Industrial Automation
Automation Industrielle
Industrielle Automation
set point
controller
+
-
plant
measurement
2.2
Control of continuous processes
Control de procesos continuos
Régulation de systèmes continus
Regelung stetiger Strecken
controlled
variables
2.2 Continuous control
2.1 Instrumentation
2.2 Continuous control
2.2.1 Plant modeling and identification
2.2.2 Controllers
2.2.2.1 On/Off (two-point) controller
2.2.2.2 PID controller
2.2.2.3 Nested Controllers
2.3 Programmable Logic Controllers
Industrial Automation
Continuous control 2.2 - 2
Motivation for this chapter
This is an intuitive introduction to automatic control as a preparation for
the PLC programming lab at Siemens intended for students who did not
enjoy control courses.
For a correct engineering approach, dedicated courses are recommended
(e.g., by Prof. Longchamp and Prof. Bonvin).
.
Content
- modeling of plants
- two-point controller
- PID controller
- nested controllers
Industrial Automation
Continuous control 2.2 - 3
Open Loop control vs. Closed Loop control
open loop:
temperature is imprecise,
depends on ambient temperature and
cooking quantity but heating level and
duration can be modulated
(e.g. let boil and then simmer during 30’)
3
2
4
1
5
sequential control
closed loop:
140
120
180
200
+
220
-
higher
/lower
temperature closely controlled,
requires measurement of the output
variable (temperature)
continuous control
temperature sensor
Industrial Automation
Continuous control 2.2 - 4
Open loop vs. closed loop
open-loop control / command
(commande / pilotage, Steuern)
keywords: sequential / combinatorial,
binary variables, discrete processes,
"batch control", "manufacturing"
closed-loop control / regulation
(régulation, Regelung)
keywords: feedback, analog variables,
continuous processes, "process control"
set-point (solicited)
valeur de consigne
Sollwert
commands
sequencer
clock
output
plant
-
error
(deviation)
plant state
display
on/off
controller
+
display
measurement
control variable
variable de commande
Stellgrösse
plant
output
plant
state
measurement
%
process value
valeur mesurée,
Istwert
Industrial Automation
Continuous control 2.2 - 5
Definitions from IEC
351-47-01 closed-loop control (feedback control)
process whereby one variable quantity, namely the controlled variable is
continuously or sequentially measured, compared with another variable quantity,
namely the reference variable, and influenced in such a manner as to adjust to the
reference variable
Closed action path in which the controlled variable continuously or sequentially influences itself
351-47-02 open-loop control
process in a system whereby one or more variable quantities as input variables
influence other variable quantities as output variables in accordance with the
proper laws of the system
Open action path or a closed action path the fact that the output variables being influenced by
the input variables are not continuously or sequentially influencing themselves and not by
the same input variables.
Industrial Automation
Continuous control 2.2 - 6
Example Cruise Control
• Control Objective:
maintain car velocity
• Measured Process Variable (PV):
car velocity (“click rate” from
transmission rotation)
• Manipulated Variable:
pedal angle, flow of gas to engine
• Controller Output (CO):
signal to actuator that adjusts gas flow
• Set point (SP):
desired car velocity
• Disturbances (D):
hills, wind, curves, passing trucks....
Source: OCAL, clker.com
Source: http://apmonitor.com/che436/uploads/Main/Lecture3_notes.pdf
Industrial Automation
Continuous control 2.2 - 7
Example Cruise Control
Source: http://apmonitor.com/che436/uploads/Main/Lecture3_notes.pdf
Industrial Automation
Continuous control 2.2 - 8
2.2.1 Plant Modeling
2.1 Instrumentation
2.2 Control
2.2.1 Plant modeling and Identification
2.2.2 Controllers
2.2.2.1 On/Off (two-point) controller
2.2.2.2 PID controller
2.2.2.3 Nested Controllers
2.3 Programmable Logic Controllers
Industrial Automation
Continuous control 2.2 - 9
Modeling
1) analysis of control systems
2) define a controller that meets physical and economical requirements
The first step is to get to know the plant, i.e., express the plant’s behavior in a
mathematical way, generally as a system of differential equations,
• White box approach: analyzing physical principles
(requires that all elements are known)
• Black box approach: identifying the plant’s parameters by analyzing its behavior
(output) in response to an input change.
+/-
?
what is the effect of increasing thrust ?
Industrial Automation
Continuous control 2.2 - 10
Modeling for regulation: continuous processes
Examples of such processes: drives, ovens, vehicles, chemical reactors
x
y
y = F (x, t)
Industrial Automation
Continuous control 2.2 - 11
Example linear plant: Electrical motor with permanent magnet
motor
J [Nms]
(inertia)
i
Ue
(command
tension)
L
ω [rad/s]
(speed)
R
T [Nm]
(torque)
ui [V]
(induced tension)
Ue = R i + L
di
dt
+ ui
di
1
=
ui = K ω
dt
T = Ki
dω
dω
dt
T
=
L
K
=
dt
(Ue – K ω – R i)
J
i
J
ω
Ue
=
K
s2 (LJ) + s (RJ) + K2
Laplace - transfer, since the plant is linear
Industrial Automation
Continuous control 2.2 - 12
Example of non-linear plant: modeling a train
obtain the relation between applied motor force (current) and the position of a train.
Ffrict Ftract

