## 74 Modelling Electric Vehicle Range

7.4.1 Driving cycles

It is well known that the range of electric vehicles is a major problem. In the main this is because it is so hard to efficiently store electrical energy. In any case, this problem is certainly a critical issue in the design of any electric vehicle. There are two types of calculation or test that can be performed with regard to the range of a vehicle.

The first, and much the simplest, is the constant velocity test. Of course no vehicle is really driven at constant velocity, especially not on level ground, and in still air, which are almost universal further simplifications for these tests. However, at least the rules for the test are clear and unambiguous, even if the test is unrealistic. It can be argued that they do at least give useful comparative figures.

The second type of test, more useful and complex, is where the vehicle is driven, in reality or in simulation, through a profile of ever changing speeds. These test cycles have been developed with some care, and there are (unfortunately) a large number of them. The cycles are intended to correspond to realistic driving patterns in different conditions. During these tests the vehicle speed is almost constantly changing, and thus the performance of all the other parts of the system is also highly variable, which makes the computations more complex. However, modern computer programs make even these more complex situations reasonably straightforward.

These driving cycles (or schedules) have primarily been developed in order to provide a realistic and practical test for the emissions of vehicles. One of the most well-known of the early cycles was one based on actual traffic flows in Los Angeles CA, and is known as the LA-4 cycle. This was then developed into the Federal Urban Driving Schedule, or FUDS. This is a cycle lasting 1500 seconds, and for each second there is a different speed, as shown in Figure 7.7. There is also a simplified version of this cycle known as SFUDS, shown in Figure 7.8, which has the advantage that it only lasts 360 seconds, and so has only 360 data points. This has the same average speed, the same proportion of time stationary, the same maximum acceleration and braking, and gives very similar results when used for simulating vehicle range.

These cycles simulate urban driving, but other cycles are used to simulate out-of-town or highway driving. Two notable examples of these are the FHDS, shown in Figure 7.9. Although widely used, this cycle has a rather unrealistic maximum speed for highway driving, and the newer US06 standard is now becoming more widely used instead.

In the European scene the cycles tend to be rather simpler, with periods of constant acceleration and constant velocity. Of particular note is the ECE-15 drive cycle, shown in Figure 7.10, which is useful for testing the performance of small vehicles such as battery electric cars. In EC emission tests this has to be combined the extra-urban driving cycles (EUDC), which has a maximum speed of 120km.h-1.

Currently the most widely used standard in Asia is the Japanese 10-15 Mode cycle. Like the European cycles, this involves periods of constant velocity and acceleration. It

600 800 Time/Sec

1000

1200

1400

Figure 7.7 The Federal Urban Driving Schedule, as used for emission testing by the United States Environmental Protection Agency

Time/sec

Figure 7.8 Graph of speed against time for the simplified federal urban driving schedule

Time/sec

Figure 7.8 Graph of speed against time for the simplified federal urban driving schedule is not unlike a combination of the European ECE-15 urban driving cycle and the EUDC. At the time of writing, this cycle must be used in stating ranges for vehicles in Japan, as well as for emission tests.

All these standards have maximum speeds in the region of 100km.h-1. For several important types of electric vehicle, including the electric delivery vehicle and the electric

Time/Sec.

Figure 7.9 Graph of speed against time for the 765 second federal highway driving schedule

Time/Sec.

Figure 7.9 Graph of speed against time for the 765 second federal highway driving schedule

Time/sec

Figure 7.10 European urban driving schedule ECE-15

Time/sec

### Figure 7.10 European urban driving schedule ECE-15

motor scooter, this is an unrealistic speed, which can often not be achieved. To simulate these vehicles other standard cycles are needed. A fairly old standard, which was developed specifically for electric vehicles in the 1970s, is the SAE J227a driving schedule. This has four versions, with different speeds. Each cycle is quite short in time, and consists of an acceleration phase, a constant velocity phase, a 'coast' phase, and a braking phase, followed by a stationary time. The coasting phase, where the speed is not specified,

Table 7.1 Nominal parameters for the four variations of the SAE J227a test schedule. These figures should be read in conjunction with Figure 7.10
 Parameter Unit Cycle A Cycle B Cycle C Cycle D Maximum speed Km.h-1 16 32 48 72 Acceleration Time Ta s 4 19 18 28 Cruise time Tcr s 0 19 20 50 Coast time Tco s 2 4 8 10 Brake time Tb s 3 5 9 9 Idle time Ti s 30 25 25 25 Total time s 39 72 80 122

but the tractive effort is set to zero, is somewhat of a nuisance to model.3 The general velocity profile is shown in Figure 7.11, and the details of each of the four variants of this cycle are given in Table 7.1 The most commonly used cycle is SAE J227a-C, which is particularly suitable for electric scooters and smaller city-only electric vehicles. The A and B variants are sometimes used for special purpose delivery vehicles.

