Linear Model Analysis of Real-Time Rendering - Real-Time Rendering: Computer Graphics with Control Engineering - page 39

Measured and Simulated Output

370

365

360

355

Simulated output
Measured output

350

345

0 1000 2000 3000 4000 5000 6000

Frame

Ve rtex Count (Input)

×10 4

4.25

4.2

4.15

4.1

0 1000 2000 3000 4000 5000 6000

Frame

FIGURE 3.14 Measured and simulated rendering system output in Experiment 3.

TABLE 3.5
Parameters of ARX Model in Experiment 3
Parameter Calculation

A(q) 1 - 4.159 q -1 + 5.814 q -2 - 1.659 q -3 - 3.322 q -4 + 3.158 q -5 - 0.8321 q -6

B(q) 1.007 × 10 -5 q -1 - 5.033 × 10 -5 q -2 + 0.0001007 q -3 - 0.0001008 q -4

+ 5.045 × 10 -5 q -5 - 1.011 × 10 -5 q -6

Operating point u = 4.1809 × 10 4 , y = 356.7121

was derived, we compared the output of the model with the actual measured data
as shown in Figure 3.14. Similar to the comparison of the outputs in Figure 3.12,
it can be observed that the simulated model produced an error rate less than 5 FPS
throughout the simulated range. Table 3.5 illustrates model parameters.
Subsequently, we imported this model into Simulink and constructed a PID-based
controller system as shown in Figure 3.15. We present the performance of this con-
trol system based on its tracking a pre-defined output level as shown in Figure 3.16.
Note that the rendering system output follows the user-defined reference very closely
at steady state and within a very short time without overshoot or oscillation.
To further validate our control framework, we replaced the system model with the
actual rendering process in a separate test. The PID controller block was executed