A dynamic dynamometer for testing variable speed drives - IEEE Xplore

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used for testing variable speed drives are usually static in nature; i.e. they present a ... adequate when determining parameters such as drive system efficiency,.
A DYNAMIC DYNAMOMETER FOR TESTING VARIABLE SPEED DRIVES' ROBERT WENDEL NEWTON MEMBER

ROBERT E. BETZ MEMBER

H. BRUCE PENFOLD MEMBER

Department of Electrical and Computer Engineering University of Newcastle Callaghan N. S.W.2308 Australia

wStandarddynamometers for testing electricmachines areusually only capable of simulating the static torque characteristics of various industrial loads. For machines which aremainly operating in steady state, thisis satisfactory. However, for inverter-fed AC machines, the dynamic performance can also be important. This paper develops a control strategy based on Local Vector (LV) control. which allows a DC machine to be controlled to simulateboth the static anddynamic characteristics of representative industrial loads. One particularly interesting aspect of this is that non-linear effects in real loads, such as backlash and stiction, can be accurately simulated. The paper presents simulation results for the dynamometer and discusses the structureof the hardware being developed for the system.

L INTRODUCTION This paper describes the control techniques and the hardware used to implement a dynamic dynamometer to test the static and dynamic performance of variable speed drive systems. Conventional used for testing variable speed drives are usually static in nature; i.e. they present a static torque load to the machine being tested. This approach is adequate when determining parameters such as drive system efficiency, maximum power output, maximum torque, and thermal limitations. Unfortunately, such a system is not at all adequate if the dynamic performance of a drive system is to be examined.

are then presented. The implementation of the entire motor test facility will be summarised and the dynamometer control hardware is then discussed. Finally, the future directions for this work and conclusions are given.

J,L LV CONTRQL DESCRIPTION[61 A. System Implementation The LV control scheme, so-calledbecause of its concern with phenomena at the system trajectory level rather than at the underlying vector-field, operates by ensuring that, for each time-local step, the control action is such as to map the observed behaviour of the controlled system on to that computed for a dynamic reference system specified by the designer, designated the trajectory system, T.in Fig. l. In this sense, it is a model reference control, but with the important distinction that the control action occurs independently of the system history at each control interval. The topology of anLV system is different from a traditional control system in that it focuses on the alteration of the behaviour of the controlled system so that it matches the user-specified reference system, represented by the behaviour reference. Once this behaviour modification has been achieved, only a simple controller is required around the reference system to define its trajectory-following properties.

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A dynamic dynamometer, the subject of this paper, is designed to enable a variety of industrial loads to be simulated, both statically and dynamically, by acontrolledelectricmachineinalaboratory situation. For example, loads that have predominantly f i s t order dynamics can be simulatedt4] regardless of the intrinsic characteristics of the electric machine. A more relevant industrial example is simulating a load with second order dynamics such as aloadconnected to atest machinevia acompliant shaft. This is acomplex dynamic system, described by a fourthorder differential equation. A dynamic dynamometer system ought to be able to reproduce the dynamics of such a system for a wide variety of load and shaft parameters. Dynamometers that meet theserequirements have only rarely been investigated in the past[*]. As is common in the literature, the details of the systems implemented are sparse. Hence, the dynamometer presented here was designed from Fist principles. It goes beyond previous systems, though, as it can also simulate loads with non-linear effects such as gear train backlash and stiction. The control technique used to achieve the above simulated loads is based on Local Vector (LV) control. The remainder of the paper is organised as follows. The basic details of LV control algorithm will be outlined along with a means of digital realisation. Its application to DCmotor control and hence the dynamometer system will be discussed. Theresults from investigatingseveralexamples

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This work is supported in part by the Centre of Industrial Control Science (CICS) and the Australian Research Council (ARC). 0-7803-1993-1194 $4.00 0 1994 IEEE

I resetting State

Fig. 1. A block diagram of LV Control strategy. The only constraint for choosing the R model is stability. The theory defines the requirements of the sample period such that the closed-loop system will have guaranteed transient performance with exponentially fast recovery from disturbances. The LV control scheme has extremely good disturbance rejection as well as a high tolerance to timevarying parameters. Its major advantage is that the plant performance is modified to a desired behaviour, which is a designchoice. For further details regarding this method, see [5][6][7].