Another schedule worthy of note for low speed vehicles is the European ECE-47 cycle, which is used for the emission testing of mopeds and motorcycles with engine capacity less than 50 cm3. It is also widely used for the range simulation of electric scooters. Like the SAEJ227 cycle it can be a little complicated to run the simulation, as the speed is not specified at all times. Instead the vehicle is run from standstill at WOT for 50 s. The vehicle is then slowed to 20km.h-1 over the next 15 s, after which this

3 It is not uncommon to get around this difficulty by simply putting in likely figures for a somewhat gentle period of deceleration.

ECE-47 cycle for the electric scooter of Figure 7.4 50-1-1-1-

ECE-47 cycle for the electric scooter of Figure 7.4 50-1-1-1-

Time/seconds

Figure 7.12 ECE-47 cycles for the same electric scooter as in Figure 7.4

Time/seconds

Figure 7.12 ECE-47 cycles for the same electric scooter as in Figure 7.4

speed is maintained for 35 seconds. Finally the vehicle is brought to a halt, at constant deceleration, over the next 8 s. This cycle has been created for the same electric scooter as was used in Section 7.3.2 an approximation to the Peugeot SCOOT'ELEC, and is shown in Figure 7.12. The MATLAB® script file for creating this is very straightforward, and is given in Appendix 2. This cycle has the benefit that it probably models quite well the way such vehicles are used, considering the age of the typical rider, i.e. full speed for a good deal of the time!

There are many other test cycles which can be found in the literature, and some companies have their own in-house driving schedules. Academics sometimes propose new ones that, they suggest, better imitate real driving practice. There are also local driving cycles, which reflect the particular driving patterns of a city. A noteworthy example is the New York City Cycle, which has particularly long periods of no movement, and low average speeds, reflecting the state of the roads there. This cycle is sometimes used when simulating hybrid electric/ICE vehicles, as it shows this type of vehicle in a particularly good light.

The actual figures for the speed at each second, which are needed to run a simulation, can sometimes be deduced from the figures given above. However, in the case of the US cycles, which consist of a specific speed at each time, it is more convenient to load data files downloaded from web sites. These can readily be found using the normal internet

search engines, though several have been supplied as MATLAB script files at the website associated with this book.4

bat ' mot_in ' mot_out ' te bat ' mot_in ' mot_out ' te

_^ Normalforward ^____ Regenerative driving braking

Figure 7.13 Energy flows in the 'classic' battery powered electric vehicle, which has regenerative braking

_^ Normalforward ^____ Regenerative driving braking

Figure 7.13 Energy flows in the 'classic' battery powered electric vehicle, which has regenerative braking

In the sections that follow it will be explained how a driving schedule can be simulated for different types of electric vehicle.

7.4.2 Range modelling of battery electric vehicles

7.4.2.1 Principles of battery electric vehicle modelling

The energy flows in a classical battery electric vehicle are shown in Figure 7.13. To predict the range the energy required to move the vehicle for each second of the driving cycle is calculated, and the effect of this energy drain is calculated. The process is repeated until the battery is flat. It is important to remember that if we use one-second time intervals, then the power and the energy consumed are equal.

The starting point in these calculations is to find the tractive effort, which is calculated from equation (7.9). The power is equal to the tractive effort multiplied by the velocity. Using the various efficiencies in the energy flow diagram, the energy required to move the vehicle for one second is calculated.

The energy required to move the vehicle for one second is the same as the power, so:

Energy required each second = Pte = Fte x v (7.23)

To find the energy taken from the battery to provide this energy at the road, we clearly need to be able to find the various efficiencies at all operating points. Equations that do this have been developed in the previous chapters, but we will review here the most important system modelling equations.

### 7.4.2.2 Modelling equations

The efficiency of the gear system ng is normally assumed to be constant, as in electric vehicles there is usually only one gear. The efficiency is normally high, as the gear system will be very simple.