x
mg
dx
v
dt
motor force
Kc
dv
1

( Ftract  mg sin(  )  m
 C x v 2  C f v)
dt m
radius
slope
mass of the train
plus contribution
of rotating parts
(wheels and rotors)
Industrial Automation
air friction
curve
friction
mechanical
friction
Continuous control 2.2 - 13
Resulting train model in Matlab
traction force
i
motor
current
acceleration
train
inertia
Fz
Km
speed
position
v
x
a
1
m
motor
gravity
v2
air
resistance
mgsin()
mg
()2
Cx
Cz
friction
|v|
abs
r(x)
curve friction
sin()
Cc
(x)
sin()
radius
slope
taken from
topography database
Industrial Automation
Continuous control 2.2 - 14
Help in modeling for electricians: use an electrical equivalent
water
temperature 
ambient-water isolation R1
ambient
temperature
a
Electrical equivalent
R1
C
heater-water
isolation
Heat
resistance R2
water
Uq
R2
x~ 
C
Ua
ua ~ a
Ua
(ambient temperature)
solicited
temperature 2
controller
energy Uq
heating
1
1
 )
dx
1
1
R R2
 x 1

Uq 
Ua
dt
C
R1C
R2C
(
dx
  Ax  Bu  C
dt
Industrial Automation
cooling
dx
  x 1  1 Ux
R2C R2C
dt
dx
  Dx  E
dt
Continuous control 2.2 - 15
Thermal (solid) vs. electrical model: conductivity
q = heat flow [J/s = W]
T = temperature [K]
T2
R = thermal resistance [K/W]
T1
q=
k = thermal conductivity [J/m/K]
(T2 – T1)
= (T2 – T1)
R
kA
d
A = surface [m2]
R=
d = distance [m]
A
I = current [A]
U = voltage [V]
R = resistance [Ω]
ρ = resistivity [Vm]
Industrial Automation
d
kA
d
U2
U1
i
i=
A
d
(U2 – U1)
= (U2 – U1)
R
R=ρ
A
ρd
d
A
Continuous control 2.2 - 16
Thermal (solid) vs. electrical model: capacity
q = heat flow [J/s = W]
T = temperature [K]
T
C = thermal capacity [J/K]
q=C
Cm = thermal specific [J/K/kg]
dT
Cm
C=
dt
ρV
Cm
=
ρAd
A = surface [m2]
d = distance [m]
ρ = density
A
d
[kg/m3]
I = current [A]
U = voltage [V]
U
i=C
i
dt
C = capacity [F]
ε = dielectric constant [F/m]
Industrial Automation
dU
A
C=ε
A
d
d
Continuous control 2.2 - 17
Plant Identification
Once the model is approximately known, the parameters must be determined by measurements.
Classical methods are the response to a pulse at the input or to a calibrated noise at the input, in
case the command signal varies little. Signal correlation then yields the parameters.
test signal
command
unknown plant
input
output
Industrial Automation
Continuous control 2.2 - 18
2.2.2 Controllers
2.1 Instrumentation
2.2 Control
2.2.1 Plant modeling and identification
2.2.2 Controllers
2.2.2.1 On/Off (two-point) controller
2.2.2.2 PID controller
2.2.2.3 Nested Controllers
2.3 Programmable Logic Controllers
Industrial Automation
Continuous control 2.2 - 19
Controllers
When a plant is known, a controller can be designed.
In practice, the plant’s parameters vary (e.g., number of
passengers in a train), and the plant is subject to
disturbances (wind, slope)
The controller
• needs to measure through sensors the state of the plant
and if possible the disturbances.
• follows certain quality laws to stabilize the output within
useful time, not overshoot, minimize energy consumption,
etc…..
Industrial Automation
Continuous control 2.2 - 20
Controller loop (boucle de régulation, Regelschleife)
disturbance
Störgrösse
perturbation
set-point
valor solicitado
valeur de consigne
(solicitée)
Sollwert
u
state
Zustand
état
controlled variable
Regelgrösse
valeur contrôlée
(possibly invisible)
controller
e
regulator
Regler
régulateur
error
Regelabweichung
déviation
y
process value
valor medido
Istwert
valeur mesurée
m
controlled system
Regelstrecke
système commandé
x
command
Stellgröße
valeur de commande
measurement
Messglied
mesure
feedback loop
lazo de realimentación
boucle de rétroalimentation
Rückführschleife
