Model-Based Control - Real-Time Rendering: Computer Graphics with Control Engineering - page 86

Simulated Output

450
400
350
300
250
200
150

100
50
0 0

0.5 1 1.5

Frame

2 2.5 3

×10 5

Input

×10 4

0
-2
-4
-6

-8
-10
-12 0

0.5 1 1.5

Frame

2 2.5 3

×10 5

FIGURE 5.17 Simulated output with gain scheduling PID controller.

of switching the PID gain values as the controller processed output errors across the
extended operating range.
The first objective of the rendering system was tracking a predefined level at
340 FPS. This is an output level in Operation Range 2 from Table 5.1. Figure 5.14
indicates that the controller can bring the output to this level quickly with no over-
shoot and track the level steadily. Thereafter, we wanted to observe the controller's
ability to track a new reference level in a different operation range. We set the new
reference output level to 390 FPS (Operation Range 1 in Table 5.1). The new reference
output level was set while the control system was running.
Figure 5.17 shows the tracking of a new reference level with some overshoot. To
drive the output toward the target reference level, the control action caused the input
to the plant to take a steep dip that indicates an abrupt over-correction. Nevertheless,
the rendering process output was still brought to the desired reference level with
negligible error (fewer than 2 FPS).

5.6 CONCLUSION
In this chapter, we introduced the concept of using control principles to track
real-time rendering performance. The controller design was based on a closed-loop
feedback system with a plant model. Although no restrictions were imposed on the
controller design, we utilised the PID algorithm as the control strategy in a real-time
rendering application.
Since real-time rendering is inherently non-linear, we provided a solution to
control this process from a piecewise approach by approximating a large operat-
ing range by grouping smaller linear ones. We also introduced the neural-assisted