Model-Based Control - Real-Time Rendering: Computer Graphics with Control Engineering - page 79

as it traverses the different operating ranges. Such an implementation may be realised
in MATLAB/Simulink as shown in Figure 5.8.
Since the PID gain values may differ greatly over the entire operating range,
scheduling these values directly into the PID controller may cause some unexpected
jitter at the border where the switch takes place. This jitter is typically manifested
as a disruption to the control mechanism and may create some inconsistencies in
plant output. A common technique to reduce the effect of this jitter is to adopt linear
interpolation between the controller's gain values.

5.3.4 n euRal Pid c ontRol
The PID controller is computationally straightforward and effective. The challenge
lies in tuning its gain parameters, especially when it is difficult to derive a system
model. In the previous section, we examined the use of a combination of separately
tuned PID controllers. The goal is to create a control system that works over a large
operating range and is resilient to the effects of the system's non-linear characteristics.
In this section, we investigate a technique that does not require the cascading of PID
controllers and eliminates the effort to tune them separately. This technique also allows
a single PID controller to be continuously tuned online while the system operates.
Artificial neural networks (ANNs) are well known to be capable of memory
retention and learning through their adaptive nature of modelling non-linear func-
tions. By utilising an artificial neuron to learn and adaptively tune a PID controller
in the single neuron adaptive PID (SNPID) control algorithm [64], it is possible to
achieve continuous control with good performance over a substantially large oper-
ating range. Figure 5.9 illustrates the SNPID control system design. Recall from
Section 5.3 that the discrete incremental PID controller may be expressed as:

n

∑ 0

() = () + () + () −− ( )

uk KekK ek Kekek ( 1 ) (5.8)

p i d

k =

where u ( k ) is the output of the controller and K p , K d , and K i are the proportional gain,
derivative gain, and integration gain, respectively. e ( k ) is the error between the refer-
ence and system outputs that serves as input to the controller. In the SNPID control
implementation [64], we have the output of the neuron given by the following equation.

T

YXW = (5.9)

x 1

w 1

Output

Reference

Error, e State

Converter

x 2 w 2

Rendering
Process

K

w 3

x 3

FIGURE 5.9 Single neuron PID control system.