IEEE Instrumentation and Measurement Technology Conference Budapest, Hungary, May 21 -23,2001.

Future Perspectives of Automotive Control

Uwe Kiencke

Institute of Industrial Information Technology Hertzstr. 16

D - 76187 Karlsruhe kiencke@iiit.etec.uni-karlsruhe.de

Abstract In the last decade, many control and comfort functions have been introduced into our vehicles. Air-fuel ra- tio control, idle speed control, knock control, exhaust gas recirculation control as well as ABS and vehicle dynamic control are standard features today. Under the pressure of tightened legal standards and of market competition, automatic control will be employed 'to an even larger extent in the future.

1 Introduction The application of automatic control has dramatically changed the performance of our vehicles. Still, the pace of progress is accelerating in this field. Automatic con- trol is an important part of this development. As an ex- ample, enhanced models for fuel evaporation and com- bustion are presented. Another emerging area is infor- mation handling in complex distributed systems. This is presented for safety-relevant systems.

2 Engine Control Various alternate propulsion systems are under dlevel- opment, such as fuel cell driven electrical motors or hy- brid drives combining an electrical motor with a con- ventional internal combustion engine. The aim is to further reduce noxious emissions as well as fuel con- sumption. It is little known that hydrogen driven com- bustion engines and electrical drives require more en- ergy compared to conventional combustion engines and fuel cells. The large size of the fuel storage is another

problem for alternate drives. Only fuel cells driven by methanol come into the range of gasoline or diesel en- gines. When fuel cells look relatively promising from a technical point of view, their high production costs are still out of range for a wide utilisation in our vehicles.

Therefore there is still a major development focus on conventional combustion engines. In combination with a small electrical starter-generator motor (e.g. 10-15 kW), engine transients can be better smoothed out re- ducing noxious emissions, and automatically controlled gear boxes may be synchronized with a lot of comfort at gear switching. The injection and combustion process must be better understood and modelled.

2.1 Evaporation Modem diesel engines with a common rail injection system can use many different forms of injection curves over time e.g. single injection, pre- and main-injection or multiple injections. For realistic simulation results and the flexibility of simulation, the fuel spray model of Constien [5 ] is used. The fuel spray model is a basis approach calculating a phenomenological burning func- tion according to the given injection curve over time or crankshaft angle.

The injection is controlled by a one-dimensional look-up table with the crankshaft angle as input entity. Fuel is injected into the virtual combustion chamber ac- cording to the respective position of the crankshaft an- gle. For every injected fuel portion, the amount of liq- uid, gaseous and burned components will be calculated over the crankshaft angle. Figure 1 shows the differ- ent states of the fuel portions injected at different times (crankshaft angels). Because it is practically impossible

0-7803-6646-8101/$10.00 02001 IEEE

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3 5 4 O ,

I liquid burned gaseous

Figure 1 : Fuel Spray Model

diameter d32, the surface A K , ~ , the in-cylinder pressure p , the engine speed n and a diffusion constant CDi f f :

The remaining liquid fuel from the fuel portion i, not evaporating according to equation 6, is passed to the next step i + 1:

(7) mK,i+l = m K , i - m K , v .

The drop diameter d T must be recalculated in every crankshaft angle step i:

to analytically describe the multitude of different drop diameters, an average drop diameter in dependence of injection pressure and mass of the fuel portion will be

Finally, the inflammation delay time rzv is calcu- lated with an empirical formula used by Constien [5] :

ZlO_O K Tzv = 2.1 . j j - ' J 2 . , (9) calculated according the Sauter [5] approach:

xi d$i . Hi xi d g i . Hi ' (1) where jj is the average pressure and T the average tem-

perature over time. d32

where H is the number of drops with the same diameter and d T is the drop diameter. The index i represents the injection time. To calculate the Sauter diameter d32 the VardeL'opaNarde [6] approach is used:

d32 = 16.58 (Re. , (2 )

where Re is the Reynolds number and We the Weber number of the flow. The Sauter diameter finally is cal- culated in dependence of the air density p ~ , the fuel density P K , the fuel surface strain CTK, the kinetic fuel viscosity d~ and the diameter of the injector nozzle d T :

Furthermore the number of drops N T , ~ in dependence of the injected fuel portion mK.i is required in order to compute the evaporation:

(4)

Due to equation 2 and 4 the surface A K , ~ of all drops accrued in time step i can be calculated:

A K , ~ = N T , ~ * . d i 2 . ( 5 )

Finally the amount of fuel m K , v evaporating in every time step can be calculated in dependence of the drop

2.2 Combustion Model In contrast to the zero-dimensional model, the two-zone model allows to calculate the temperatures for the two areas of the unburned and the the bumed mixture. The flame front between these two areas are supposed to be infinitesimally thin, so that gases may be transferred from unburned to burned zone without a time delay. As presented later in equation 18, the flame front is still as- sumed to have a finite volume for exhaust gas calcula- tion. The schematic structure of the model can be seen in Figure 2. In every area, the mixture and the temper- atures are supposed as homogeneous. The pressure is the same in both zones.

