THE CONTRIBUTION OF COMPUTER SIMULATION METHODS TO TRACTION PROPULSION DEVELOPMENT
B. J. CARDWELL, I. K. S. JOHNSON, G.W. BAINES BEM - LOUGHBOROUGH U.K.
(Dr. Cardwell is now a traction consultant for Cecube Ltd.*)
(Mr Baines is a senior design engineer for Alstom)
The advent of vehicle distributed microprocessor and micro-controller technology has produced irrevocable changes in traction propulsion systems. Most significantly multi-processor operating and control systems have dramatically increased electronic system complexity. The rapid transition of control methods from hardware to software has led to sophisticated schemes for the control of both AC and DC traction drives. These schemes require detailed theoretical analysis and simulation to predict performance and stability. General purpose, PC based, engineering analysis software and bespoke system modelling are now an essential ingredient of the design process. This paper discusses the role of both types of facility in the development of a modern traction drive.
The use of separately excited DC (SEPEX), and PWM inverter fed AC traction drives, to achieve more stringent performance specifications is now commonplace. To achieve the requirements of traction operators for predictability and repeatability of performance, traction drive control systems have become significantly more complex involving the careful integration of microprocessors, power electronics, machines and transmissions. In particular much attention has been focused on accurate tractive effort profiling, speed control, and high adhesion (creep) control in both locomotive and EMU applications.
With extra complexity and ever shorter commissioning periods, the traditional techniques of 'on site' determination of control strategies is not only inefficient but in many cases impossible. To resolve these difficulties, manufacturers are turning to computer-aided simulation techniques that accurately describe system requirements and behaviour. Many of the facilities already exist for creating a drive design environment on networked computers and PC systems. This represents a major advance towards an integrated design and manufacture philosophy, where the system engineer has the opportunity to explore system interactions, parameter optimisations, and fault and protection mechanisms prior to manufacture.
Such an approach results in the development of dedicated computer-aided drive simulation packages for full system evaluation, with a modular format for reconfiguration. This can be used to simulate and investigate the performance of advanced traction drives. Using this approach overcomes the difficulty in modifying system topology which is the major objection to equation based simulation. It allows a simulation to be patched together using modules of the required complexity in a way analogous to conventional analogue computer methods at a lower level. Whilst commercially available general purpose circuit analysis packages such as SABER and SPICE are highly flexible, and can readily model sub-systems in a complex configuration, such as a power converter or gate driver circuit, the package library is rarely sufficiently comprehensive to simulate the whole drive system.
SIMULATING LOAD BEHAVIOUR AND IDENTIFICATION
The essential starting point of any major simulation is to accurately identify the plant being modelled. In traction applications this usually means using well-established models for DC and AC motors, converters, alternators, etc. In these cases the identification task is confined to accurate estimation of parameters by calculations, simulation or direct measurement. A case where this is not so is the wheel / rail interface adhesion characteristic. This process was modelled by data assimilation from several sources (1, 2, 3).
A model was created to investigate the real time dynamic performance of the Class 60 Heavy Haul Freight Locomotive wheel and axle assembly. The model was run on a Continuous System Modelling Program (CSMP). This combines versatility in terms of data input and interaction of a traditional analogue computer, with the computing speed associated with a digital simulation. The focus of the study was self-induced axle torsional oscillations, in particular their effect on axle life.
The dynamic model and associated parameters are shown in Fig. 1. The model consists of two polar inertial elements joined by a torsional spring to represent the wheelset. A third inertia is then joined to the system by means of a gearing effect and another torsional spring. This addition represents the effect of the motor armature, motor shaft and the gearbox. The torque, T, applied to the motor armature represents an electro-magnetic torque, which is calculated using a simple control model. Electrically the system is modelled using all six axles, with the leading axle slipping and free to oscillate, and the other five slipping at a constant rate and hence constrained not to oscillate under any conditions. This is represented by a constant back-EMF for the five 'constrained' motors, and a constant current source supply. The torque to the 'free' motor will then vary according to its own angular speed.
The system described may be represented by a dynamically equivalent system, with three rotors on a single shaft. This system has two torsional modes of oscillation:
1. A single node on either shaft section, with the outer rotors oscillating ANTI-PHASE.
2. Two nodes, one on each section of the shaft, with the outer rotors oscillating IN-PHASE.
(i.e. 1 is a low frequency mode and 2 is a high frequency mode).
The frequencies were both theoretically calculated and verified by modelling as 53Hz and 108Hz respectively, subject to a 20% variation (increase) due to wheel wear.