The efficiency of the motor and its controller are usually considered together, as it is more convenient to measure the efficiency of the whole system. We saw in Chapter 4 that motor efficiency varies considerably with power, torque, and also motor size. The efficiency is quite well modelled by the equation:

where kc is the copper losses coefficient, ki is the iron losses coefficient, kw is the windage loss coefficient and C represents the constant losses that apply at any speed. Table 7.2 shows typical values for these constants for two motors that are likely candidates for use in electric vehicles.

Table 7.2 Typical values for the parameters of equation (7.24)

Parameter Lynch type PM motor, with 100 kW, high speed brushes, 2-5 kW induction motor kc 1.5 0.3

C 20 600

The inefficiencies of the motor, the controller and the gear system mean that the motor's power is not the same as the traction power, and the electrical power required by the motor is greater than the mechanical output power, according to the simple equations:

Equations (7.25) are correct in the case where the vehicle is being driven. However, if the motor is being used to slow the vehicle, then the efficiency (or rather the inefficiency) works in the opposite sense. In other words the electrical power from the motor is reduced, and we must use these equations:

Pmot_in = Pmot_out X T]m Pmot_out = Pte X Tjg (7.26)

So equations (7.25) or (7.26) are used to give use the electrical and mechanical power to (or from) the motor. However, we also need to consider the other electrical systems of the vehicle, the lights, indicators, accessories such as the radio, etc. An average power will need to be found or estimated for these, and added to the motor power, to give the total power required from the battery. Note that when braking, the motor power will be negative, and so this will reduce the magnitude of the power.

The meaning of these various powers, in and out of the motor, traction power and so on, is shown in Figure 7.13.

The simulation of battery behaviour was explained in Section 2.11. To summarise, the procedure now is:

1. calculate the open circuit battery voltage, which depends on the state of charge of the battery;

2. calculate the battery current5 using equation (2.20), unless Pbat is negative, in which case equation (2.22) should be used;

3. update the record of charge removed from the battery, correcting high currents using the Peukert coefficient, with equation (2.17); however, if the battery power is negative, and it is being charged, equation (2.23) should be used instead;

4. The level of discharge of the battery should then be updated, using equation (2.19).

Provided that the battery is not now too discharged, the whole process should then be repeated one second later, at the next velocity in the cycle.

7.4.2.3 Using MATLAB® or EXCEL® to simulate an electric vehicle

In the preceding section we saw how the various equations we have derived can be used to calculate what goes on inside an electric vehicle. To see how far a vehicle can go before the battery is flat we do this in a step-by-step process through the driving cycle. The way this is done is represented by the flowchart shown in Figure 7.14.

The first stage is to load the velocity data for the driving cycle to be used. This is usually done as by a separate MATLAB w script file. The way of doing this is explained in Appendix 2.

The next is to set up the vehicle parameters such as the mass, the battery size and type, and so on. The electrical power taken by the accessories Pac should be set at this point.

Having done that, data arrays should be created for storing the data that needs to be remembered at the end of each cycle. These could be called 'end of cycle arrays'. The most important data that needs to be kept is a record of the charge removed from the battery, the depth of discharge of the battery, and the distance travelled.

The next stage is to set up arrays for the data to be stored just for one cycle; this data can be lost at the end of each cycle. This is also the charge removed, depth of discharge, and distance travelled, but we might also save other data, such as information about torque, or motor power, or battery current, as it is sometimes useful to be able to plot this data for just one cycle.

Having set the system up, the vehicle is put through one driving cycle, using the velocities given to calculate the acceleration, and thus the tractive effort, and thus the motor power, torque and speed. This is used to find the motor efficiency, which is used to find the electrical power going into the motor. Combined with the accessory power, this is used to find the battery current. This is then used to recalculate the battery state of charge. This calculation is repeated in one second steps6 until the end of the cycle.

5 If the vehicle uses a conventional DC motor, it might be more convenient to calculate the current using the more-or-less linear relationship between torque and current. If the connection is known, this can occasionally be a useful simplification.

6 One second steps are the most convenient, as most driving cycles are defined in terms of one second intervals. Also, many of the formulas become much simpler. However, it is quite easy to adapt any of the programs given here for different time steps, and shorter steps are sometimes used.

