Feb 14, 2019 | Dynamics of Real Time
11.1 Introduction There are many examples of dynamic systems with state-variable derivatives that have discontinuities. A simple example is a spacecraft attitude control system with on-off reaction-control thrusters. Other examples include dynamic systems with...
Feb 14, 2019 | Dynamics of Real Time
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 either a single...
Feb 14, 2019 | Dynamics of Real Time
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, the overriding...
Feb 14, 2019 | Dynamics of Real Time
8.1 Introduction Multi-rate integration provides a method for improving performance in simulating dynamic systems consisting of identifiable slow and fast subsystems. In multi-rate integration, the fast subsystem is simulated with an integration step size given by ,...
Feb 14, 2019 | Dynamics of Real Time
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 integration method...
Feb 14, 2019 | Dynamics of Real Time
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 contain linear...
