SIMULATION

This paper discusses the advantages of using fixed-point arithmetic in a hybrid environment. The particular ex ample used is that of a hybrid simulation system. The paper discusses the performance penalties which are paid in using floating-point arithmetic as opposed to fixed-point arithmetic. The paper points out the amount of digital- computer time used in fixed-point to floating-point con version. It also suggests a new hardware device, a floating point/fixed-point digital-to-analog converter. This paper points out one application in which this device could be useful.

Continuous parameter tracking systems utilizing the out put-error method have been analyzed by intuitive argu ments¹ and by linearized equations². This paper presents a method for analyzing the convergence properties of this type of system; it is applicable when the input signal is either a single sinusoid or a sum of sinusoids. The method is based on the technique advanced by Kryloff and Bogo liuboff³.

Simulation programs are currently being developed by the Cornell Aeronautical Laboratory, Inc. (CAL) to implement analytical studies of the dynamics of automobile accidents.

One CAL digital computer program simulates responses of the crash victim during a longitudinal collision (i.e., a frontal or rear impact). The eleven-degree-of-freedom non linear mathematical model is being used to evaluate the effects of belt-type restraints and energy absorption prop erties of vehicle interiors and structures.

In another CAL research program, an eleven-degree-of- freedom nonlinear mathematical model of an automobile traversing irregular terrain and encountering obstacles has been formulated and programmed for a digital computer. This simulation provides an analytical means of evaluating existing and proposed roadside energy-conversion systems.

The two simulation programs are described and their outputs are compared with experimental responses.

Methods are presented for the automatic preparation of functions of one or more variables for economical calculation by high-speed digital computers. The cost of calculation is considered according to the factors of number of functions, complexity, requirements for precision, and the frequency with which functions are to be calculated. Contrary to classic approaches, con sideration is not given to minimizing computational error for its own sake. On the contrary, the maximum allowable error may be sought in order to minimize computational costs. In this respect, each function is represented by an error envelope that specifies the required limits of computational precision. It is the error envelope rather than the function itself which is dealt with. The approximation techniques dealt with in this paper are limited to piecewise linear ap proximation of functions of one or two independent variables.

Projects requiring the maintaining and computation of large quantities of continuous functions are fre quently to be found in industry and research; for example, in the simulation of real-time processes— aircraft flight and flight trainer simulations, simula tion for control and regulation of continuous pro cesses as in chemical plants, weather calculations, radiation studies, etc.

In addition, computer service centers, providing computational services to many users, may extend the range and effectiveness of their mathematical function program library by the use of the economical com putational methods of this paper.