TORQUE CONTROL OF AC INDUCTION MOTOR TRACTION DRIVES WITHOUT FLUX OR SPEED MEASUREMENT DEPENDENCY
B. J. CARDWELL BRUSH ELECTRICAL MACHINES - LOUGHBOROUGH U.K.
(Dr. Cardwell is now a traction consultant for Cecube Ltd.*)
The wide variation of induction motor characteristics with temperature, coupled with unpredictable track and load conditions, make the inclusion of closed loop tractive effort control essential wherever there exists a requirement for repeatability and predictability of performance. Such a requirement is often necessary on rapid transit systems and multiple unit operations. In particular the variation of rotor resistance (typically 50% over normal operating conditions) will result in tractive effort variations. Open loop control methods require measurement of individual wheel diameters, in order that the inverter frequencies may be compensated to maintain equal output torques. The alternative would be to keep wheel diameters matched. Open loop schemes also suffer the risk of motor torque pull out.
For many years methods have been proposed for closed loop control of voltage sourced, inverter fed (vsi) motors. The major area of interest has been the development of vector control technology. The concept of field orientation as proposed by Blaschke (1,2) is a method of controlling AC machines by transforming their dynamic structure into that of a conventional separately excited DC machine.
An induction motor represents a complex control plant because of the intricate coupling between the external control inputs of voltage and frequency, and the internal quantities of rotor current, flux and torque. By defining the flux axis as a reference, vector control independently regulates the stator current flux current and its orthogonal component to control the torque level. Two main techniques exist to achieve this: (a) by flux measurement (involving flux sensors) and (b) by slip control (involving accurate speed measurement). Method (a) may also be effected by flux estimation derived from measured stator voltage and currents (Gabriel (3)), but this results in significant performance degradation. Method (b) eliminates the need for a flux sensor because the flux phase is determined from integrating the sum of the slip and motor angular frequencies (Nagase (4)). Consequently, high precision rotor speed measurement is necessary.
With both techniques a complex control strategy results, without eliminating the need for flux or accurate speed sensing, both of which are undesirable in a traction environment. The torque control scheme described here requires only peripheral measurement of instantaneous DC link power, yet has a dynamic performance similar to that of simplified field-orientated systems and is achieved with a reduction in control complexity. The proposed method of direct torque control bears similarity in principle to that described by Hajdu and Jardan (5), although developed independently, and is ideally suited to non-DSP microprocessor implementation.
THE PWM OPTION
A central component of any voltage sourced inverter control scheme is the pulse width modulator (PWM). It has to exhibit low harmonic generation if the PWM-vsi is to have significant advantage over a current fed inverter. To achieve this, a harmonic elimination PWM strategy has been adopted (Patel (6), Buja (7)). One feature of harmonic elimination is that in minimising motor harmonics (which reduces motor heating and torque ripple) an optimum lineside harmonic distribution is effected.
The predictable appearance of lineside harmonics (which occur at the sixth harmonic frequency and multiples thereof), enables their positioning in a frequency band compatible with the signalling system, by the appropriate choice of PWM carrier frequency. An extensive steady state analysis of harmonic elimination has already been performed by Taufiq, Goodman and Mellitt (8). It points out that a further advantage of harmonic elimination is that the maximum value of the fundamental component, before reaching minimum pulsewidth limits, is much higher than with either the natural or regular sampled PWM schemes.
By employing a harmonic elimination / spectral placement technique, a satisfactory steady state performance from the PWM is achieved without recourse to a pre-conditioning chopper. However, under maximum acceleration and braking conditions, similar to those experienced on modern rapid transit systems other effects become important. These include the natural resonance and damping of the line filter circuit, and critically the rate of updating voltage (modulation depth) and frequency demands to the PWM. If the PWM demand is updated only once per inverter cycle (to allow time for computation of new waveform segment) then at least two phases will always experience a frequency change at a point on the waveform not corresponding to zero phase. This results in a DC offset appearing on the current in these phases (see fig. 1), which reduces the achieved torque of the motor and causes the appearance of a major lineside component at the inverter fundamental frequency.