START

START

Figure 7.14 Flowchart for the simulation of a battery powered electric vehicle

The end of cycle data arrays are then updated, and if the battery still has enough charge, the process is repeated for another cycle. This is process is shown in the flowchart of Figure 7.14.

MATLAB® lends itself very well to this type of calculation. In Appendices 3 and 4 you will find example MATLAB® script files that find the range for a model of the famous General Motors EV1 vehicle. It should be easy enough to relate these to the text and all the equations given above. The main complications relate to zero values for variables such as speed and torque, which need careful treatment to avoid dividing by zero. The vehicle is running an urban driving cycle.

The file prints a graph of the depth of battery discharge against distance travelled, and this is shown in Figure 7.15, for two different situations. It can be seen that the vehicle range is about 130 km.

One of the very powerful features of such simulations is that they can be used to very quickly and easily see the effect of changing certain vehicle parameters on the range. For example, it is the work of a moment to change the program so that the conditions are different. For example, we can 'put the headlights on' by increasing the value of the average accessory power Pac. We can also simulate colder weather by increasing the internal resistance by 25% or so, raising the Peukert coefficient and reducing the battery voltage very slightly. The simulation can then be re-run. This has been done with Figure 7.15. This shows how the depth of discharge rises under normal clement weather, daytime conditions, and also under colder conditions when in the dark. We can instantly see that the range, usually given as when 80% discharge is reached, drops from a little over 90 miles to about 70. The official stated range, in the GM literature, is '50 to 90 miles, depending on conditions.' Our simulation confirms this. We could further adapt the program to include hills, or more demanding driving, which would bring it below the 70 mile figure.

0 20 40 60 80 100 120 140 160 180 Distance travelled/km

Figure 7.15 A graph of depth-of-discharge against distance travelled for a simulated GM EV1 electric car on the SFUDS driving cycle. In one case the conditions are benign, no lights, heating or air conditioning are in use. In the other case the battery is degraded slightly by cold weather, and all the vehicle headlights are on

70 miles

91 miles

The ECE-47 driving cycle was explained in the previous section. This can equally well

be used for such range testing. In Appendix 5 we have given another MATLAB w script file for the same electric scooter that has been used for Figures 7.4 and 7.12. This vehicle has been set up with a NiCad battery, unlike the GMEV1, which uses lead acid. If the MATLAB® script file in Appendix 5 is studied, it will be seen that the vehicle has been fitted with three 100 Ah batteries, with the same properties as the NiCad batteries simulated in Section 2.11.3. Some range data, taken to 80% discharged, is given in Table 7.3.

 Percentage regenerative braking Range on ECE-47 cycle 75% (not possible in practice) 51.30 km 50% 50.47 km 25% 49.59 km None 48.82 km

The range of the scooter appears to be about 50 km, which is longer than the 40 km in 'urban nominal mode' claimed by the Peugeot SCOOT'ELEC, which uses the same batteries. This is probably due to the fact that, as we shall see in the next section, this ECE-47 driving cycle seems very well suited to the Lynch type motor we are using in our model. It may also be due to conservative claims in the vehicle specification.

Table 7.3 is also another demonstration of the power of simulations like these to quickly find the effect of changing vehicle parameters. In this case we have changed the proportion of the 'braking power' that is handled by the motor. In other words, we have changed the degree of regenerative braking performed. It is sometimes thought that this makes a huge difference to battery vehicle range. In the case of a scooter, it clearly does not. With no regenerative braking at all the range is 48.82 km. 50% is probably the highest practical possible motor braking, and this extends the range less than 2 km, or 4%. This does make some difference, but we should note that it is not a very great improvement. It is left as an exercise for the reader to do the same for the GM EV1; here the difference will be much greater, because it is a heavy vehicle, and well streamlined.

### 7.4.3 Constant velocity range modelling

Compared to the modelling of the driving cycles we have just achieved, constant velocity simulation is much easier. However, the basic round of calculations is the same as those outlined in the previous section. The system is simpler since the values of speed and torque are never negative or zero.

It would be possible to write a new and much shorter MATLAB script file for such a simulation. However, a quicker and easier solution, which makes use of the programs already written, is to create a 'driving cycle' in which the velocity is constant. This can be done in one line in MATLAB, thus:

This creates an array of 100 values, all equal to 12.5, which corresponds to 45kph. A line like this, at any desired velocity, can replace the lines ECE_47, or SFUDS, at the beginning of the simulations given in the Appendices. This may not be the most elegant method, but it is probably the quickest. Constant velocity simulations are clearly very unrealistic, and so are of limited use.

