Model-Based Control - Real-Time Rendering: Computer Graphics with Control Engineering - page 71

While real-time rendering may be considered similar to other computing pro-
cesses such as Web service, database queries, and network communication, it has
distinctively different task handling properties. In the work of Hellerstein et al.
[54], the tasks of feedback control are piecewise in nature and may be scheduled
according to changes in system loading. However, real-time rendering involves a
series of interdependent tasks (pipeline stages) that cannot be chosen selectively
for processing. Therefore task scheduling algorithms are not applicable to this pro-
cess because each rendered frame must follow a sequential order to create visual
animation effects.

5.3 PID CONTROL AND TUNING
PID controllers [55] have accumulated a long history since the industrial revolu-
tion and are known to operate in more than 80% of the world's control systems.
The fundamental PID control algorithm works on simple structures and produces
good performance without the need for heavy computation. This means that PID
controllers are inherently fast and easy to design, operate, and maintain. The PID
control action in a closed-loop feedback system takes a parallel mode form as shown
in Equation (5.1).

t

d
dt et

0

() = () + () + ()

ut Ket Ked K ττ (5.1)

p i d

At the implementation level, a PID controller's discrete form may be expressed as
Equation (5.2)

n

∑ 0

() = () + () + () −− ( )

un KenK ek Kenen ( 1 ) (5.2)

p i d

k =

where

KT
T

KT
T

p pd

K = , K =

i d

i

where u ( n ) is the control action and T p , T i , and T d denote the time constants of the
proportional, integral, and derivative terms, respectively.
For a PID controller to be effective, we see from Equation (5.2) that the gain
values of the controller must be set correctly. The process of determining these
parameters is known as controller tuning . A comprehensive summary of the tech-
niques for tuning the PID controller is provided in Reference [55]. For our system,
the PID controller is tuned using the Robust Response Time Tuning Algorithm from
the MATLAB ® Control Design Toolbox [56].