Model-Less Control - Real-Time Rendering: Computer Graphics with Control Engineering - page 89

6 Model-Less Control
6.1 INTRODUCTION
In this chapter we consider a different perspective for controlling the rendering
process. While conventional data-driven system identification strategies may be
adopted to derive a rendering process model, the result may not necessarily imply
that an accurate model can be derived without resolving certain technical challenges
in data processing.
To circumvent such problems, this chapter investigates an approach to control-
ling the rendering process by allowing the user to exploit a priori information about
the rendering process without the need for an explicit rendering model by using
a soft computing method known as fuzzy control. The fundamentals of fuzzy set
theory and the mathematics for a conventional fuzzy inference system are provided
in Section 4.2.2 in Chapter 4.
6.2 FUZZY CONTROL SYSTEM
The construction of a fuzzy logic control system is relatively similar to the PID
control system described in Chapter 5. Based on the same architecture described by
Figure 5.2 in that chapter, we introduce the fuzzy controller is used in place of the
PID controller. As in the case of the PID controller in which the quantity of the input
to the plant is varied directly, no strict rule applies to the selection of the input to a
fuzzy control system. Certain fuzzy control systems such as applications for tem-
perature and process control utilise the rate of change of the input to the plant instead
of the numerical value of the quantity. In this research, the rate and the direction of
change (increase or decrease of vertex count) are used.
The design of a fuzzy control system consists of two phases. First, we develop
the fuzzy control system in a simulation environment where the plant model is used.
After the control system is validated to work correctly, we replace the plant model
with the actual rendering process as done in previous experiments.
Unlike a PID control system, a fuzzy logic controller functions on linguistics
variables instead of numerical values. As described in Section 4.2.2, a fuzzy logic
system is defined primarily by the type or structure of the controller, the rule base,
and the membership functions of the input and output of the process to be con-
trolled (Figure 6.1). In this research, we adopted the Mamdani fuzzy model. The rule
base was constructed based on a straightforward inverse input-output relationship
between the frame rate and the rate of change of vertex count. This fuzzy inference
rule set is shown in Table 6.1.
The fuzzy logic toolbox in Simulink ® /MATLAB ® provides comprehensive
tools such as the rule editor and membership function editor to accelerate the
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