Transcript 01_1 - Ferdowsi University of Mashhad
ميحرلا نمحرلا الله مسب
Advanced Control
Lecture 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
u
(
t
)
u s
K c e
(
t
)
K c
I
0
t e
(
t
)
dt
K c
D de
(
t
)
dt
Sampling Time :
T s
, Number of Sampling :
k
, Time :
t
=
kT s
Upper rectangula r approximat iom : 0
t e
(
t
)
dt
i k
1
e
(
iT s
)
T s
Backward Finite Difference :
de
(
t k dt
)
e
(
kT s
)
e
(
k
1 )
T s T s
Discrete Form of PID Controllers
Position Form
u
(
t
)
u s
K c e
(
t
)
K c
I
0
t e
(
t
)
dt
K c
D de
(
t
)
dt u
(
k
)
u s
K c e
(
k
)
K
c T s I i K
1
e
(
i
)
K c
D
e
(
k
)
e
(
k
1 )
T s
Velocity Form
u
(
k
)
u
(
k
1 )
K c
e
(
k
)
e
(
k
1 )
K
c T s I e
(
k
)
K c
D T s
e
(
k
) 2
e
(
k
1 )
e
(
k
2 )
Discrete Form of PID Controllers
Velocity Form
u
(
k
)
u
(
k
1 )
g
0
e
(
k
)
g
1
e
(
k
1 )
g
2
e
(
k
2 )
Where:
g
0
K c
1
T s I
D T s
g
1
K c
1 2
D T s
g
2
K c
D T s
Discrete Form of PID Controllers
Backward Shift Operator (q -1 ) : y(k-n)=q -n y(k)
u
(
k
)
e
(
k
)
g
0
g
1
q
1 1
q
1
g
2
q
2
Tuning of Digital PID : Moore et al. (1969) Use the continuous tuning formula of PID controller with corrected dead time
t
0
c
t
0
T s
2