Digital computer continuous system simulation languages (CSSL) are directly applicable to the high speed programs needed for multi-run analogue/hybrid computer studies. This is true because the required digital computer operations can always be interpreted as solution of simple difference equations, which are simply solved, step by step, with the conventional digital integration algorithms built into the simulation language. In this report, the very high digital computing speed needed for fast analogue/computer Monte Carlo simulation is obtained with a block diagram simulation language translating directly into fast executing assembly language.

Block-diagram programs, for instrumentation, control, and simulation systems are especially easy to translate, since no explicit precedence analysis is needed. Block-diagram primitives range from simple adders to complete real-time controllers. They are pure-procedure, reentrant microprograms or threaded code in read-only memory, which may be pre-programmed and plugged in for special applications. In addition to hand "assembly" and optimizing compilation of block-diagram programs, we exhibit the new direct-executing MICRODARE II system, which embeds block-diagram "assembly" in an advanced BASIC dialect serving for interactive editing, job control, and file manipulation. Execution speeds of the new systems permit LSI-11 microcomputers and PDP-11 minis to match and exceed those of a CDC 6400; a number of examples are shown. The report continues with a discussion of future multi-task, multiprocessor real-time BASIC systems incorporating MICRODARE. We finally describe a new two-processor system consisting of an LSI-11 running MICRODARE software joined by a two-port memory to an ultra-fast bit-sliced 2903/2910 processor executing block-diagram microprograms.

This survey article traces the development of analog/hybrid and digital simulation of continuous systems since the early 1950's, describes modern aspects, and discusses future trends.

Control and trajectory optimization involves the minimization of a performance index (PI) of integral form where some optimal control law exists in a dynamic system. In this paper, a hybrid minicomputer with an adaptive random-search algorithm implements an iterative search for the optimal control. The search assumes that some initial control is randomly perturbed and a fast analog computer generates respective PI from the analog response of the dynamic system. An improved PI informs the digital computer to utilize the perturbed control as a basis for the next iteration; otherwise a new perturbation replaces the old perturbation in the next iteration. The search terminates when no further improvements occur.

To obtain successively improved control-variable functionsku(t), we propose to add a random perturbation δu(t) toku(t). A fast analog-computer run then solves the dynamical system equations and computes the given criterion function. If the latter has been improved, thenk+1u(t)=u(t)+δu(t) is stored digitally for the next iteration; otherwise 5u( t) is discarded and a new control pertubation is tried.

For very fast function generation with small fixed-point digital computers, the n-bit argument word x is split into an N-bit word representing the breakpoint abscissa Xi for table-lookup by indirect addressing, and an n-N bit word representing the interpolation difference X-Xi. The complete procedure takes only about 50 machine cycles (50 μs) for equal breakpoint intervals, and about 70 machine cycles for variable breakpoint density. A sine-cosine generator for digital or hybrid-computer simulation is exhibited as an example.

The linear-circuit performance equation for an important class of mode-switched operational amplifiers is derived to identify errors caused by finite feedback loop gains, switch resistance, and follower-amplifier source impedance. Errors due to capacitor dielectric absorption, switching spikes, dc leakage, and current limiting are discussed with reference to an electronically switched integrator (sample-hold or analog-memory circuit), and various design requirements are listed.

A new electronic slicer circuit produces output pulses whenever a random input voltage x(t) is between two slicing levels X - Δx/2 and X+Δx/2. The slicer pulses gate a counter to produce a direct digital readout count equal to the estimated first-order probability density of the input signal. The system was designed for random process studies with conventional electronic analog computers and has compatible accuracy.