After charge exchange, the fuel injection and the evaporation process start and will be calculated as de- scribed above. When the cylinder temperature is high enough and the inflammation delay time is expired the combustion process starts in the flame front. The com- bustion process may already start while fuel is still injected. The mass air flow from the unburned area through the flame front into the bumed area has to be calculated. The volume of the unburned area decreases and that of the burned area increases until the entire combustion chamber is filled with bumed gas and the combustion ends. During the combustion, the exhaust gases are calculated in the flame front.

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2.3 Combustion Process aw - fuel mr dure

To describe the combustion process for the two-zone model the basic formula for mass- and energy-balance must be solved. Furthermore, the flame process in the flame front and the air-fuel ratio in the flame fronl. must be derived.

The instantaneous air-fuel ratio AV in the comliusted zone results from the following equation: Real Process Model

Figure 2: Schematic Structure of the Two-Zone Model (10)

mv - mB - mBr AV =

Lst . (mB + ~ B T ) '

where mv is the mass of the burned mixture, TTLB the total amount of burned fuel, m ~ , . the residual gas of the burned area and L,t the stoichiometric air-fuel ratio.

The air-fuel ratio X i in the flame front represents how much fuel and air merge out of the unburned zone into the flame front to be burned. The evaporation model yields the input values for the flame front. In diesel engines, the inflammation starts first with a rich mixture getting leaner during the combustion. A definition of the air-fuel ration X i in the flame front can be found in [13]:

d m v d m s d m &

(1 1) xi = d v d v d w

L,t-(*+*) . According to the mass- and energy-balance of the

two-zone model, the pressure change in the combustion chamber can be derived (see appendix for variables) as:

m - mRO

m - mRo . (1 + Xi . L,t) - Xi ' L,t

The following simplification [7] were made in the simulation:

The simplification is applied because it was not possible to solve the dependence of the internal energy U on the pressure and of the ideal gas constant R v on pressure, temperature and air-fuel ratio.

In order to solve equation 12, the masses of the burned and unburned areas are necessary. The mass change dm, of the unburned area is

the mass change of the burned area is

. TU) in dependence of the injected fuel mass minj and the mass of the residual gas m ~ o in the combustion cham- ber. The volume of the unburned area VU can be cal- culated considering to the specific heat capacity c,, and the heat loss Qwu through the covered combustion chamber wall by the unburned area:

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p - V Diagram A" -Value

-g 100

k

9

5 2 50

0 2

O vdume110-4 m!, tamel SI Mean Tempeidure . UnburnedArea Burned Area

3500

2 2000 2000

1500 1000

500 500 0 500 0 200 0 200

monkshaft angle I"]

Figure 3: Simulation Results of 2-Zone Model

With equation 16, the volume of the burned area V B ~ can now be calculated:

The volume of the flame front V, can be derived as follows:

(mp) - m:') ) . Rm . Tv v, = N 7 (18)

'05 m2.baT 'Pz

where m c ) is the mass of the burned area in step n and p z the combustion chamber pressure.

2.4 Results of the Two-Zone Model The modeled engine has a displacement volume of 490 c m per cylinder (10 cm upstroke, 7.9 em drill). The injection pressure is 800 bar and includes a pre- injection. The engine simulation is done for idle-speed condition with approximately 960 crankshaft revolu- tions per minute.

In Figure 3 the results of the simulation are shown. After 0.5 s of simulation time the amount of injected fuel was increased at constant engine speed. The upper left graph shows the pressure over volume of the com- bustion chamber. Furthermore, an increased amount of fuel results in a higher combustion pressure and there- fore in a higher power output. The air-fuel ratio Xv in the combusted zone varies at the beginning of the

Simul dim Fksults Measured Pressure I

Figure 4: Comparison of Simulation Results and Mea- sured Data

simulation because of the EGR. After increasing the injected fuel portion with a constant air-mass, the air- fuel ratio AV of the burned area decreased because of a richer mixture.