controller can be implemented by mechanical elements, electrical elements, computers,...
controlled variable can not always be measured directly.
Industrial Automation
Continuous control 2.2 - 21
Human body as a regulator example
Consider a person taking a shower as a control system
disturbances
feed-forward
controller
set point
valor solicitado
valeur de consigne
Sollwert
feed-back
controller
command
x
plant
m
y
other
constraints:
energy, cost,
cleanness
measurement
process value
valor medido
valeur mesurée
Istwert
Industrial Automation
Continuous control 2.2 - 22
Where is that controller located ?
• high-end: in a set of possibly redundant
controllers (here: turbine control)
• directly in the sensor
or in the actuator
(analog PIDs)
• as a separate device (analog PIDs)
(some times combined with a recorder)
set-points
• as an algorithm in a computer
(that can handle numerous "loops").
sensors
Industrial Automation
actors
Continuous control 2.2 - 23
2.2.2.1 On/Off (two-point) controller
2.1 Instrumentation
2.2 Control
2.2.1 Plant modeling
2.2.2 Controllers
2.2.2.1 On/Off (two-point) controller
2.2.2.2 PID controller
2.2.2.3 Nested Controllers
2.3 Programmable Logic Controllers
Industrial Automation
Continuous control 2.2 - 24
Two-point controller: principle
The two-point controller (or bang-bang controller, regulator, Zweipunktregler,
Régulateur tout ou rien) has a binary output: on or off (example: air conditioning)
control
variable
energy
set-point
heater
room
temperature
off on
measured value
thermometer
Industrial Automation
Continuous control 2.2 - 25
Thermostat
Thermostat maintains desired (reference) temperature despite
disturbances (such as doors opening/closing, variations of outside
temperature, number of persons in the house, etc.)
Industrial Automation
Continuous control 2.2 - 26
Two-point controller: Input variable as ramp
%
1.20
1.00
value
0.80
Setpoint
Upper bound
0.60
Lower bound
0.40
Output
0.20
0.00
0.00
1.00
2.00
3.00
4.00
5.00
6.00
7.00
8.00
9.00
time (s)
Industrial Automation
Continuous control 2.2 - 27
Hysteresis and Deadband of a Valve
Hysteresis: difference between the
valve position on the upstroke and its
position on the down stroke at any
given input signal (static friction)
Deadband: no movement,
generally occurs when the valve
changes direction.
Source: http://www.processindustryforum.com/solutions/valve-terminology-basic-understanding-of-key-concepts
Industrial Automation
Continuous control 2.2 - 28
Two-point controller: Hysteresis / Deadband
temperature
upper switch point
1.00
lower switch point
0.80
0.60
0.40
Note the different time
constants for heating and
cooling: non-linear system
0.20
0.00
time
If the process is not slow enough, hysteresis and deadband are included
to limit switching frequency and avoid wearing off the contactor.
(thermal processes are normally so inertial that this is not needed)
Industrial Automation
Continuous control 2.2 - 29
2.2.2.2 PID Controller
2.1 Instrumentation
2.2 Control
2.2.1 Plant modeling and identification
2.2.2 Controllers
2.2.2.1 On/Off (two-point) controller
2.2.2.2 PID controller
2.2.2.3 Nested Controllers
2.3 Programmable Logic Controllers
Industrial Automation
Continuous control 2.2 - 30
Proportional Integral Derivative Controller
• generic control loop feedback mechanism (controller)
• widely used in industrial control systems
Mode of operation:
1. calculate "error" e(t), the difference between measured PV and SP.
2. try to minimize error by adjusting the process control output m.
disturbance
set-point
u
state
controlled variable
controller
(possibly invisible)
regulator
e
process value
y
error
command
controlled system
m
x
measurement
t

