximately equal (≈2-A) which means that the current angle is near the ideal optimum i.e. 45◦ . This is expected since the machine is unloaded (and hence unsaturated) and has low iron losses. On the other hand during the transients, the machine is fully fluxed and the q-axis current is considerably larger than the d-axis current. The current angle has been increased above 45◦ (≈ 60◦ ) to maximise the machine torque in the presence of saturation (Fig. 6). Fig. 7 clearly illustrates the smooth and accurate speed control in these periods. Therefore, the test Syncrel is accurately controlled so that the torque per ampere is optimised under all operating conditions.
V. CONCLUSIONS The main contribution of this paper is the presentation of practical implementation aspects of a new sensorless digital controller for the Syncrel. The high performance of this implementation has been confirmed by both computer simulation and experimentally over a wide range of speeds (down to zero) using a 5.8-kW axially-laminated machine. The results presented have illustrated the superiority of this sensorless scheme compared to other existing algorithms in terms of quality and accuracy of speed control. Smooth response, using a maximum torque per ampere control objective, has been demonstrated during starting, speed reversal and standstill. It should be emphasised that the results have been generated for the inertially loaded machine. The steady-state optimum torque performance of a fully-loaded Syncrel under sensorless control will be considered in a future paper. APPENDIX EXPERIMENTAL SYSTEM HARDWARE Fig. 10 shows the physical configuration of the test rig. The torque transducer (Torquemaster from Vibro-Meterr in Switzerland) has a torque rating of 100-Nm and a peak transient capability of 200-Nm with a specified accuracy of 0.1-Nm. The signal conditioner and digital display unit carry out the torque and speed signal processing and allow the torque, speed and calculated power values to be displayed
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Fig. 10. Research Test Facility
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Fig. 9. Syncrel torque response to a changing speed reference between ±1000–rpm and zero
both digitally and as analogue signals. A nice feature of the transducer is the excellent frequency response (≈1-kHz), making it suitable for transient testing. Unfortunately, the current design of a test system made it impossible to record the machine torque dynamic response on a digital oscilloscope due to very noisy analog output signals from the transducer display unit. This noise resulted from capacitive earth-leakage currents (induced by inverter switchings) flowing via the machine bearings, shaft and finally through the transducer housing. At one stage these currents erased the non-volatile RAM settings in the signal conditioner’s electronics. The transducer is connected to the load machine and the Syncrel via special, low resonance couplings. In order to protect the transducer from damage due to large transient torques, the taper lock couplings are fitted with shear pins rated below its peak torque. The load machine side of the transducer has a brake mounted to allow the shaft to be clamped in a desired position so that the locked rotor tests
can be conducted. The DC load machine has a through shaft enabling the attachment of a 10-bit absolute position encoder. It is fed from a Ward-Leonard based DC supply. This traditional configuration was chosen since the machines required for the implementation were available and because it allowed simple regeneration back into the three phase mains. The test machine is a 5.8-kW inverter fed Syncrel having a conventional 7.5-kW induction machine stator of DF132M frame size and a cageless axially-laminated rotor. A 10-kW IGBT inverter (for more detail refer to [6]) and the rotor were designed and built in the Department workshop. The transistor firing is controlled from a main control computer. The rotor was constructed based on a 7.5-kW Syncrel design from the University of Glasgow in Scotland [15]. Its design was not optimal, only allowing the machine to produce a maximum shaft power of about 5.8-kW at 1500-rpm with rated current. One of the main reasons for relatively modest output capability was the small air-gap (0.48-mm as compared to 0.517-mm in [15]). In addition, due to difficulties in obtaining 0.5-mm grain oriented steel laminations in Australia, standard 0.35-mm laminations were used instead, resulting in less steel being present in the rotor. Consequently, it has lower iron losses but saturates easier leading to a lower saliency ratio and Ld − Lq for the machine. Some characteristic design and optimum torque performance parameters of the test Syncrel are summarised in the accompanying table. The tests carried out to estimate the machine dq inductances and inertia constant were described in [6]. The heart of the whole test system is an Intelr Pentium 90-MHz processor based personal computer. The advantage
TABLE I TEST SYNCREL PARAMETERS
of using this platform is its low cost and the large variety of software development tools available. The inverter hardware and a 10-bit absolute encoder are interfaced to the CPU bus by means of the two programmable I/O boards with interrupt capabilities - a custom built control signal generation board (Fig. 11) and a commercial 12-bit multiplexed A/D data conversion board (Data Translation DT2821 series). Issues related to design and functionality of these boards were addressed in [6].
[2] [3]
Fig. 11. Control Signal Generation Board
Hall-effect transducers (HEME’s) and precise potential dividers are used to measure the machine currents and inverter dc link voltage. Analogue measurement signals from the system are sampled and transferred to the PC’s memory using DMA (for more detail refer to [6]). The hardware has been designed so that all important measurements are isolated and have a bandwidth of about 40-kHz. This allows simple connection of data acquisition equipment and oscilloscopes.
[4]
[5] [6] [7] [8]
ACKNOWLEDGMENT The authors would like to acknowledge Mr.Tim Wylie who constructed much of the experimental system hardware, Dr.Brian Cook who was involved in the inverter design, and Mr.Peter McLauchlan and Mr.Russel Hicks who built the Syncrel rotor. REFERENCES [1]
M.S.Arefeen, M.Ehsani, and T.A.Lipo, “An analysis of the accuracy of indirect shaft sensor for synchronous reluctance motor,” IEEE Transactions on Industry Applications, vol. 30, no. 5, pp. 1202–1209, September/October 1994.
[9] [10] [11]
[12]
[13]
Power Torque Voltage (rms) Current (rms) Current angle Speed Poles
5.8-kW 37-Nm 415-V 14.3-A 60◦ elec 1500-rpm 4
Ld unsaturated Ld saturated Lq Ld /Lq unsaturated Ld /Lq saturated Inertia constant Rdc (cold)
88.9-mH 76.8-mH 9.8-mH 9.1 7.8 0.23-kgm2 0.6-Ω
Stator slots Air-gap Rotor diameter Rotor length Insulator thickness Lamination thickness Lamination-insulation layers Pole arc Pole piece
36 0.48-mm 126-mm 175-mm 0.38-mm 0.35-mm 43 120◦ elec brass
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