7.4.4 Other uses of simulations

The data produced during these simulations range of a vehicle. At each one second step including:

• vehicle acceleration;

• tractive effort;

• motor angular speed;

• motor efficiency;

has many more uses than just predicting the of the cycle many variables were calculated,

All of these variables are of interest, and it is instructive to plot them over one cycle. This can be done with great simplicity in MATLAB , and it gives very useful results. The basic principle is to create two arrays with names such as XDATA and YDATA and allocate them values during a cycle. For example, if the loop counter is C then C will have the same value as the time in seconds. If we wanted to plot the value of the motor power during one cycle, then we would include the lines:

into the code for a cycle. This can be seen very near the end of the script file given in Appendix 3. Near the end of the program, the main program that uses one_cycle, we would include the line:

plot(XDATA, YDATA);

For this type of plot the program could be simplified so that only ONE driving cycle is performed. An example of this type of plot output is shown in Figure 7.16. This shows the motor output power. It can be seen that the motor power is very modest, with a maximum of only about 12 kW. The motor has a maximum power of about 100 kW, so the simplified FUDS driving cycle is not testing the vehicle at all hard.7

7 This can be confirmed by looking for the maximum acceleration during the SFUDS cycle, which is only about 1 ms 2, whereas the GM EV1 is capable of over three times this value.

Power of GM EV1 electric motor during an SFUDS cycle

12000 10000 8000

2000 0

-2000

0 50 100 150 200 250 300 350 400 Time/seconds

Figure 7.16 A graph of the power of the electric motor in a simulated GM EV1 electric car during one run of the SFUDS driving cycle

Another example of a particularly useful plot is that of motor torque against motor angular speed. To produce this graph only two lines of the program need changing. The X and Y data lines become:

For this type of plot the points should be left as disconnected points - they should not be joined by a line. MATLAB easily allows this, and a suitable plot command is given near the end of the script file of Appendix 5. In Figure 7.17 this has been done for the electric scooter simulation. This maps the operating points of the motor. This graph should be carefully compared with Figure 6.7 in the previous chapter. It can be seen that, at least with this driving cycle, the motor is frequently operating in the region of about 120rads-1 speed, and low (~10Nm) torque. From Figure 6.7 we can see that this is precisely the area where the motor is most efficient. The motor is thus extremely well matched to this particular driving cycle. This probably explains why the range simulation results were rather better that given in the specification for Peugeot SCOOT'ELEC, to which our model is quite similar.

### 7.4.5 Range modelling of fuel cell vehicles

The principal energy flows in a fuel cell powered vehicle are shown in Figure 7.18. The energy required to drive the various fuel cell ancillaries that were discussed in Chapter 4

Power of GM EV1 electric motor during an SFUDS cycle

0 50 100 150 200 250 300 350 400 Time/seconds

Figure 7.16 A graph of the power of the electric motor in a simulated GM EV1 electric car during one run of the SFUDS driving cycle

Torque speed mapping for electric scooter motor

Torque speed mapping for electric scooter motor

20 40 60 80

Figure 7.17 A plot of the torque/speed operating points for the electric motor in an electric scooter during the ECE-47 test cycle. In the indicated region, many points are superimposed, as the vehicle is at a constant velocity

20 40 60 80

Figure 7.17 A plot of the torque/speed operating points for the electric motor in an electric scooter during the ECE-47 test cycle. In the indicated region, many points are superimposed, as the vehicle is at a constant velocity

Figure 7.18 Energy flows in a fuel cell powered electric vehicle

have not been explicitly shown, but these can be accounted for by adjustments to the value of the fuel cell efficiency.

The modelling of such a system is extremely complex, largely because of the fuel processor system. This has very many sub-processes with highly variable time constants, some quite long. The simulation of such fuel processing systems is extremely important, but too complex for an introductory text such as this. In addition, most of the important data is highly confidential to the companies developing these systems.