1
de(t ) 

m(t )  ub  K p  e(t )   e( )d )  Td

T
dt
i t0


K p , Ti , Td tuning parameters
Industrial Automation
Continuous control 2.2 - 31
Step response
Gain:
PV steady state change
CO steady state change
Source: http://www.stanford.edu/class/archive/ee/ee392m/ee392m.1034/Lecture6_Analysis.pdf
Industrial Automation
Continuous control 2.2 - 32
Plant model example
The following examples use a plant modeled by a 2nd order differential equation:
y  y'T1  y"T2  m
differential equation
m
y
1

m 1  sT1  s 2T2
y
plant
Laplace transfer function
(since system is linear)
Temporal response
Typical transfer function of a plant with slow response, but without dead time
(However, such a plant can also be approximated by a first-order low-pass and a dead time).
1.4
delay
time constant T
1.2
1
step response
In the examples:
T1 = 1 s
T2 = 0.25 s2
0.8
0.6
0.4
0.2
0
time
0
1
2
3
4
5
6
7
8
9
10
d ~ 0.2, T= 1.5s
Industrial Automation
Continuous control 2.2 - 33
P-controller: simplest continuous regulator
proportional factor,
control gain
set-point
controlled
variable
command
variable
P-controller
u
e
y
Kp
x
m
plant
error
measurement
process value
the P-controller simply amplifies the error to obtain the command variable
m(t) = ub +Kp • e(t) = Kp • (u(t) –y(t))
works, but if plant has a proportional behavior, an error always remains
Industrial Automation
Continuous control 2.2 - 34
P-Controller: Step response
m(t), y0(t)
2
command
1.5
large error
smaller asymptotic error
1
x large
0.5
x small
0
0
-0.5
1
2
3
4
5
6
7
8
9
10
Numerical:
Kp = 5.0
set-point
The larger the set-point, the greater the error.
Industrial Automation
Continuous control 2.2 - 35
P-Controller: Effect of Load change
u1 =
disturbance
proportional factor
controlled
variable
P-regulator
u0 = set-point
e = error
Kp
plant
m = command
variable
command
2
measurement
y0 = process value
1.5
value
u0 (Solicited)
1
0.5
u1 (load change)
0
0
1
2
3
4
5
6
7
8
9
10
-0.5
Not only a set-point change, but a load change causes the error to increase or decrease.
(A load change, modeled by disturbance u1, is equivalent to a set-point change)
Industrial Automation
Continuous control 2.2 - 36
u0(t), y0(t)
P-Controller: Increasing the proportional factor
2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
-0.2 0
1
2
3
4
5
6
7
8
9
10
time [s]
increasing the proportional factor reduces the error, but the system tends to oscillate
Industrial Automation
Continuous control 2.2 - 37
PI-Controller (Proportional Integral): introducing the integrator
equation
symbol
t
y   x( )d
x
t0
1
s
y
older symbol
x
d
y
input
inflow [m3/s]
y = level [m]
output
t2
level (t) =
(inflow()) d
t1
Time response of an integrator
Industrial Automation
Example of an integration process
Continuous control 2.2 - 38
PI – Regulator : Equations
t
Time domain
1
m  K p (e(t )   e( )d )
Ti t 0
Laplace domain
1 ~
~
m K P (1 
)e
sTi
Ti = reset time, tiempo de integración, temps d’intégration, Nachstellzeit
Industrial Automation
Continuous control 2.2 - 39
PI-Controller: response to set-point change
value
Kp = 2,0, Ti=1,0 s
2.2
2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
-0.2
Solicited
Output
Command
Integrator
0
1
2
3
4
5
6
7
8
9
10
time
The integral factor reduced the asymptotical error to zero, but slows down the response
(if Kp is increased to make it faster, the system becomes unstable)
Industrial Automation
Continuous control 2.2 - 40
PD controller
Basic idea of the PD regulator: take into account not only the value of the error, but
the rate at which the error changes.
Example: when parking a car in front of a wall, the driver not only looks at the
distance to the wall, but also at the speed at which the car approaches the wall.
Industrial Automation
Continuous control 2.2 - 41
PD-Controller: Introducing the differentiator
equation:
symbol: x
y
dx
dt
s
A perfect differentiator does not exist.
Differentiators increase noise.
Differentiators are approximated by
feed-back integrators (filtered differentiator):
y
temporal response:
input
Nf
x
1
Td
output
∞
Industrial Automation
y
1
s
Instead of differentiating, one can use an
already available variable:
e.g. the speed for a position control
Continuous control 2.2 - 42
PD - controller
command
variable
proportional factor
set-point
PD - controller
error
m
Kp
u
plant
Td
derivative
factor
x
s
measurement
process value y
Adding the D-part allows to react vigorously to changes in set-point or perturbations.
Industrial Automation
Continuous control 2.2 - 43
PD – Controller: Equations
Time domain
Laplace domain
de(t ) 

