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بسم الله الرحمن الرحيم
Advanced ControlLecture four
Mohammad Ali Fanaei
Dept. of Chemical Engineering
Ferdowsi University of Mashhad
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