The plots in the lower row show the mean temper- ature in the combustion chamber and the temperature progression in the unburned and burned area. The tem- peratures for these two areas are calculated during com- bustion only. Before the combustion process starts all temperatures are identical. The jump in the lower right plot indicates the beginning of the combustion.

Figure 4 is a comparison of simulation results with measured data of an engine test bed. The dates have been measured at engine test bed of Siemens Regens- burg, Germany. The test engine was a 2 liter common- rail diesel engine at idle speed (approximately 1000 crankshaft revolutions) with maximum engine load. Therefore the load of the simulation was also at its max- imum.

It can be seen, that the maximum pressure of the sim- ulation and the real engine are nearly equal. Further- more, the cycle of the simulation hits the real engine data. More real engine dates for the combustion cycle can be found in [12].

3 Safety-Relevant Distributed Sys- tems

In the future, many intelligent systems are integrated into complex distributed systems. The individual sub- systems operate autonomously. They are however de- pendent on the interaction with other subsystems. The aim is to develop a design process for such systems in which several objectives are regarded. A first objective is to ensure real time ability. A second one is to con-

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sider fault propagation. This is important, since elec- tronics are penetrating into more and more areas, even safety-relevant systems such as in automotive "drive- by-wire'' applications. A suitable way to describe the

The power operation for natural number is similar to the conventional algebra defined by the canonical extension of the multiplication operation. - a n = a @ a @ a @ @ E n . a nEN (24) propagation of information in distributed systems is the

Extended Max-Plus Algebra. n-time Multiplication

3.1 Extended Max-Plus Algebra A great disadvantage of the known max-plus or min- plus algebra [l], [4] or [lo] is, that either maximum or minimum operations are exclusively defined. In [3] a new approach was presented for a max-min-plus alge- bra which combines maximum and minimum operation in one algebra, which overcomes the above difficulties. This algebra has been developed to the extended max- plus algebra (EMPA) with additional features useful for the design of distributed real-time systems. The funda- mental set RE of this algebra is defined as

For real exponents it is no longer possible to define the power operation via the n-time multiplication. In that case we define the power operation direct via the multi- plication operation of the known conventional algebra.

a r : = r . a r& (25)

The abstract element E is defined as the absorbing ele- ment of the power operation.

a" = E (26)

The power operation is necessary for the transforma- tions form a structure graph in a weighted graph and vice versa.

= %U { E } (19) 3.1.2 Extension of the algebra to matrices

with the abstract element E which has no longer a For matrices in the EMPA, the absorbing null element correspondence to +00 or -00, like in the max-plus or min-plus algebra. A possible interpretation of t: could [r '-:I &] (27) be: "not present" or "not existent".

- N E E = . 3.1.1 Scalar Operators

is defined as quadratic matrix of &-Elements.

E & ...

The max-operator 8 denotes the "addition of the EMPA" in analogy to the max-plus algebra. It describes the maximum of two elements a, b E

a @ b = m a & , b ) = a f n , a > b (20)

Similar to the max-operator e, the min-operator @' de- scribes the minimum of two elements a, b E ZE.

a e' b = min(a , b ) = b f~ a > b (21)

It can also be defined by the maximum operator @ for all a and b, inclusively E.

a e' b = (a-' @ b-l)-l Va, b E X E (22)

Analogous to that, I is the identity element for matrices.

ye E ... &I

In the EMPA, the operators (+, - , *, / ) of the conven- tional algebra are working always elementwise to matri- ces. Applied to vectors and matrices, the @-operator or $'-operator respectively delivers the elementwise max- imum or minimum respectively.

In analogy to the max-plus algebra, the @ de- notes the "multiplication in he EMPA". It is equal to the addition of the regular algebra.

The matrix multiplication of the EMPA distinguishes between the maximum multiplication @ and the dual minimum multiplication 8'.

a @ b P a + b

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k

n=l [A @ I B ] i k = $' (ai, 63 b, j ) (32)

For natural numbers, the power operation of matrices is defined similar to the scalar case by the canonical extension of the multiplication operation. Opposed to that, the power op-eration of real numbers and matrix exponents is defined elementwise.

3.2 Real-Time Conditions In distributed systems correct co-operating is bound to the observance of real time conditions for the execution of subtasks and the transfer of messages between the subsystems. A prerequisite for the function of the whole real time system is, that all subsystems receive their in- formation with sufficient repeating rate and within the given real time conditions. This is necessary for the correct execution of their functions. Thus it is possible to get knowledge about the correct co-operation of the subsystems by their behaviour of communication.

