Advanced Dynamic-system Simulation: Model-replication by Granino A. Korn

By Granino A. Korn

Study the newest strategies in programming subtle simulation platforms. This state-of-the-art textual content provides the most recent strategies in complex simulation programming for interactive modeling and simulation of dynamic platforms, comparable to aerospace cars, keep watch over structures, and organic structures. the writer, a number one authority within the box, demonstrates software program that could deal with huge simulation experiences on general own pcs.

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1-8). The servo controller produces the motor-control voltage voltage as a function of the measured position error error = x – u and the rate of change xdot = dx/dt continuously measured by a tachometer on the motor shaft. Figure 1-8 shows a simulation program. The sinusoidal servo input u = A * cos(w * t) reduces to a step input for w = 0. We model a simple linear controller with voltage = – k * error – r * xdot (1-5) Some nonlinear controllers will be discussed in Chapter 7. The controller gain k and damping coefficient r are positive controller parameters.

This is precisely why we wrote each difference equation (2-1b) as an assignment to a “predictor variable” Qi rather than to qi. It is always safe to rewrite difference equations such as (2-2) as Qi = Fi(t; q1, q2, …; p1, p2, …) and to program updating assignments qi = Qi following the difference equations as in Section 2-1. info Sampled-data Assignments and Difference Equations 35 + 0 – 0 scale =4 400 q1 vs. 90 t = 0 | q1 = 0 | q2 = 1 drun -----------------------------------------------------------------DYNAMIC -----------------------------------------------------------------SAMPLE 10 | -for better display only Q1 = q2 | Q2 = a*q2 + b * q1 | -- difference eqs.

2 When there are no vector operations or subscripted variables, DESIRE again automatically prevents sort errors with “undefined variable” messages. When there are vector operations, we proceed as in Section 1-9. info 34 Models with Difference Equations, Limiters, and Switches Following the assignments (2-1a) and (2-1b), we must set new statevariable values qi for the next sampling time with N updating assignments qi = Qi (i = 1, 2, … , N) (2-1c) To summarize, a complete difference-equation program (2-1) starts with sorted defined-variable assignments (2-1a).

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