**5. Algorithm of discrete PID controller tuning using piecewise-linear neural network**

Whole algorithm of piecewise-linear neural model usage in PID controller parameters tuning is summarized in following terms (see Fig. 10, too).

Fig. 10. Control algorithm scheme for second order nonlinear system


system behaviour in some neighbourhood of actual state. This difference equation can be used then to the actual control action setting due to many of classical or modern control

In following examples, discrete PID controller with parameters tuned according to algorithm introduced in paragraph 3 is studied. As it is mentioned above, controlled system discrete model in form of Z – transfer function is required. So first, difference equation (22)

<sup>1</sup> <sup>2</sup> <sup>1</sup> <sup>2</sup> <sup>120</sup> *y k a y k a y k b uk b uk c b b u MM M* ( ) ( 1) ( 2) ( 1) ( 2) ( ) (24)

1 2 *c*

1 1 2 1 2 1 12 1 2

 

*b b*

In Z domain, model (24) witch respect to (Eq. 25) is defined by Z – transfer function (26).

*Y z <sup>M</sup> bz bz Uz az az*

**5. Algorithm of discrete PID controller tuning using piecewise-linear neural** 

Whole algorithm of piecewise-linear neural model usage in PID controller parameters

*<sup>u</sup>*(*k*) *yS*(*k*) *<sup>r</sup>*(*k*) **+**

<sup>0</sup> *uk uk u* () () (23)

(26)

NONLINEAR SYSTEM

*DELAY DELAY*

*yS*(*k*-1)

*u*(*k*-1)

*u*(*k*-2)

*yS*(*k*-2)

NEURAL MODEL

(25)

should be transformed in following way. Let us define

Equation (24) becomes constant term free, if (Eq. 25) is satisfied.

tuning is summarized in following terms (see Fig. 10, too).

 *a*1, *a*2, *b*1, *b*<sup>2</sup>

POLE ASSIGNMENT

> DISCRETE PID CONTROLLER

Fig. 10. Control algorithm scheme for second order nonlinear system

0

*u*

( ) ()1

where *u*0 is constant. Then, (Eq. 22) turns into

techniques.

**network** 

**-**

*D*(*z*-1)


10. *k = k +* 1, go to 4.

Introduced algorithm is suitable to control of highly nonlinear systems, especially.
