Model-Based Control - Real-Time Rendering: Computer Graphics with Control Engineering - page 81

Graph of PID and SNPID System Outputs

400

Reference
SNPID system output
PID system output

350

300

250

200

150

100

50

0 0

1000 2000 3000 4000 5000 6000 7000 8000 9000 10,000 11,000 12,000 13,000 14,000 15,000

Frame

FIGURE 5.10 Comparison of system outputs using SNPID and PID controllers.

Experiment —To compare the performances of the SNPID and PID controllers,
we created a MATLAB simulation consisting of a closed-loop feedback system using
the system model derived in Experiment 3 from Chapter 3, Section 3.5.3. The system
first ran with the SNPID controller, then with the PID controller over the same dura-
tion of 15,000 frames. During the simulation, we allowed the system output to stabi-
lise before a new reference was set. In contrast to previous modelling experiments,
we wanted to validate the performance of the SNPID controller over a large operat-
ing range. To achieve this, we deliberately set the reference changes in bigger steps.
Simulation results —Figure 5.10 presents the simulated system outputs from
the SNPID and PID controllers. Figure 5.11 shows their respective and correspond-
ing control actions. Figure 5.10 indicates that the SNPID controller provides faster
response than the PID controller with almost no overshoot at the system output. The
SNPID controller was approximately two times faster than the PID controller in
reaching new steady-state references.

5.4 EXPERIMENTS
In this section, we present the details of the experiments conducted to validate the
control framework described in this chapter. The objective was to demonstrate the
implementation of a closed-loop feedback control system involving the real-time
rendering process with the plant and PID controller. The rendering process to be
controlled was the same as the application mentioned in Chapter 3. Figure 5.12 is
a screenshot of the application. The details on deriving the system model and its
parameters are also provided in Chapter 3.
Using the derived linear model, we first described two experiments in MATLAB:
one executed fully in a simulation environment and the other an actual rendering
process. In the actual rendering experiment, the plant and controller run on sepa-
rate computers as described in Section 5.2.1. Two sets of data were collected. Each