Hence, it is necessary to update more regularly than this, and a multiple of three times a cycle represents a suitable symmetric rate. Unfortunately this increases the real-time PWM processing requirement by a factor of at least three. The PWM will also need to sample the demand at a frequency dependant rate, which has consequences for the outer control loop.
THE TORQUE CONTROL SPECIFICATION
The torque controller operates in steady state on a constant flux magnetisation law until full modulation is achieved, corresponding to the flux being limited by supply volts. However, the controller permits wide deviations from the law under transient conditions, bringing the whole of the volts / frequency plane into use. This is essential if a well behaved, jerk free controller is required. The following list of requirements was included in the specification of the control scheme.
i. To be capable of controlling more than one motor from each inverter
ii. No speed or flux sensors necessary
iii. The resulting software to be able to drive motors with a wide power rating range
iv. Good accuracy of achieved torque
v. Bandwidth greater than 5Hz
vi. The detection and correction of wheel slip / slide
vii. To interface with a variable sampling rate harmonic elimination PWM
viii. To prevent torque pull out
As a result the controller should provide smooth starting, and restarting from coasting periods and rail gaps, under jerk rate limited demands.
The control loop schematic is shown in fig. 2, and the design is based on the Steinmetz model of the induction motor.
The torque developed, can be estimated from the following equation:
T = n(Vfilt Ilink - Pstator) / (6.2832*f)
where Vfilt = filtered link voltage
Ilink = link current
Pstator = estimate of stator loss
f = instantaneous inverter frequency
n =number of pole pairs.
To prevent interaction of link voltage ripple with the controller a 4th order infinite impulse response (lIR) digital filter operates on the instantaneous link voltage. The passband of the filter has to be comparable to the desired bandwidth of the controller, but must also have significant attenuation at the line filter resonant frequency.
The transfer function of an induction motor and closed loop torque control can be approximated by fig. 3. if the rotor leakage reactance is ignored. For operation at constant flux the transfer function of the motor becomes linear. The remainder of the loop consists of the controller term, G, and the input frequency to torque transfer function, A. By a suitable choice of G, the product GA can be linearised and a classical z-plane control approach to the design of the compensation adopted. In this way the order of the control can be designed to give the desired rate of change of acceleration error. Consequently, a suitable controller term is 3rd order, requires frequency dependent gain, and adaptive compensation time constants which depend on load and motor parameters.
The adaptive nature of the controller requires a digital synthesis. The variable update rate of the PWM (typically from 2.5ms to 30ms) will cause beating when interfaced to a controller of fixed sampling rate. From the z-plane analysis of the controller a fixed sampling rate of 5ms was found to be adequate. However, to prevent beat frequencies from being generated at the interface, the control term is arranged such that its final stage is a pure integrator sampled at the PWM update rate. This produces a beat-less combination of digital controller and PWM.
The chosen implementation required a dual processor system with one microprocessor dedicated to PWM waveform generation, whilst the other performed torque control. A synchronisation interrupt is generated by the PWM at its update instants, which activates the torque processor to immediately perform the final integration before passing the new frequency and modulation depth to the PWM processor.
The input to the final integrator of the frequency control term is the frequency slew rate. From knowledge of the torque demand the expected slew rate can be computed, and after adding an operating margin, this provides a slew rate limit. If the slew rate reaches the limit for a period of time and the torque error from the controller exceeds a preset threshold, then wheel slip (or slide) is deemed to have occurred. A procedure to reduce the demand to the controller is then entered to regain adhesion. When the torque error returns again to below the threshold adhesion has been recovered, and the demand can be slowly increased back to the desired value.
The controller enables profiling of achieved tractive effort by the adjustment of input parameters. A reference level determines the maximum demand torque permissible for a particular motor or number of motors in parallel. Corner speeds (frequencies) then define the start of constant power, and power inversely proportional to frequency regions (see fig. 4). This curve defines an envelope of maximum performance. A check is performed in the torque controller to ensure that the motor pull out torque capability exceeds this envelope. If it does not the envelope is dynamically modified in accordance with the torque that may be safely achieved. The torque demand to the controller may then be set at any desired level within the envelope, or in the case of a demand error a safe limiting demand is applied.
