بسم الله الرحمن الرحيم

Advanced Control

Discrete forms of PID controllers

Reference: A. Visioli, Practical PID Control, Springer 2006

Computer Control

1. The computer requests a value from the A/D converter. The A/D converter samples the process signal, converts it to a number, and stores it in the computer memory or a register.

2. The computer performs the control calculations on the sampled process signal(s) and computes the output(s) to the process.

3. The computer output is sent to the D/A converter, which converts it to an electronic signal, updates the output, and holds it constant until the next update.

Computer Control

A good rule of thumb is that the sample time should be about one-tenth of the effective process time constant

Discrete Form of PID Controllers

Position Form

dt

tdeKdtte

KteKutu Dc

t

I

ccs

)()()()(

0

Sampling Time : Ts , Number of Sampling : k , Time : t = kTs

k

iss

tTiTedtte

10

)()(:iomapproximatr rectangulaUpper

s

ssk

T

TkekTe

dt

tde ))1(()()( :Difference Finite Backward

Discrete Form of PID Controllers

Position Form

Velocity Form

dt

tdeKdtte

KteKutu Dc

t

I

ccs

)()()()(

0

)1()()()()(1

kekeT

Kie

TKkeKuku

s

DcK

iI

sccs

)2()1(2)()()1()()1()( kekekeT

Kke

TKkekeKkuku

s

Dc

I

scc

Discrete Form of PID Controllers

Velocity Form

Where:

)2()1()()1()( 210 kegkegkegkuku

s

Dc

s

Dc

s

D

I

sc

T

Kg

TKg

T

TKg

2

1

0

21

1

Discrete Form of PID Controllers

Backward Shift Operator (q -1) : y(k-n)=q-ny(k)

Tuning of Digital PID : Moore et al. (1969)

Use the continuous tuning formula of PID controller with corrected dead time

1

22

110

1)(

)(

q

qgqgg

ke

ku

200s

c

Ttt