A longitudinal friction-creep characteristic was used to model the wheel / rail interface (Fig. 2). Where the characteristic slope is positive, the interface introduces positive damping to the wheelset angular motion making increased adhesion available. Where the slope is negative, the interface introduces negative damping to the wheelset angular motion, allowing axle torsional oscillations to propagate.
The characteristic used represents 'coal-yard' conditions (Fig. 2), a very steep characteristic with low overall adhesion level.
Initially no damping was used in the model other than that at the wheel / rail interface. Although the magnitude of the oscillations may be shown to increase with both vehicle speed and creepage, the likelihood of their occurrence is inversely proportional to their severity, due to the rapid fall-off in demanded tractive effort with speed.
In all cases the initial armature torque value was set such that it corresponded to a 'stable operating point' on the friction-creep characteristic i.e. the point on the characteristic where the available adhesion corresponds to an initial set creepage. The results show clearly the presence of the two modes of oscillation as described.
On a typical run at half maximum speed and 5% initial creepage, the oscillations build up as expected until about 1 second has elapsed, whereupon the amplitude of the oscillations no longer increases, but fluctuates indicating a position of limiting oscillation has been reached. This 'stability' condition is reached because the creepage amplitude increases with the oscillation amplitude (about a mean value of 5%) until the positively damped region of the friction-creep characteristic is encountered. When this occurs, the creepage on either wheel is less than the value corresponding to the peak of the characteristic. This phenomenon provides enough positive damping to balance the system and hence gives rise to bounded instability.
The Maximum Principal Stress Time History (Fig. 3) is arrived at by considering bending stresses in the axle from load conditions defined in BR Reports BASS 503 and T 72, and combining these with the shear stress levels due to torsional oscillations predicted. From Mohr's circle for stress, the peaks on the plot all correspond to σ1, and the troughs to σ2. The discontinuous region in between is defined by the value of the maximum shear stress.
TRACTION CONTROL ALGORITHMS
Having identified the system to be controlled and then established a suitable model, the design emphasis turns to generating control algorithms to achieve the objective performance. This requires not only a system functional requirement, but also knowledge of the implementation hardware to achieve an acceptable real-time solution. The dedicated high level language simulation is the ideal environment for generating real-time algorithms, allowing flexibility of modelling structure to emulate the real-time implementation. As well as essential items such as control equations and discrete operations, other real-time constraints may be included such as dynamic range limits and coefficient quantisation. There is also opportunity to investigate problems associated with multi-rate sampling, essential in complex systems where the processing power is limited. Realistically, dedicated simulations are time-domain based using a state space approach. The control algorithms are grouped into several modules or subroutines, and the equations integrated by difference equation methods, which can be easily translated into real-time. Several design techniques exist for digital systems, the most commonly used being direct digital control (DDC). A flow chart depicting the sequence of design tasks involved in DDC is given in Fig. 4.
An example of DDC design via simulation is the Class 60 freight locomotive. The exacting control and adhesion specification necessitated the development of a specialist control strategy, which included a model of the wheel / rail interface previously mentioned. By use of direct speed measurement from a Doppler radar mounted on the loco frame, a means of limited creep control via alternator control of all 6 parallel traction armatures has been devised, that supplements the good natural adhesion characteristic of SEPEX motors. Provided just 1 of the 6 motors is achieving the required adhesion level the creep of the remaining axles is limited. If the final motor loses adhesion, armature current control ceases and radar controlled creep takes over. A block diagram of the system that achieves this is in Fig. 5.
In some systems DDC does not produce a workable solution. This is an indication that PID control is not adequate. If a PID controller does not work, it is certain an embedded version will not either. The solution is to look to alternative forms of analysis to derive a controllable system. Induction motor drives are known to exhibit certain forms of instability (4) which demand special attention. Specifically, sampled data transforms are very powerful analytical techniques, of which impulse invariant and the bi-linear transforms are the most common. The latter was used extensively to model and control an AC drive (5) for Class 455 EMU, introduced in to operation on the UK DC electrified Southern Zone after 1990. This example shows that z-plane techniques could be used to generate recursive models for simulation as well as control algorithms. This approach confines the modelling to the time domain rather than generating simulation via frequency plane models.
SYSTEM DESIGN AND VERIFICATION
Computer modelling may be used to answer questions posed early in the system design phase of a project. Such an example was the decision whether to use compensated motors on Class 60.
