Digital computers in time- critical simulation

by PETER WRIGHT

In simulation exercises involving flight, missiles and nuclear plants, for example, real-time or faster than real-time operation is necessary. This can be achieved by the use of very high speed computers

Abstract: Tim-e-critical simulation of continuous dyMmic systems is vital if the simulation must be perfwmed in real time or if

there is a costpersolutian criterion. The paper &scribes the use of a programmable digital computer as opposed to the traditional analogue and hybrid computer solutions to

such simulations.

Kqworak time-critical simulation, digital computers, analogue computers, hybrid computers, real-time systems.

Peter Wright is general manager of Applied Dynamics International Ltd.

T ime-critical simulation of con- tinuous dynamic systems is an increasingly important growth

area in computer development, as the

power and effectiveness of such simulation techniques become more apparent. For the purpose of this arti- cle a sufficient definition is as follows: a continuous simulation system is con- sidered to be time-critical if:

l it involves hardware or man-in-the-

loop, or both, and hence must be performed in real time, or

l there is a cost per solution criterion to be met which involves minimiz- ing the time per solution, leading to faster than real-time simulation.

In this area of simulation, it has been found that effective solutions are now

offered by very fast, programmable digital computers specifically designed for the purpose. Such computers rep- resent a significant departure from the

traditional analogue and hybrid com- puter solutions to such simulations.

Before looking at comparisons be- tween these two approaches, it is use- ful to consider briefly today’s simula- tion environment. During the 1960s aerospace and weapons development programmes provided the major im- petus to time-critical simulation stu- dies. After a lull of several years in the

early 197Os, government programmes, particularly in the USA, are again pro- viding a strong stimulus to simulation activities in these areas, and a number of examples will be given later in this

article.

However, there are other major forces acting today which further the growth of time-critical simulation. In the past five or six years, the rapid

30 0011-684x/83/09003&04$03.00 0 1983 Butterworth & Co (Publishers) Ltd. data processing

increase in the cost of energy has caused growing awareness of the need for energy conservation, and the de- velopment of new sources of energy. This in turn has lead to a rapid growth in large-scale simulation activities both

for engineering purposes and, in avia- tion, for pilot/operator training, due to the greatly increased cost of operating aircraft.

Examples of continuous simulation

One of the largest growth areas for high-speed computer applications in- volves flight simulation for training commercial and military air crew. The US Air Force alone is currently pro-

curing flight simulators worth over $2 billion. Computers are used in these simulators both for real-time solutions of the aircraft and avionics systems equations, and also to mechanize com- puter-generated imagery for visual, in- frared and radar scene displays.

Energy conservation efforts in chem- ical plants have led to the creation of complex energy distribution net- works, greatly complicating control system design and operator training. Detailed system simulation has hence become a necessity.

Simulation is playing a major role in the development of magneto-hydrody- namiclsteam coupled power plants.

Detailed simulation of nuclear reac- tors, such as the thermal hydraulics of the nuclear cooling system, is now tak- ing place, so that the appropriate con- trol strategies can be quickly reached in the event of a small accident, which could quickly escalate without the cor-

applications

rect countermeasures being taken. Sophisticated electronic fuel control-

lers are being developed for jet engines in an effort to reduce overall engine weight and fuel consumption. De- tailed engine simulations are being used to check out the operations of these new controllers, over a wide

range of flight conditions, prior to their use with actual engines.

A number of other examples could easily be cited. The models used in these simulations have a number of features in common. They are large, involving tens or even hundreds of state variables and algebraic equa- tions. They are also stiff, having time constants of characteristic frequencies differing by a factor of a thousand or more, and they are nonlinear, contain- ing empirical or analytic functions of one, two or more variables.

Analogue vs digital

In time-critical simulation, the type of computer used is generally determined by the requirements of the simulation. The traditional solution has been to

look at analogue or hybrid computers. However, in many applications such a solution is simply not adequate, and a general purpose digital computer would usually be chosen, provided that it has adequate computational speed to simulate system characteris- tics, including dynamics, with an acceptable degree of realism and fideli- ty. For example, the great majority of large flight crew and operator training simulators in use today have been de- signed around the use of a general pur- pose digital simulator.

On an (analogue computer, simula- tion is accomplished by interconnect- ing electronic units, each one perform- ing its own simple mathematical func- tion. Since all these interconnected elements ‘operate in parallel, the ana- logue com.puter is well suited to certain restricted types of time-critical simula- tion. A standalone analogue computer, however, has two very serious limita- tions for rnore general simulation use.