m(t )  K p  e(t )  Td

dt 

~ ( s)  K 1  T s e~ ( s)
m
p
d
Td = derivative time, temps de dosage de dérivée, Vorhaltezeit Tv
Industrial Automation
Continuous control 2.2 - 44
PID-Controller (Proportional-Integral-Differential)
integral factor
integrator
proportional factor
1
Ti
error
1
s
Kp
set-point
process value
command
variable
plant
Td
s
PID controller
derivative
factor
measurement
The proportional factor Kp generates an output proportional to the error, it requires a nonzero error to produce the command variable.
Increasing the amplification Kp decreases the error, but may lead to instability
The integral time constant Ti produces a non-zero control variable even when the error is
zero, but makes the system instable (or slower).
The derivative time Td speeds up response by reacting to an error change with a control
variable proportional to the steepness of change.
Industrial Automation
Continuous control 2.2 - 45
PID controller: Equations
time domain
Laplace domain
t

1
de(t ) 

m(t )  K p  e(t )   e( )d )  Td

T
dt
i t0






~
Td s
m( s )
1



K
1


p
~
Nf 
e ( s)
sTi
(1 
s) 

Td


Real differentiators include this filtering
Kp = proportional factor, gain, Reglerverstärkung,
Ti = reset time, temps de dosage d’intégration (Nachhaltezeit, TN)
Td = derivative time, temps de dosage de dérivée, Vorhaltezeit Tv
Note: some manufacturers define the terms differently, e.g.
Industrial Automation
~ ( s)
m
1
 1 