For the modelling of the flow of information it is use- ful to distinguish between the cyclic and acyclic pro- portion of the arising communication. The share in cyclic communication is characterised by fixed repeat- ing rates. The modelling is raised by a signal rate model of the flow of information. It is based on an object- oriented map of the structure of the distributed system. The algebraic description of the signal rate model pro- vides the calculation of the repeating rates of all mes- sages in the system. The share in acyclic communica- tion consists of messages, which are stochastically ac- tivated by processes. On their way through the system they will trigger another messages. The time of appear- ance of these acyclic messages depends directly on the run times of the individual processes in the distributed system. The run times can be calculated by a operation time model. In [8] this is extended to different logical connections. A distinction is met whether a node is al- ready activated with the first arriving of a signal (min operation), or if the node must be activated by all input signals (max operation).

Therefore we combined min- and max-plus algebra. The abstract element could be seen as a not existing path. In the modelling of technical problems the edges of digraphs are often representing weightings like time, costs or capacities. Functionality of the system mod- elled as objects are the nodes of the digraph. There are no branching points or conjunctions out-side the objects (Figure 5). Common problems of weighted digraphs are

Figure 5: Example Consequence Graph

the calculation of the longest or shortest path as well as the synchronisation of processes in the nodes or the propagation of information through the graph. The aim is e.g. to calculate the time needed until all nodes of a graph have been activated by a trigger-event from any node of the graph. With the presented algebra a solution of this problem is possible. A graph is described by ma- trices Amax including all edges leading to maximum nodes and Amin including all edges leading to mini- mum nodes. & is representing the maximum weights of paths with the length k. For k = 0, the matrix & is equal to the identity matrix. The matrix & can be calculated in an iterative way.

A1 = 8 Amas CB (& 8' Amin B' &) (33) A, = A1 8 Amax B (A, 8' Amin e' A,) (34) ... (35)

(Ak-18' Amin CB' Ak-1 ) (36) Ak = Ak-1 @&a$ @

If circuits are part of the graph, existing of MAX nodes only, a further step is necessary. In this case the cir- cuits have to be calculated separately by partitioning the graph into two subsets, both without MAX circuits. For the detailed calculation see [2]. The calculations from time analysis can be either used to evaluate the com- pliance with the real-time constraints or vice versa, if the constraints are given, the system feasibility can be checked by propagating these time constraints through the system.

3.3 Failure Propagation Analysis We have got, as described, a graph with MIN and MAX nodes, which can be seen as AND and OR nodes in a

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logical model of a system. Thus we can use the :same model con-struct for timing and structure of the system. All existing edges are now marked with ’e’ in the ma- trices and vectors instead of weights or times. All other entries are still ’E ’ , in case of not existing edges.

We define the behaviour of the node types as fol- lows. While MAX nodes need all inputs free of failure to work correct themselves, MIN nodes need only one correct input. This de-pends of course on the ”intelli- gence” in an MIN node. As such strategies are imple- mented in safety critical systems, e.g. using fail-silent nodes, this is, at least for the moment, a realistic way to define. We have the matrices A,,, as matrix of MAX nodes, Amin as matrix of MIN nodes, B as matrix of inputs and as matrix of outputs. For calculation of failure propagation the vectors for the states of system nodes X ( k ) , the states of inputs u(k) and the states of outputs E( k) are introduced. Because the Max-Min- Plus Algebra is a stepwise calculation, k marks the step or the length of a path. The components are valued ’0’ if the node is free of fault and ’ 1’ if the node is faulty.

With the matrix operations of Max-Min-Plus- Algebra each single node could be defined faully and the failure propagation is easily derived for .X(k + 1) and y ( k + 1). Even multiple faults are possible to de- fine at any node or input of the system. Thus Fault sce- narios can be defined and the effects can be calculated. All affected nodes can be seen in the resulting vectors by applying the following equations.

- ~ ( k + 1) = [&in 8’ x ( ~ ) I e [&in x ( ~ ) I @ U(k)l€3 IC (37)

- Y(k + 1) = [CT @J X(k 4- l)] Y(R) (38)

The matrices Amin, Amaz, B and C have entries [E , e], as described above. The first part of equation (4.1) in- cludes the propagation for MIN nodes, the second part for MAX nodes, the third part includes the state vector of the inputs and finally there is the current state vec- tor. The Maximum calculation in the equations results, that a ’ 1’ is dominant and thus once a node is marked, it stays in that state. The calculation can be stopped after convergence, which is the case latest after k = n steps, while n marks the number of nodes.