However, the simulation of a system running directly off onboard stored hydrogen is not nearly so complex. Indeed in many ways it can be less difficult that for battery vehicles, at least to a first approximation. The efficiency of a fuel cell is related, as we saw in Chapter 4, to the average voltage of each cell in the fuel cell stack Vc. If the efficiency is referred to the lower heating value (LHV) of hydrogen, then:

Now, we know from Chapter 4 that at lower currents the fuel cell voltage rises, and thus also the efficiency. However, we also saw in Chapter 4 that a fuel cell system will also have many pumps, compressors, controllers and other 'balance of plant' that use electrical power. This use of electrical power is higher, as a proportion of output power, at lower currents. The result is that, in practice, the efficiency of a fuel cell is, to quite a good approximation, more-or-less constant at all powers. (Note, this contrasts with an IC engine, whose efficiency falls very markedly at lower powers.)

At the present time, a good target value for the efficiency of a fuel cell operating off pure hydrogen is 38% referred to the LHV. So, from equation (7.28), we have:

Note that the fuel cell will probably, in fact, be running at about 0.65 V, but the difference between this and 0.475 represents the energy used by the balance of plant.

This value of average cell voltage can then be used in the formula8 for the rate of use of hydrogen in a fuel cell:

H2 rate of usage m = 1.05 x 10~8 x = 2.21 x 10~8 x P (7.30)

Notice that this formula does not require us to know any details about the fuel cell, such as the number of cells, electrode area, or any details at all. It allows us to very straightforwardly calculate the mass of hydrogen used each second from the required electrical power. Indeed, this simulation is a great deal easier than with batteries because:

• there is no regenerative braking to incorporate;

• there are no currents to calculate;

• there is no Peukert correction of the current to be done.

8 Derived in Appendix 2 of Larminie and Dicks (2003).

By way of example, we could take our GM EV1 electric vehicle, and take out the 594 kg of batteries. In their place we could put the fuel cell system shown in Figure 4.23, and the hydrogen storage system outlined in Table 5.3. The key points are:

• mass of 45 kW fuel cell system = 250 kg (estimate, not particularly optimistic);

• total mass of vehicle is now (1350 - 594) + 8.5 + 51.5 + 250 = 1066 kg.

Appendix 6 gives the MATLAB script file for running the SFUDS driving cycle for this hypothetical vehicle. It can be seen that the simulation is simpler. Some example results, which the reader is strongly encourage to confirm, are given in Table 7.4 below. In both cases 80% discharge is taken as the end point, i.e. 1.7 kg of hydrogen remaining in the case of the fuel cell.

An alternative approach that might well be found helpful, that certainly results in a much simpler MATLAB program, is to compute the energy consumed in running one cycle of the driving schedule being used. The distance travelled in one cycle should also be found. The number of cycles that can be performed can then be computed from the available energy and the overall efficiency. This approach obviously gives the same result.

### 7.4.6 Range modelling of hybrid electric vehicles

All the modelling we have done so far has involved equations which the system followed in a more-or-less predetermined way. However, when we come to a hybrid electric vehicle, then this is no longer so. Hybrid electric vehicles involve a controller, which monitors the various power in the system, and the state of charge of the battery, and makes decisions about the power to be drawn from the engine, battery, and so on. Very little about the energy flow is inevitable and driven by fixed equations. Furthermore, the strategy will change with time, depending on issues such as when the vehicle was last used, the temperature, the need to equalise the charge in the batteries from time to time, and a host of other criteria. The decision making of these controllers is not at all simple to simulate.

Another complication is that there are so many different configurations of hybrid electric vehicle.

The result is that the simulation of these vehicles cannot be attempted or explained in a few pages of a book like this. Indeed, the use of a simple program such as MATLABW on its own is probably not advisable. At the very least the SIMULIN^ extension to MATLAB should be used. There are a number of vehicle simulation programs available

Table 7.4 Simple fuel cell simulation results, showing great improvement in range over a battery vehicle

Simulation, SFUDS driving cycle in both cases

Range

GM EV1 with standard lead acid batteries, good conditions GM EV1 with a fuel cell and cryogenic H2 store.

148 km 485 km or described in the literature, for example Bolognesi et al. (2001). Among the most well known of these is ADVISOR® (Wipke et al. 1999), which is MATLAB®-based.

The program for the energy controller in a hybrid system, which is a sub-system of vital importance, will often be written in a high level language such as C. It makes sense to incorporate the simulator in the same language, and then it should be possible to use the very same control program that is being written for the controller in the simulation. This has obvious reliability and efficiency benefits.

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