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*

1

112

}

Unit Delay3

Plant output Fig. 2. The SIMULINK block diagram for the LV controller algorithm.

B. Digital Implementation

Note thatthe principles of‘time-1ocalness”andbehaviourmodification lead the system behaviour to map to the reference behaviour only over the current time step, kTs -+ (k + l)Tp Hence the initial conditions forRandSatthecommencementofthesteparethesame. The control applied to the plant system during this time step is such thatthein~ementaltrajectorybetweens andR willbeforcedtozero. This gives the control:

The computional steps required for digital implementation of the algorithm are as follows: (i) Using appropriate initialconditions andexternal input, tiin.simulate one time step of eachof systems R and T.Initial conditions of R and T are equal at the beginning, but for subsequent steps, as described later, thii will not necessarily be true. We ensure that the system R (which has desirable dynamic properties) follows the system T (which generates a desirable trajectory) by using proportional feedback (as shown in Fig. 1) KR:

(ii) FrompastmeasurementsoftheoutputofthesystemS.ys,upto and including the present time step, estimate the next time step output .(k

+ 1)Ts

derivative, j s . A necessary assumption at this point is that the previous control is applied to S during the next time step, which begins at Us. To ensure that the derivative is computed as close to kT, aspossible, thesampling periodshouldbeless than thecontrol interVal. (iii) Using thecunent and futureoutput derivatives from the incremental trajectories inboth thebehaviour reference and the subject systems, compute the change in derivative, i.e.

(4) where g is the estimate of the input gain term. Experience has demonstratedthatthis termmustbeatleast aslarge asthetheactualvalue of the input gain term. (iv) Atthenext timestep, (k + l)Ts, fromthemeasurementsoftheoutput, ya and either measurements or estimates of the output derivative, yp set the initial conditions of the behaviour reference system, R, forthenext stepequaltothefmalconditionsofthesubjectsystem, S. This resetting is done regardless of the accuracy with which the inaemental trajectory for S actually mapped onto that for R. This implements stTict “time-localness”. (v) The initial conditions of the trajectory reference system, T,for the next step are simply the final conditions of the previous step. The subject system, S , of course, does this by virtue of its construction. (vi) Repeat the algorithm from the beginning for the next time step. This digital formulation of the LV control algorithm lends itself to straight forward implementation using high level languages. In [8], for example, the algorithm was coded with approximately fourteen lines of ‘C’ code which can be executed as part of the overall control system in less than50

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p. For the purposes of preliminary simulation investigation, a modified form of the LV controller was used in a SIMULINK[9] block. shown in Fig. 2.

-Te

The basic model used to investigate dynamometer implementation was a drive machine (the test machine) connected via arigid shaft to a load machine (the dynamometer). The dynamic load problem essentially involves making the load machine appear to be some desired load, including all relevant static and dynamic characteristics of that load. Ideally, the loadmachinecharacteristics will be fully known while assuming minimal information about the drive machine. Conventional control techniques have been used to simulate simple load types (a first order, inertial load) with some success[4].The LV control strategy seemed appropriate for this problem since the plant is implicitly made to behave with the dynamics of the behaviour reference model. Therefore, one simply would have to implement the desired system in the behaviour reference and the appropriate control would be produced. The same model could also be implemented in the trajectory block of the controller with the puxpose of correcting deviations of the behaviour reference model caused by unknown disturbances of the controlled plant. A particular advantage of the LV control approach in this problem is that it does not matter whether the behaviour reference model is linear, nonlinear, minimum phase or non-minimum phase (although it has to be stable). Therefore, simulation of non-linear effects such as backlash and stiction should be a relatively simple extension of the linear load case. Non-miniium phase systems are also possible.

W

LOAD

DRIVE Fig. 3.Amodelofaninertialloadsimulationfor testingthedynamometer.

