Dynamics of Real Time

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 dynamic errors and stability in traditional simulation are just not applicable in the real-time case. A vast array of simulation and control tools and other technology have been developed over the past decades that help abstract the complexity of real-time. However, without a deep understanding of the first principles nature of this technology the real-time engineer can fall into many traps. This book is made available to help anyone strengthen their knowledge of the dynamics of real-time and help us all develop better solutions as the world of complex systems becomes increasingly complex.

Dynamics of Real Time
by Dr. Bob Howe, Applied Dynamics Founder

Chapter 1 – Introduction

Chapter 2 – Z Transforms Applied to Real-Time

Chapter 3 – Dynamics Errors for Fixed-Step Integration Methods

Chapter 4 – Dynamics of Digital Extrapolation and Interpolation

Chapter 5 – Dynamics of Digital-to-Analog and Analog-to-Digital Conversion

Chapter 6 – Special Methods for Simulating Linear Systems

Chapter 7 – Modified Euler Integration

Chapter 8 – Multi-rate Integration

Chapter 9 – Variable-Step Real-Time Simulation

Chapter 10 – Asynchronous Real-time Multi-rate Simulation with Single and Multiple Processors

Chapter 11 – Real-time Simulation of State-variable Derivatives with Discontinuities