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Furthering Innovation
Technical Library: Dynamics of Real-Time
Dynamics of Real-Time Simulation – Chapter 10 – Asynchronous Real-time Multi-rate Simulation with Single and Multiple Processors
10.1 Introduction In this chapter we show how the real-time variable-step integration described in Chapter 9 can be combined with the multi-rate integration described in Chapter 8 to implement asynchronous real-time multi-rate simulation using eithe…
Dynamics of Real-Time Simulation – Chapter 9 – Variable-Step Real-Time Simulation
9.1 Introduction In the real time simulation of dynamic systems it has been traditional to use a fixed time step for numerical integration. Indeed, we have made this assumption in all of the previous chapters of these notes. As noted in Chapter 1, t…
Dynamics of Real-Time Simulation – Chapter 7 – Modified Euler Integration
7.1 Introduction We have seen in Chapter 1 that Euler or rectangular integration is the simplest numerical integration algorithm. Because of its simplicity it requires fewer digital instructions to implement and therefore runs faster than any other …
Dynamics of Real-Time Simulation – Chapter 6 – Special Methods for Simulating Linear Systems
6.1 Introduction In the simulation of dynamic systems it is often found that at least portions of the system can be described by linear ordinary differential equations. For example, control systems, although generally nonlinear, will frequently cont…
Dynamics of Real-Time Simulation – Chapter 3 – Dynamics Errors for Fixed-Step Integration Methods
3.1 Introduction Error analysis of numerical integration algorithms is traditionally based on the residual error terms in the Taylor series expansion representing the integral. Although such error measures do establish the dependence of the error…
Dynamics of Real-Time Simulation – Chapter 1 – Introduction
1.1 Overview of Real-time Digital Simulation Simulation of physical systems using digital computers continues to play an ever increasing role in all aspects of today’s technological society. In general the basis for simulation resides in mathemat…
Dynamics of Real Time Simulation
Computational methods in real-time simulation and control are in general not well understood by scientists and engineers, even when they have had extensive experience in non-real-time simulation. In particular, many of the methods used to control dy…
Dynamics of Real-Time Simulation – Chapter 2 – Z Transforms Applied to Real Time
2.1Introduction The method of Z transforms was originally developed for analysis of sampled-data control systems, i.e., dynamic systems utilizing a mixture of continuous and discrete time signals. This is just the case, for example, when a digita…