B. Compliant Shaft Example The more difficult problem of an inertial load connected to the test mahine via a compliant shaft and a 1:1 gearbox with backlash was investigated using the simulation package SIMULINK. The general configuration of the system is shown in Fig. 4. The differential equations for the shaft and load are

(7) where J and f refer to the inertia and friction coefficient of the drive machine (d) and the load (L), 0 is the angular position of the shaft, K is the shaft stiffness, and T, is the electromagnetic torque produced by the test machine.

cTe

To investigate the application of the LV control strategy to the dynamometer problem, two example loads were investigated. The first is a first order dynamic system. The secondexample has the load connected to the test machine via a simulated compliant shaft and gearbox with backlash.

COMPLIANT

\

JV. SIMULATING I X)AD DYNAMICS In all of the work presented it has been assumed that the electromagnetic torque, T,, for both machines is known. This presents no difficulties for the load machine since the system model is known accurately. The drive machine model will not, in general, be known and hence the determination of of T, could be difficult. The shaft measurements that are assumed available are the shaft torque and the shaft angle. The angular velocity and acceleration are estimated fromthe shaft angle and are assumed available in the following control strategies.

DRIVE Fig. 4. A model of the benchmarking load simulation for testing the dynamometer. To implement this on the LV controller, the method employed was to use one of the system equations, (6).modified so that the input is T . KOL, as the behaviour reference model while simulating both equations externally, shown as the trajectory system in Fig. 5 , to generate an accurate control reference.

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A. First Order Example Fig. 3 shows a model of a first order dynamic system, an inertial load connected to the drive machine by a rigid shaft. The governing equation for this system is:

where JT andfr refer to the total inertia and friction coefficient of the system, T, is the electromagnetic torque of the drive machine, TF is the fixed load torque and o is the angular velocity of the system.

In modelling the backlash effect accurately, a further modification to equation (6) was required. This involved observing the output, x. from a deadzone function (set to the backlash angle) of the difference between the shaft angles. The effective shaft torque produced should then be K ( 0 2 ; ) where 0; = 0>x and 0; is the desired from the trajectory model. Therefore, if the deadzone is active, then the shaft torque is zero else it is Kx as required. The value of 0; is fed into the behaviour model, leading to Jd,iw6d

A LV controller was used to control the dynamometer such that it tracks the angular velocity of the desired dynamic system. The reference is provided by the angular position form of (5). This form of the LV controller ensures that at most there can only be avery small steady state offset error between the desired and actual angular position.

+ f d r i w b d + (SW)KOd = Te -k (~W)m&

(8)

where SW = 0 for x = 0 and 1 otherwise, replacing (6). Note that the switch function is required since 0; contains 0; and not Od. The combined dynamics then mimic the required dynamic performance.

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file contains a BMAC controlled compliant shaft simulation beck1p.h. The plant model ia the idmal model of rigid shaft coupled machines.

--

File order:time omrgr N-I omegm traj Contlol

roal rhrh torquo omogr orror

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Double click loads the initialisation file BMBKIN1T.M

Switch function

Fig. 5. The SIMULINK block diagram for the LV controller that simulates the second order load dynamics.

For the simulationresults,boththedriveandloadmachinesare separately excited DC machines with the following armature circuit model:

using the standard notation. The parameters chosen for the machine were & = O.IQ,L, = O.OOIH,g = 2 (pole-pairs), andL = I35Wb. To shorten simulation time for the second example, the load machine mechanical dynamics were made ideal. The results were almost exactly the same as for the more complicated simulation.

Jdrive

= 0.1 kgm2

fdrbc= 0.001 Nms

Jload

= 0.3 kgm2

fled = 0.0015 Nms

Jdesjred = 0.08 kgm2 [Ili,(drive) = 15 A

A. First Order Example The results, in simulation, of providing a repeated step change to the test machine connected to the dynamometer, with the desired load characteristics listed inTable I, are presented below. Note that the desired load parameters are smaller than the actual parameters of the loadmachine. This indicates that during the acceleration phases of the simulation, the controller has to produce torque in the same direction as the drive machine torque so that the effective inertia is lowered appropriately. Fig. 6 shows the angular velocity response of the dynamometer, a ramp corresponding to the integral of the applied torque step change, exactly what would be expected from an inertial load. Fig. 7 and Fig. 8 show the error between the dynamometer simulated and an actual inertial load simulated for both the angular velocity and angular position. Note that the