A jerk limit is imposed on changes to the torque demand. The jerk rate is a software parameter set to a predetermined value. Load weighing may also be performed on the demand torque when required.
The torque controller gives a mean output torque equal to the estimated torque when following a constant torque demand. When constant power is demanded (see fig. 5) the relatively high loop gain also keeps the following error small (~2%). Any significant deviation of the resultant TE from the demanded value is due to inverter and transmission losses. Where these are known it is a simple matter to compensate the estimated torque accordingly.
Computer simulation results of the system driving a 6 pole, 300kW, traction induction motor, show the controller to have the required bandwidth and response characteristics for traction applications. The controller is well damped (see fig. 6) apart from very low frequencies, where the reduced slope of the induction motor torque / slip characteristic and errors in torque estimation (due to the predominance of motor losses) causes a deterioration in response.
Because of its wide range of operating frequencies the PWM is required to mode change as the inverter frequency changes. Mode changes introduce transient disturbances in the motor current and consequently on the driving TE at the wheel. Compensation in the control loop has resulted in the minimisation of these torque disturbances (see fig. 5), including the disturbance at the transition to quasi-square, which is minimised by this implementation. Finally, because indirect control is imposed on the motor current under transient conditions, the risk of power device failure at start up, or when re-synchronising after a rail gap, is reduced.
A brief review of harmonic elimination PWM techniques is given, and the advantages explained. A method of interfacing this type of real-time computed PWM into the TE control system is discussed, resulting in a computer assessment of achieved performance, and how this compares with the controller specification. This type of closed loop torque control of inverter fed induction motors, requires neither speed nor flux transducers mounted on the motor. Feedback is provided by an estimate of torque, based on a filtered measurement of instantaneous DC link power. The benefits of this control system for multiple unit operation are discussed, including the application of slip / slide control.
1. F. BLASCHKE, 'Das Prinzip der Feldorientierung, die Grundlage fur die TRANSVECTOR - Regelung von Drehfeldmaschinen' Siemens Z vol 45, p757, 1971.
2. F. BLASCHKE, 'Das verfahren der Feldorientierung zur regelung der Asynchronmaschine' Siemens Forschungs und Entwicklungsberichte 1, 1972.
3. R. GABRIEL, W. LEONHARD and C. J. NORDBY, 'Field Oriented control of a standard AC motor using Microprocessors’ IEEE Trans. Ind Appl, vol IA-16, pp186-192, Mar/April 1980.
4. H. NAGASE, Y. MATSUDA, K. OHWISHI, H. NINOMIYA and T. KOIKE, 'High performance Induction Motor Drive System using a PWM Inverter' IEEE Trans Ind Appl, Vol IA-20, pp 1482-1489.
5. E. HAJDU and R. K. JARDAN, ‘Voltage Sourced Inverter Drive with Direct Torque Control' Second International Conference on Power Electronics and Variable Speed Drives, 24-26 Nov 1986, pp 80-84, Birmingham, U.K.
6. H. S. PATEL and R. G. HOFT, 'Generalised Techniques of Harmonic Elimination and Voltage Control in Thyristor Inverters' Part I - Harmonic Elimination, IEEE Trans Ind Appl, Vol IA-9 pp 310-317, 1973.
7. G. S. BUJA and G. B. INDRI 'Optimal Pulsewidth Modulation for feeding AC motors' IEEE Trans on Ind Appl, vol IA-13 pp 38-44, 1977.
8. J. A. TAUFIQ, C. J. GOODMAN and Prof. B. MELLITT 'Railway Signalling compatibility of Inverter fed Induction Motor Drives for Rapid Transit' IEEE Proc Vol 133 Pt B March 1986.
* This paper is a major revision and modernisation of work first performed in 1987.
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