With an early analysis of design it is possible to sketch strategies which permit an evaluation and in con- sequence an improvement of system design. This is necessary especially within safety critical fields., where, above all, the effects and possible causes of failures must be examined. At present mainly two rnethods

are applied. The Failure Mode and Effect Analysis (FMEA) represent a systematic methodology for the in- vestigation of safety-relevant systems. A system is re- garded as total system in a first step and determined, which functions it must fulfil. In a second step the system is divided into subsystems. These sub-systems are considered separately from each other. The subsys- tems are divided into function groups. With the Fault Tree Analysis (FTA) a system, in contrast to the FMEA, is examined from unwanted events endangering safety. At the top of the fault tree stands the un-wanted event and in hierarchically subordinated levels error causes or logic functions of error causes are represented. The individual elementary events are indicated with proba- bilities of failure. Thus probabilities for occurring un- wanted events can be calculated.

In contrast to the usual methods, we look at first hand only on the system in structural context. Further extensions can be easily made towards the probabilis- tic propositions of FMEA and FTA. With the algebraic modelling technique introduced here, a measure can be defined how important a node is for the system or in reverse how tolerant a system is to an error in a cer- tain node, apart from the investigation, how far an er- ror can spread. With the help of the defined algebra it is very easy to calculate not only the forward propa- gation but also the backwards oriented cause analysis. The main advantage of this approach is, that the prop- agation of a fault can be seen from each node and the effect of additional nodes can be shown. First we define a reachability graph for every node in the system, then we distinguish two directions of evaluation in different sub-graphs.

Reachability Graph: A node a is reachable from a given starting node b, if there exists a path from node b to node a. The Reachability Graph includes all reach- able nodes for the given starting node.

Consequence Graph: The starting point is a faulty node. From this node the propagation can be calcu- lated with equations 37 and 38. Besides it can be said, how much steps are needed to reach other nodes and thus how important a node is for another. The differ- ence to the Reachability Graph are the different defini- tion of MAX and MIN nodes, because a single failure is stopped by a MIN node with more than one inputs.

Cause Graph: Hereby the causes for a faulty node are calculated backwards. It can be said what could cause a fGlure at this node. Again additional informa- tion is behind the number of steps. The information, where a failure could come from to cause a failure in

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the regarded node, is given by the adjacency matrices. These can be applied "backwards". Thus a Cause Graph can be set up for any node of the system.

A measure for evaluation is the Importance Wij of a node X i for node X j . A cause graph for node X j is existing of uj nodes, except itself. There are 2"j com- binations, because of possible values '0' or '1'. If a value is given to node X i there are 2"j-l possibilities left. The number of combinations (Di j ) dominated by X i for a node X j is calculated as weight.

(39)

The higher the value, the more important is this node for the goal node. A very high Wij is a big risk for the whole graph. Another value in a cause graph is the Tolerance Measure. t i j is the number of all input values with X j free of fault, while X i is faulty.

If Tij is very low, the system is less tolerant against a failure in node X i .

The Importance and the Tolerance Measure are a good basis for a first predication how susceptible a sys- tem is to failures. In addition a system performance measure should judge the results of introducing addi- tional redundancy or functionality [9].

4 Summary and Outlook The presented models are basis for new control strate- gies and safety relevant systems for the automobile in- dustry.

Enhanced engine models are an important means to future control strategies. For detailed information about the combustion process, the temperatures and the ex- haust gases are appropriated in a two-zone model. It is a compromise between acceptable results and simula- tion efforts. The existing two-zone model is extended to a four-stroke engine model. At present it is possible to calculate the engine cycles in idle speed online on a dSpace@ environment for all cylinders. The final target is the realtime calculation of the exhaust gases during engine operation. The results of this online calculation can be utilized as inputs for a closed-loop exhaust gas control.

With a unique modelling technique as given by the Extended Max-Plus Algebra it is possible to combine

realtime and logical modelling. This is a major step towards a modular system design for distributed sys- tems. By using the same system graphs for realtime demands and failure propagation analysis the formulas give a great insight into system behaviour. It is possi- ble to calculate failure propagation from each node of a system.

Several strategies are given to evaluate system design and measure fault tolerance. It can be measured how important nodes are for a given node. The next steps to be done are the further combination of time and log- ical issues and a more detailed modelling of the struc- ture. Based on this a measure must be created, which includes more parameters as time, costs and failure be- haviour amongst others. This is the point, where opti- mization is successful.

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