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f h i r d = 0.01 Nms

IIli,(load)

= 40 A

1

0.M

B. Compliant Shaft Example The results, in simulation, of providing a step change to the test machine connected to the dynamometer. with the desired load characteristicslisted inTable 11. are presented in Fig. 9, Fig. 10, and Fig. 11. These results are exactly what would be expected from an actual load with the specifiedparameters. Note the flat regions in Fig. 9. These correspond to the backlash regions, points of zero shaft torque. For an example of using an LV controller on a physical machine system, see [8].

0.04 0.02 (

4.02

TABLE II PARAMETERS USED FOR BENCHMARK EXAMPLE

4.w 4.06 4.08 1

2

3

4

delta = 100p

Fig. 7. The angular velocity error for the fust order example.

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1

Fig. 8. The angular position error for the fust order example.

2

3

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Fig. 10. Angular velocity for compliant shaft with backlash.

15 10 .............. .:. ............:. .............;. .............;.............

-15........... -20-

Fig. 9.Theshaft torque for thecompliant load with backlash, showing the step input.

....I ............. .i.............. i.. ............i.............

0 I 2 3 4 Fig. 11. The control signal for the compliant shaft backlash model.

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general house keeping. The use of such powerful processing allows sophisticated control algorithms to be written in high level languages.

EXPERIMENTAL SYSTEM

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=CHOPPER DCLOAD

I

TORQUE & POSITION MEASUREMENTS

I I D WE

486+860 SYSTEM

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1 2 3 4 Fig. 12. The error in the angular position between a simulated compliant load with backlash and the dynamometer.

f : W

: ...... ....................................

13. Dynamometer Controller Implementation Programming the control algorithm necessitates the implementation of high order Runge-Kutta routines. The trajectory system, for instance, is currently a fourth order system. Future work into higher order systems and extra non-linearities will lead to even more demanding computations. Additionally. these routines must be solved in real-time and in short periods: utilising the full capacity of the chopper will require 100ps control periods. Add to this the requirement that measured signals must be sampled at an even higher rate and conditioned appoPriately (derivative calculation for instance) and the choice of a core processor becomes severely limited.

. . . f . . 1 1 . . . . . . . . . ' . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .............

.v:..............:_

.........

............. :. .............:. ...........

-lot -12 I

0 I 2 3 4 Fig. 13. The error in the angular velocity between a simulated compliant load with backlash and the dynamometer.

Again, for comparison, a model of the desired system was simulated in parallel to thedynamometer simulation. The error in angular position and velocity are shown in Fig. 12 and Fig. 13 respectively. Note that there is a close correspondence between the dynamometer load simulation and the actual performance of a dynamic system, indicating an accurate simulation of the desued load.

VI. SYST-ATION

(DYNAMOMETER)

The test machine is coupled to the load system (i.e. the dynamometer) via a Vibrometer 100Nm torque fnrwd~cer.The dynamic load machine is a I 5 kW,3000 rpm DC motor, connected to a full bridge chopper of similar construction to the inverter. The drive voltage is supplied by a Ward-Leonard generator set thereby allowing easy regeneration. A specialised computer system controls the chopper and also takes additional feedback from a ten-bit grey code angular position encoder.

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Fig. 14. A block diagram of the machine experimental system.

.............. .............j ..... ......

v

S E + + DUAL 21020

[41

A. General Overview The experimental system consists of the drive system and the load system shown in Fig. 14. The power electronics, whichcontrols the testmachine, consists of a 10 kW, 10 kHz IGBT based inverter and a control computer. The control computer is a multi-processor system, consisting of an Intel 80486 processor, an Intel 860 RISC processor, and two Texas Instruments TMS32OC25 DSPs. The Intel 860 is used for the control computations, while theTMS32Os are used for filtering sampled data from the drive system. The Intel 486 is used for coordination of the other processors and