K


T
s


p
d
e~( s)
sTi
1

s



Continuous control 2.2 - 46
PID response summary
Plarge (Kp = 15)
less error, but unstable
PI: no remaining error,
but sluggish response
(or instable, if Kp increased)
1
Psmall (K=5) asymptotic error
proportional only
differential factor
increases responsiveness
load change (load decreases)
0
0
1
2
Solicited
3
Psmall
4
5
Plarge
6
PI
7
8
PID
9
10
U1
Play with Matlab: http://ctms.engin.umich.edu/CTMS/index.php?example=Introduction&section=ControlPID
or control.xls
Industrial Automation
Continuous control 2.2 - 47
PID-Controller: empirical settings
Rise time
Overshoot
Settling time
Steady-State Error
Kp
Decrease
Increase
Small Change
Decrease
Ti
Decrease
Increase
Increase
Eliminate
Td
Small Change Decrease
Decrease
Small Change
increasing
See examples on http://en.wikipedia.org/wiki/PID_controller
Source: http://www.stanford.edu/class/archive/ee/ee392m/ee392m.1034/Lecture6_Analysis.pdf
Industrial Automation
Continuous control 2.2 - 48
Extract from a controller’s manual: it’s empirical !
Optimization according to Ziegler-Nichols:
Assuming that the process is stable at the operating temperature:
1. Set the Parameters ‘ti’ und ‘td’ to OFF.
2. Actual value differs now from solicited value by proportional factor.
3. As soon as temperature stabilizes, reduce proportional band ‘Pb’,
until temperature starts to swing => swinging period „T“.
4. Slowly increase proportional band until
temperature just stops swinging
=> band value ‘B’.
5. Set values of Pb, Ti and Td
according to table
But what do you do if this method does not work ?
How do you know that this plant can be controlled by a PID controller? (many cannot)
How do you prevent overshoot ? (this method does not)
Trial-and-error can’t replaces a serious analysis -> see “for further reading”.
Industrial Automation
Continuous control 2.2 - 49
2.2.2.3 Nested controllers
2.1 Instrumentation
2.2 Control
2.2.1 Plant modeling
2.2.2 Controllers
2.2.2.1 On/Off (two-point) controller
2.2.2.2 PID controller
2.2.2.3 Nested Controllers
2.3 Programmable Logic Controllers
Industrial Automation
Continuous control 2.2 - 50
Several controllers act together: Electricity Generator
DP
Active power
frequency (Pf)
controller
Df
DQ
Reactive power
voltage (QV)
controller
DV
Steam
Controllable
excitation
source
Main
steam
valve
Valve
control
mechanism
Turbine
Generator
Voltage
sensors
Frequency sensor
Mechanical power
Industrial Automation
3-phase Electrical Power DP + j DQ
Continuous control 2.2 - 51
Generator Regulator structure
excitation
current
voltage
PID
excitation
Ie
U = k × Ie × ω
load
speed
ω
frequency
PID
turbine
generator
voltage
measure
measure
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Continuous control 2.2 - 52
Nested control of a continuous plant - example
Example: position control of a rotating shaft
Position
PD
Speed
sol
cmd
is
torque regulation
(protection)
PID
Torque
sol
cmd
is
PID
sol
cmd
is
encoder
M
tacho
amplifier
Current
Velocity
Position
Nesting regulators allow to maintain the output variable at a determined value
while not exceeding the current or speed limitations
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Nested loops and time response
position control
speed control
torque control
robot arm trajectory
A control system consists often of nested loops,
with the fastest loop at the inner level
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Continuous control 2.2 - 54
Advanced Control
controller
disturbances
plant
model
x
economical
objectives,
control
algorithms
Cost functions
m
plant
command
(setpoints for further
regulators)
y
measurement
process value
Istwert
valeur mesurée
This is a high-level control in which the set-points are computed based on economical objectives
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Continuous control 2.2 - 55
Exercises
http://tinyurl.com/p6sx4ol
A Control System…
a) is dependent not only on current environment but on past environment as well
b) describes the direction PV moves and how far it travels in response to a change in
CO (steady state)
c) set of devices to manage, command, direct or regulate the behavior of other
device(s) or system(s)
What is the set point?
a) Variable you want to control
b) Desired value of control variable
c) Signal that is continuously updated
What has only one tuning parameter so it’s easy to find “best” tuning, but permits offset?
a) P only
b) PI
c) PD
What is proportional to both the magnitude of the error and the duration of the error?
a) P only
b) PI
c) PD
https://docs.google.com/forms/d/1CSfJ7yoGdRxNphQ75quNioe5Z0i94XAqqM7zz9g8Ms/viewform
Industrial Automation
Continuous control 2.2 - 56
Exercises
A Control System…
a) is dependent not only on current environment but on past environment as well
b) describes the direction PV moves and how far it travels in response to a change in
CO (steady state)
c) set of devices to manage, command, direct or regulate the behavior of other
device(s) or system(s)
What is the set point?
a) Variable you want to control
b) Desired value of control variable
c) Signal that is continuously updated
What has only one tuning parameter so it’s easy to find “best” tuning, but permits offset?
a) P only
b) PI
c) PD
What is proportional to both the magnitude of the error and the duration of the error?
a) P only
b) PI
c) PD
https://docs.google.com/forms/d/1CSfJ7yoGdRxNphQ75quNioe5Z0i94XAqqM7zz9g8Ms/viewform
Industrial Automation
Continuous control 2.2 - 57
More Questions 
http://tinyurl.com/p6sx4ol
Which statements are correct?
1. The path or length of time the PV takes to get to its new steady
state does not enter into the calculation of the process gain.
2. Increasing Kp can lead to oscillations.
3. Step response analysis is used when tuning a closed loop
plant.
4. For PID control a model of the plant is needed.
5. Feed-forward is a open-loop control technique.
6. In nested control the inner loop controller reads the output of
outer loop controller as setpoint.
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Assessment
How does a two-point regulator works ?
How is the a wear-out of the contacts prevented ?
How does a PID regulator works ?
What is the influence of the different parameters of a PID ?
Is a PID controller required for a position control system (motor moves a vehicle)?
Explain the relation between nesting control loops and their real-time response
What is feed-forward control ?
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Continuous control 2.2 - 59
To probe further
"Computer Systems for Automation and Control", Gustaf Olsson, Gianguido Piani,
Lund Institute of Technology
“Modern Control Systems”, R. Dorf, Addison Wesley
“Feedback Systems”, Karl Johan Aström, Richard M. Murray
http://www.cds.caltech.edu/~murray/books/AM08/pdf/am08-complete_28Sep12.pdf
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