First, its size must grow in direct relationship to the complexity of the

model being simulated. For large simulations, therefore, the standalone analogue computer becomes prohibi-

tively expensive. Second, the analogue computer does not have the memory capability for storing large blocks of data. Thus, in simulations which re- quire, e.g. storage of data for multivar- iant functions, the standalone ana-

logue computer approach is clearly in-

adequate. The hybrid computer was de-

veloped as a simulation tool encompas- sing the best features of both analogue and general purpose digital compu- ters, and it has been used for many time-critical simulations which would not be feasible with the use of one or other type of computer alone. Howev-

er, the hybrid also has several impor- tant limitations. For one thing, the us- ers must concern themselves with programming two different computers and an interface. Also, the general pur-

pose digital computers which form part of the hybrid computer system are simply not fast enough to perform the run-time computational tasks assigned to them in many simulations, without causing significant errors.

One method used to overcome the limitations of the analogue computer has been based on its great computa- tional bandwidth, much greater than is required in many applications. A number of iterative techniques have been developed which allow the ana- logue computer components to be used in a time-shared fashion, where the digital computer acts as a function storage and playback device.

Despite their proven usefulness, these techniques entail two major drawbacks. In the first place, the simulation programming is much more complex and time consuming. Second, the speed of the interface con- verters and the I/O speed of the digital computer limits the extent to which the analogue components can be time shared and hence provides a bound to effectiveness of this approach.

The latest solution to time-critical simulation is the extremely high speed

digital computer, with a multi- processor architecture specifically de- signed for the continuous modelling of

large dynamic systems. An example of this approach is the AD 10, introduced by Applied Dynamics International

some four years ago. Although programmable, the AD

10 has not been designed as a general purpose computer. It requires the use of a host computer, to load its program and data memories, to debug prog- rams, to run diagnostics, etc. Howev- er, it is intended for standalone opera- tion during run-time, and only re- quires the host computer for offline or

nonrun-time tasks. Each processor within the AD 10 is

a functionally unique entity, designed to perform a single task or a narrow group of closely related tasks (see Figure 1). This multiprocessor struc- ture permits a number of operations to be overlapped, or performed in para- llel during an instruction cycle. Each processor contains its own program memory and instruction counter, the instruction word length varying up to 80 bits. Microprogramming is used within each processor to achieve addi- tional parallelism.

The AD 10 is a synchronous system

with an instruct.ion cycle time of 100 ns and with data transfers within the computer taking place at speeds of up to 20 million words per second. The data memory, which employs dynamic MOS memory devices, is organized in interleaved pages to take advantage of the high data transfer rate.

The AD 10 employs emitter-cou- pled logic for its varous processors and controllers. Bipolar memory devices are used for program memory and for the high-speed general purpose regis- ters incorporated in the various pro-

cessors. Although the AD 10 uses very fast logic devices, its high speed is pri- marily due to its system architecture and the design of each processor as it relates to the time-critical simulation task.

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Software package

The main software package for the AD 10 is MPS 10, a high level program- ming approach designed to take full advantage of the computer’s structure. The user need have no knowledge of AD 10 architecture or assembly to be able to program large and complex simulations. In MPS 10, an applica- tion program is written as a sequence of calls to a set of subroutines called modular programs-no code is gener- ated to be stored in program memory. Each application program is mapped into the very large data memory. Only the modular program library fur- nished as part of MPS 10 does not need to be concerned with the size of their application program (see Figure 2).

There are numerous projects which can be chosen to illustrate the speed and power of this new approach to time-critical simulation of large, stiff, nonlinear systems. Many of these ap- plications involve hardware and/or man-in-the-loop where real-time simulation is an absolute necessity. They cover such diverse areas of activ- ity as missile and aircraft (both fixed and rotary wing) simulations, jet and

Figure I. system architecture of the ADIO.

Figure 2. Program software relationships.

AD 10

rocket engine simulations, and sirnula- tions of complex control mechanisms and servomechanisms, an example of the latter being the remote manipula- tor system for the space shuttle, seen in action only a few months ago. A selec- tion of some of these applications is now given.

Apart from the first example, in- cluded for its intrinsic interest in showing how a new field of simulation is tackled, coverage is of avionics/ aerospace and defence subjects, as simulation problems in these areas are particularly well known.

Nuclear power plants Following the disaster in the USA at Three Mile Island several years ago, there has been a lot of attention given to the study of small accidents that are too small to initiate automatic shut- down procedures. The Nuclear Reg-

ulatory Commission has sponsored a number of studies, one of these being at Brookhaven National Laboratories.

Two AD 10s are being used to mod- el the thermal hydraulics of the reactor cooling system, and it is interesting to note that the same model has also been implemented in FORTRAN on a CDC 7600 which proceeds at one tenth of real time.

If an emergency arises, different control strategies can be simulated much faster than real time, and the appropriate strategy examined and approved before implementing it on the reactor.