Eksentially, all time critical operations are (floating-point) mathematical functions involving at least fourth order matrices. This indicates that some form of DSP could be useful. This processorneeds to perform two functions: control calculations (the LV control algorithm) and signal conditioning. Concurrent processing of these functions is required and hence two DSPs could be used in parallel with some form of communication between them. Software and debugging support is another important issue as complex software needs to be developed and possibly even ported from other platforms (the simulation software) for incorporationin the final system. The Analog Devices 21020 40-bit floating point DSP suited these needs with a superior single chip performance, simple interfacing and solid support. A dual processor system has beendesigned for zero waitstateoperation andiscapableof giving asustainedperformance of 67 MIPS and 150 MFLOPS. 1)ualportmemoryservesasthemaincommunicationbetweentheprocessors while dual serial interfaces allow simple host computer interfacing. An extemal bus is accessible to both processors through a simple arbiter. Illis bus provides for any peripheral interfacing, including extemal ROM, sampling systems and transducer controllers. Fig. 15 shows the schematic of the processor system.

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[7] H.B. Penfold, I.M.Y. Mareels and R.J. Evans, “Adaptively Controlling Non-linear Systems Using Trajectory Approximations”. Int. J. Adaptive Control and Signal Processing,Special issue on non-linear control. Vol. 6. No. 4. pp.395411. July 1992.

I

11-

I

21020 33MHz

d

[8] Bet% R.E.. Penfold, H.B.. and Lagerquist, R.. “LV Control for the

256Kx48.

Synchronous Reluctance Machine”, Australasian Universities Power Engineering Conference 1993 (AUPEC’93).

=> 150 MFLOPS

[9] The Math Works, Inc.. SIMULmrK Users Guide, March 1992, Cochituate Place, 24 Prime Park Way, Matick. Massachusetts 01760 ARBmR

(COMBINED) r

Fig. 15. Control hardware schematic of the dual processor board (half shown) for use with the dynamometer.

yIL CONCLUSIONS AND FUTURE DIRECTIONS The development and simulation of the control techniques to allow a DC machine dynamometer to simulate the static and dynamic characteristics of a second order dynamic system, a compliant shaft with gearbox backlash benchmark example, have been presented. The simulation results obtained have been very encouraging and an experimental system is currently being constructed to test the control strategies. The immediate direction of this work is to expand the range of loads that can be emulated with a dynamic dynamometer. This will include: introduction of a gear train other than 1:l; implementing a double compliant shaft; inclusion of stiction effects; implementing a non-minimum phase system, useful for control algorithmtesting;using measurementestimates instead of the ideal ones currently used (a Kalman filter is is being developed for this purpose). Comparison between the LV control strategy and other methods will also be undertaken. CKNOWJ .F-DGMENTS The authors would like to acknowledge Dr.Brian Cook, Tim Wylie, Peter McLauchlan. Russel Hicks, and Ian Powell who are helping to develop the hardware components for the complete experimental system which is described in this paper.

IX.REFERENCES C.R. Wasko, “500HP. 120 Hz Current-fed Field Oriented Control Inverter for Fuel PumpTest Stands”, in Con5 Rec. 198621st Annu. Meet. IEEE Ind. App. Soc., pp. 314-320.

L. Koch and P. Zellar, ‘Test Stand for Dynamic Investigation of Combustion Engines’, Automobiltechnische&itschr& vol. 89 no. 11, p~ 585-586,589-592, NOV.1987. A.C. Williamson, “AnImproved EngineTesting Dynamometer’,in Fourth International Conference on Electrical Machines and Drives, IEE Conference Publication 310, 1989, pp. 374-378. R.W. Newton, R.E. Betz and R.H. Midd1eton“Dynamic Dynamometer for Electrical Machine Testing”, in Proceedings IEAust AUPEC’93.Wollongong, Australia, Sept-Oct, 1993 H.B. Penfold and R.J. Evans, “Control Algorithm for Unknown Timevarying Systems”, Int. Journal of Control,Vol. 50, 1989, pp. 13-32. H.B. Penfold, Nonlinear Control: An Altemative Perspective, PhD dissertion, Department of Electrical and Computer Engineering, University of Newcastle, Australia, April 1990

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