WSEAS TRANSACTIONS on ELECTRONICS

# 3 Extension Controller

Sometimes the engineering process is not able to setup a mathematical model that can accurately describe and control an integrated plant system. In other words, the traditional controller is not able to obtain the satisfactory results. Utilizing the extension controller to control a plant, can often obtain unexpected terrific results. The listed references used the PI controller, fuzzy controller and extension controller and the results were compared. The extension controller was verified to produce better performance than the traditional PI controller, and is similar to the fuzzy controller via the experimental results [9]. Using a GPS receiver to carry out frequency stability and time syntonization will influence the precision due to an unstable oscillation frequency in the GPS receiver, clock bias and integer ambiguity and so on. This paper proposes using the extension set and element model concept to design the extension controller, as shown in Figure 1. [10][11]

Figure 1. Extension Control System Functional Block Diagram

The basic extension controller concept is to transfer the signal point of view to deal with the control problem. Using a relational function of the control output signal as the control input correction let the control signal transfer to a reasonable range.

### ISSN: 1109-9445

152

Guo-Shing Huang

First, obtain the classical domains in the control output plane:

f f R_{G }=(G,C ,V )=

⎢ ⎢ ⎢ ⎢ ⎣ ... C_{fn }C_{f 2 }⎡G C_{f1 }

=

⎢ ⎢ ⎢ ⎢ ⎣ ... C_{fn }C_{f 2 }⎡G C_{f1 }

1 2 . . . f f f n V V V ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦

0 1 0 1 0 2 0 2 0 0 , , . . . , n n a b a b a b < > ⎤ ⎥ < > ⎥ ⎥ < > ⎥ < > ⎥ ⎦

G is the GPS receiver; G_{f }is characteristic of the GPS receiver.

the control Where C_{f }_{1 },

## C_{f 2 }, …, C_{fn }is to express n different characteristics

such as the oscillation frequency of GPS receiver, integer ambiguity of G . And V_{f 1 }, V_{f }_{2 }, …, V_{fn }

respectively is G about the range of C_{f }_{1 }, C_{f 2 }, …,

C_{fn }value, namely classical domains.

t h e n f i V

=< a_{0n },b_{0n }>

i = 1, 2, …, n

The extensional domain in the control output plane is expressed as:

## R_{S }= (G_{o },C_{of },V_{of }) =

o G ⎡ ⎢ ⎢ ⎢ ⎢ ⎣

=

⎡G_{o }⎢ ⎢ ⎢ ⎢ ⎣

C_{of 1 }C_{of 2 }... C_{ofn }

⎥ V_{of 2 }⎥

V_{of 1 }⎤

V_{ofn }⎥ ⎦

... ⎥ ⎥

C_{of 1 }C_{of 2 }... C_{ofn }

< a_{p1 },b_{p1 }

< a_{p }_{2 },b_{p 2 }< ... > < a_{pn },b_{pn }

> > > ⎤ ⎥ ⎥ ⎥ ⎥ ⎦

### G_{o }

is the GPS receiv

er.

G_{of }

is the control

## characteristic of the GPS receiver. Where C_{of }_{1 },

C_{of 2 }, …, C_{ofn }is n different characteristics such as the GPS receiver oscillation frequency, integer

ambiguity of G_{o }. And V_{of }_{1 }, V_{of }_{2 }

, …, V_{ofn }

G C_{ofn }

o

about the value, namely

>

i = 1, 2,…, n

domains. thenV_{ofi }=< a_{pn },b_{pn }

range of extensional

is

…

,

respectively C_{of 1 }, C_{of }_{2 }

,

Issue 7, Volume 4, July 2007