automatic control system
DESCRIPTION
Automatic Control System. V. Performance of steady-state. Terms of feedback control. controller. plant. controlled variable. compensator or control task. transmitter. manipulated variable. error signal. actuator. comparing element or error detector. disturbance variable. - PowerPoint PPT PresentationTRANSCRIPT
Automatic Control System
V.
Performance of steady-state
plantcontroller
Terms of feedback control
reference input element
reference signal
comparing elementor error detector
error signal
compensator or control task
action signal
feedback signal
actuator
transmitter
manipulated variable
disturbance variable
controlled variable
block model of the plant
Working points in steady-state
U
YM Y
UMIn steady-state the value of the action signal U,manipulated UM, and controlled Y variables,and the feedback signal YM are constant.
W
Y
UM
U
YM
In steady-state the output of a loop’selement is the input of the next block.The steady-state characteristics of the elements must be fitted each other. The disturbance w variable’s deviationof the average value changes the plant’s steady-state characteristic curve.It’s important: A new steady-state can be achieved by the system.
W0
Choosing steady-state characteristics of controller
The steady-state characteristic of the plant, transmitter and the actuator is given by the technologies. We can
choose only the steady-state characteristic of the controller.
If higher action signal belongs to higher feedback signal then the characteristic is direct.If lower action signal belongs to higher feedback signal then the characteristic is reverse.
The dynamic behavior of the controller eliminates the steady-state error..
Y
UM
U
YM
W0
In this case there isn’t a new steady-state value of system.
Choosing steady-state characteristics of controller
A bad choice of controller steady-state characteristics also causes an unstable control loop.
Y
UM
U
YM
Sometimes the technologies requirements need a reverse characteristics of the actuator. Sometimes the steady-state characteristics of technologies is concave and not convex.
W0
In this case there is a new steady-state value of system.
Transfer functions of feedback loop
)s(yM
)s(uGP(s)
)s(e )s(d )s(yGR(s)
GW(s)
GA(s)GC(s)
GT(s)
)s(r
TPAC
PACyr GGGG1
GGG
r
y)s(G
TPACer GGGG1
1
r
e)s(G
)s(w
TPAC
PWyw GGGG1
GG
w
y)s(G
TPAC
TPWew GGGG1
GGG1
w
e)s(G
System type of feedback loop
n
1kk
m
1jj
i0
TPAC0
)sT1(
)s1(
s
KGGGG)s(G
System type is the number of the pure integral lag in the loop. The possible values are 0, 1, 2. K0 is the loop gain.
Opened-loop transfer function, Bode form.
)s(yM
)s(uGP(s)
)s(e )s(d )s(yGR(s)
GW(s)
GA(s)GC(s)
GT(s)
)s(r
)s(w
A ship wants to turn to the port. The continuous movement of the steering wheel turns the ship. The surface of the ship against the river backwash also continuously increase. How much is the deflection error if r(t)=0.2*t*1(t) is the changes of the reference signal and w(t)=0.1*t*1(t) is the changes of the disturbance variable. The domains are: Y = ± 80 [°], R = 4 – 20 [mA].
)s(e
)s(w
)s(y)s(r
s
s
1.01
15
s1
1
s2.01
1
s5
1
5.0
Examplev
s5.01
2.1
The steady-state error of closed loop control
er ewt s 0lim e(t) lim s{G (s)r(s) G (s)w(s)}
s
1
s2.011
s5.01
s11
s5.012.1
s1.01s1
51
)1(s2.01
1)1(5.0
ss
2.0
s2.011
s5.01
s11
s5.012.1
s1.01s1
51
1slim
20s
)s(e
)s(w
)s(y)s(r
s
s
1.01
15
s1
1
s2.01
1
s5
1
5.0
s5.01
2.1
0.2 1 0.1 0.5 0.6If s 0, then 0.1mA
5 1.2 5 1.2 6 6 60.5 0.5
The steady-state error of closed loop control
x0,1 mA
20 4 mA 80 80
The size of the error might be appropriate, but we do not know anything about the quality characteristics.
0,1x 160 1
16
)s(e
)s(w
)s(y)s(r
s
s
1.01
15
s1
1
s2.01
1
s5
1
5.0
s5.01
2.1
Setpoint tracking
The setpoint tracking depends on:• Order of the feedback system.• The loop‘s gain (K0).• The form of the reference signal
The setpoint tracking means that the controlled variable (y(s)) is able to follow the prescribed value by the changes of the reference signal (r(s)) after the transient has died.We assume that the disturbance variable (W0(s)) equals the designed value (w(s)=0).We can examine this with the error transfer function:
in
1kk
m
1jj
i0
er
)sT1(
)s1(
s
K1
1)s(G
Setpoint tracking
1(t)
t 1(t)
Standard signal
Order of the feedback system
0
1
K
0
1
K 1t
t
0 21
0
0
0
0
1
K2t *1(t)
t
Disturbance suppression
The disturbance suppression depends on:• Order of the feedback system.• The loop‘s gain (K0).• The form of the reference signal.• The attack point of the disturbance variable.
The disturbance suppression means that the controlled variable (y(s)) is able to hold the prescribed value by the changes of the disturbance variable (w(s)) after the transient has died. We assume that the reference signal (R0(s)) equals the working point value (r(s)=0).We can examine this with the disturbance-error transfer function:
in
1kk
m
1jj
i0
TPWew
)sT1(
)s1(
sK
1
)s(G)s(G)s(G)s(G
Disturbance suppression
1(t)
t 1(t)
Standard signal
Order of the feedback system
0
1
K
0
1
K 1t
t
0 21
0
0
0
0
1
K
Entering point of disturbance
0 010 21
0
1
K
0
0
1
K
0
1
K
2t *1(t)
t