A specific example has been the de- velopment of a spatial dynamics model of a reactor, based on a multinode rep- resentation, rather than a point source model. A 42 node reactor neutron kinetics model has been programmed in MPS 10. At each node, the model

32 data processing

applications

consists of a set of seven equations de- scribing the behaviour of the prompt neutron group and six delayed neutron groups at Ithat node. The set of equa- tions at any one node is coupled to the set of equations at each of the other nodes within the reactor representa- tion. This model is very stiff - the time constants for these equations range from about 1Oms to 100s or more.

The elements in the 42 x 42 coupling matrix are dependent upon many fac- tors, such as fuel and coolant tempera- tures and reactor controller action. For simulation purposes, these coupling elements are treated as constants. The incorporation of a means for varying some, if not all, of these coupling coef- ficients is a straightforward task in MPS 10, that can be performed once the necessary functional relationships have been defined.

To summarise briefly, this model has 294 state variable equations with a 42 x 42 element coupling matrix. The MPS 10 program for this model has a frame-time of 1.8 ms, i.e. the time required for one complete pass through all the equations.

Flight simulation - six degrees of freedom In the simulation of a typical small jet aircraft, the equations of motion are written in terms of an aircraft body axis coordinate system. The aerodyna- mic functions include three or four variables, nine of three variables, ten of two variables and four of one vari- able. Coa’rdinate transformations in- clude two conversions from rectangu- lar to polar coordinates, and one three angle, on’e two angle and one single angle vector rotation.

The si:mulation also includes an elementary flight control system to allow the aircraft to be partially or fully flown under autopilot control, includ- ing loops for pitch, roll and yaw con- trol.

The AD IO frame-time is approx- imately 3.30 ms. With this frame-time accurate simulation is possible at solu- tion rates up to 100 times faster than

real time. Such high computational speeds are very useful in design para- meter studies.

Random turbulence in aircraft Another example in this same applica- tion area involves the simulation of a complete aircraft when subjected to random turbulence, with special emphasis on wind shear profiles. Air- craft performance under these condi- tions is especially critical in the approach and landing phase, as well as on takeoff. Many hundreds of approac~l~~gs and takeoffs must be simulated under given conditions in order to determine with confidence the mean touchdown velocity or, more im- portantly, the probab~ity of stall and loss of control under severe wind shear conditions.

Because of transport aircraft crashes in recent years due to wind shear, the FAA and NASA are studying this problem very intensively, with many wind velocity profile measurements being made under severe atmospheric condiitons using doppler radar.

Missiles The problem of the evaluation of stochastic or random inputs has proven to be one of the most costly exercises in computing, and it is perhaps in this area that the extremely high speeds of modern multiprocessor simulators have shown to greatest advantage.

An excellent example is in the simulation of guided missiles, where the noise in the target tracker is simu- lated as a random signal with a spe- cified probab~ity density function and power spectral density. For a given launch condition many simulated mis- sile flights must be run on the compu- ter in order to obtain the RMS {root mean square) miss with a reasonable level of confidence. For example, RMS miss to 10% accuracy requires approximately 100 complete simula- tion runs; 1% accuracy requires some 10000 runs.

Satellite space vehicles

The development of satellite space

vehicles has greatly increased the problems faced by the aerodynamicist, since the structures are typically large, and very flexible. The importance of providing a real-time simulation is very apparent in space structure de- sign, since the complementary ground trials and tests possible with normal aircraft have little relevance.

Typical of this group of problems is the recent development of a space tele- scope weighing about 6 OOOkg, 20m in height and with an overall width, in- cluding its extended solar panels, of some 5Om. The structure is highly flexible, and yet must be capable of being positioned on some distant star or other light source with extreme accuracy. An AD 10 was successfully employed on this project.

Helicopter simulation The last example given is one of the most challenging: the simulation of helicopters in real time. All previous simulations had to be based on the use of a disc model for the rotor blades, due to lack of computational speed, but the most effective modelling tech- niques must involve a detailed repre- sentation of the blades themselves.

The blade approach divides each blade into a number of elements, and the local veloclity components at the pressure centre of each element is then computed to enable the subsequent calculation of angle of attack and Mach number. This in turn provides the ele- ment lift, drag and pitch moments which can be summed to provide com- posite force and moment components acting on the blade.

In a commercial simulator for the Bell Model 222, main and tail rotors have 12 elements each, and the main rotor has one rigid and four elastic de- grees of freedom. Using MPS 10 on the AD 10, the integration frame-time for the simulation is under 1.9 ms, there- by more than achieving the required timeof5ms. q

Applied Dynamic:~ International Ltd, Oxford House, Oxford Stxer, Wellingborough, North- ants NN8 4MG, IJK. Tel: (0933) 72666.

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