An uncompensated motor model was constructed on the Continuous System Modelling Program. This model was then verified by setting it up as two SEPEX Class 47 traction motors connected as a motor generator (Hopkinson test). By performing step changes in load it was possible to compare results of the model with directly measured results. A comparison is shown in Fig. 6, and provides the modelling verification required. Using the validated model, with a bi-phase converter added to control the field, results showed that uncompensated SEPEX motors could only be stabilised if the supply frequency of the bi-phase converter was very high and the armature current error was small. The problem was that the rate of change of armature current caused by armature reaction exceeded that correctable by field control with maximum voltage forcing. As higher field forcing voltage was unacceptable, as was net positive feedback, a compensated motor design was chosen instead.
This type of model verification is important when major design decisions are to be made. At this point project hardware is not generally available to verify the model, so cross verification on other existing equipment is a good and necessary alternative. Where a model is particularly complex, the development of two simulations can be justified to 'build confidence' before applying the model to the creation of control algorithms.
Having established a system model, this is the ideal tool for investigating robustness of the design to parameter variation. Detailed analysis to determine the sensitivity of non-linear systems, and hence its robustness would be beyond the scope of most practising engineers, but the system model provides a means by which critical design parameters may be verified.
PROCEED WITH CARE
Along with its real-time processor counterpart, digital simulation can produce plenty of pitfalls for the unwary. Numerical errors include quantisation, rounding, step length and aliasing. It is suggested that sampling and word length effects be designed as negligible relative to the control accuracy specification. When computer performance constraints (or emulated microprocessor constraints) frustrate this objective, then the consequence of any degenerate effects need to be evaluated.
Coefficient quantisation is of increasing severity as the rate of change of phase increases. This implies that whilst a first order lag may be insensitive to coefficient quantisation, a fourth order notch filter requires at least 32 bit representation.
Even with adequate coefficient word length the accumulative round-off error can lead to significant noise and loss of control accuracy. The advent of 32 bit microprocessors eased the quantisation problem, although input/output variables are generally restricted to 12 bits for noise reasons. Whether these issues are pertinent to a digital simulation can only be judged case by case, but investigation to discount quantisation error problems should not be ignored. Working with the luxury of floating point arithmetic in simulations or real-time normally makes quantisation levels negligible.
The choice of step length is central to any digital design or simulation, with conflicting requirements giving rise to compromised optimum values. With a simulation the step length may be set as short as desired without the constraint of real time, however, this may result in unacceptably long run times. Increasing the step length will degrade the accuracy and give rise to aliasing effects. Most equation solving utility packages incorporate error parameters or controls that guarantee the accuracy of the solution to a specified value. Real-time implementations can not generally afford the luxury of accuracy testing, so the control accuracy specification is a major design parameter when determining the sampling frequency.
A guide to how computer simulation may be employed in the traction environment is presented. The methodology of successful simulation has been divided into three principal areas: system identification, control algorithms, and modelling verification. Emphasis is placed on the need for accurate modelling as the basis for complex drives design. The use of reliable simulation is a prerequisite to advanced drive design and manufacture, giving the practising engineer insight into performance and access to results, which otherwise would not be available until a prototype was tested or fleet commissioning commenced. Conversely, poor simulation may lead to false assumptions and errors, leaving the project engineer less likely to achieve the design requirements.
1. D S ARMSTRONG, 'Adhesion / Slip Characteristics in Traction', BR Research Technical Memorandum TM TBC 015, December 1988.
2. F LOGSTON Jr and G ITAMI 'Locomotive Friction - Creep Studies ASME Paper No 80-RT-1, April 1980.
3. H FIEHN, M WEINHARDT, N ZEEVENHOOVEN 'Dutch Railways three phase electric traction test vehicle - adhesion measurements', Elektrische Bahnen 1979 77 (12), 329-338.
4. F FALLSIDE, A T WORTLEY ‘Steady state oscillation and stabilisation of variable frequency inverter fed induction motor drives’, Proc IEE, Vol. 116, No 6, June 1969.
5. B J CARDWELL ‘Torque control of AC induction motor traction drives’, Electric Railway Systems for a New Century’, Conference Pub 279, lEE London, September 1987.
* This paper is a 2006 revision of a paper first published in 1989.
Figure 1 CLASS 60 TRACTION DRIVE SCHEMATIC
Figure 2 TYPICAL ADHESION VERSUS CREEP DATA FOR VARYING CONDITIONS
Figure 3 PREDICTED ONSET OF BOTH TORSIONAL MODES OF OSCILLATION
Figure 4 ITERATIVE DESIGN PROCEDURE FOR DIRECT DIGITAL CONTROL (DDC)
Figure 5 BLOCK DIAGRAM OF CLASS 60 CONTROL STRUCTURE
Figure 6 COMPUTER MODEL VERSUS TEST RESULTS FOR STEP CHANGE CURRENT
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