Feedback Control Roundup
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•
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Where is this class going?
Why control?
What is feedback?
What are those block diagrams, and
how do they relate to the equations?
• How does PID work?
• How do controllers go out of tune, how
can I recognize them, and what do I do?
Where is this class going?
• Things I want you to learn
– “Assume steady state” does not work in real life.
– Engineering is a synthesis of what you have
learned, not a collection of separate topics
– How to analyze and describe a dynamic system
– How to understand control systems:
• Anything called a “regulator”
– Trade-offs in control design
– How to save the day when the irresponsible
control engineer goes on vacation
Where is this class going?
• Content remaining
– Control applications: feedforward, cascade,
decoupling
– Ways to analyze the effect of control on
closed loop stability
– Frequency domain analysis of dynamic
systems
– State space (very good for mechanical
systems)
Why control?
• We use control to:
– Keep a value close to its desired value:
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•
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Room temperature, thermostat
Car speed, cruise control
Boiler drum level
Boiler fire-side pressure
– Trade off variation between controlled and
manipulated variables
• Torque and position or speed
• Flow and level in a surge tank
• Temperature and heat stresses induced by heat
Where are we, as mechanical
engineers, going to encounter
control?
• Any time something moves, that motion must
be regulated.
– Equipment: motors and guides
– Fluids: flow rate, pressure and temperature
• Control is implemented through mechanical
equipment
– Motors, valves, dampers
– Limitations or faults in this equipment will affect
control (and thus system) performance.
What is Feedback?
1.
2.
3.
4.
5.
6.
7.
The controlled variable is measured.
It is then compared to a desired value, or setpoint.
The difference between setpoint and measurement is called the error.
The controller calculates a control output depending on the error.
The control output is sent to some physical equipment, a valve or similar, to
affect the process. This physical equipment is called the Final Control
Element.
The process responds to the change made by the final control element.
or 1. The process response is measured
Speed
Error
in
km/h
Desired
speed in
km/h
+
Cruise
Control
Desired
Throttle
Position
Throttle
Actuator
Speed in km/h
Speed
Sensor
Actual
Throttle
Position
Engine,
Transmission,
Wheels
Disturbances wind, slope,
bad fuel
Speed
What are those block
diagrams?
• Block diagrams are a visual representation of the
actual dynamic system and its governing equations.
• Each line is a signal - something that varies over
time, and can be measured or calculated.
• Each block is a “functional element” - something that
does something, and is governed by differential,
integral or algebraic equations, and describable as a
transfer function.
Block Diagram
Disturbances wind, slope, bad
fuel
Speed
Error
in
km/h
Desired
speed in
km/h
+
Cruise
Control
Desired
Throttle
Position
Throttle
Actuator
Speed
Sensor
Speed in km/h
Actual
Throttle
Position
Engine,
Transmission,
Wheels
Speed
Standard Nomenclature
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•
•
•
•
•
•
PV, or y : controlled variable
SP or ysp : setpoint, desired value
OP or u (text uses p): controller output
e : error, ysp - y
d or l : disturbance or load (wild) variable
ym : measured value of y
G : a transfer function
–
–
–
–
–
–
•
•
•
•
Gp : process transfer function
Gc : controller transfer function
Gv : final control element (valve) transfer function
Gm : measurement element transfer function
Gd or GL : Disturbance (Load) transfer function
Gcl : closed loop transfer function
K : transfer function gain
 : time constant
 : time delay (dead time)
 : damping ratio (also called damping factor)
Block Diagram
Disturbances wind, slope, bad
fuel
d
The purpose of the C.L.T.F. is to describe the
entire system with a single transfer function
that can be analyzed.
Desired
speed in
km/h
+
ysp
Speed
Error
in
km/h
- e
Cruise
Gc
Control
Desired
Throttle
Position
u
Throttle
Gv
Actuator
ym
Speed
Gm
Sensor
Speed in km/h
Actual
Throttle
Position
Disturbance
Gd or GL
Process
Engine,
Transmission,
Gp
Wheels
Speed
y
Block Diagram
Disturbances wind, slope, bad
fuel
d
Disturbance
or GL
ClosedGd
Loop
Process
Desired
speed in
km/h
+
ysp
Speed
Error
in
km/h
- e
Disturbance
Transfer Function
Actual
Desired
Throttle
Throttle
Engine,
Position
Closed
Loop
Position
Cruise
Throttle
Transmission,
Gp
Gc Setpoint
Gv
Control
Actuator
Wheels
u
Transfer Function
ym
Speed
Gm
Sensor
Speed in km/h
Closed Loop System
Speed
y
Block Diagram
y = Gd * d + Gp * Gv * u
rules
are
applied
around the block
= •These
Gd
*block
d +transfer
Gp
* Gv
*function
Gc
*is
e used
•The
•Each
•Summers
diagram
(circle
with
is
x
inside)
multiplied
to figure
add
out
byinputs,
its
theinput
or, to
if
diagram:
= get
Gd
*its
dinput
+output:
Gpequations
*isGv
* Gc * directly.
(ysp
- ym)
governing
the
marked
with
a - sign, that input is
yd =+ Gd
* Gv
d +* Gp
* (ysp
Gv *- uGm * y)
= Gd
*
Gp
*
Gc
*
subtracted
u = Gc * e
e * Gc * ysp - Gp * Gv * Gc * Gm * y
= Gd * ud =
+ Gc
Gp ** Gv
e
=
ysp
ym *=Gc
Gm -* ym
y
y + Gp * eGv
= ysp -* Gm
ym * y = Gd * d + Gp * Gv * Gc * ysp
y ( 1 + Gp
* Gc* *yGm) = Gd * d + Gp * Gv * Gc * ysp
ym* Gv
= Gm
y = (Gd/(1 + Gp Gv Gc Gm)) * d + ( Gp Gv Gv/(1 + Gp Gv Gc Gm)) * ysp
Desired
speed in
km/h
+
ysp
Speed
Error
in
km/h
- e
Cruise
Gc
Control
Desired
Throttle
Position
u
Throttle
Gv
Actuator
ym
Gm
Speed in km/h
Actual
Throttle
Position
Disturbances wind, slope, bad
fuel
Engine,
Transmission,
Gp
Wheels
d
Gd or GL
Speed
y
Block Diagram
Disturbances wind, slope, bad
fuel
d
Desired
speed in
km/h
+
ysp
Speed
Error
in
km/h
- e
ClosedGd
Loop
Gd or GL
Disturbance
1 + Gp Gv Gc Gm
Transfer Function
Actual
Desired
Throttle
Throttle
Engine,
Position
Closed
Loop
Position
CruiseGp Gv Gc Throttle
Transmission,
Gp
Gc Setpoint
Gv
Control
Actuator
Wheels
1 + Gp Gv
u Gc Gm
Transfer Function
ym
Gm
Speed in km/h
Closed Loop System
Speed
y
How does PID work?
• PID control acts on the error.
• The control action is the sum of three terms:
– Proportional: Kc * the error now
– Integral: Kc/TauI * the integral of error since the
controller was turned on
– Derivative: Kc*TauD * the rate of change of the
error now
P animation
QuickTime™ and a
MPEG-4 Video decompressor
are needed to see this picture.
PI animation
QuickTime™ and a
MPEG-4 Video decompressor
are needed to see this picture.
Animation
QuickTime™ and a
MPEG-4 Video decompressor
are needed to see this picture.
Comparison
Comments
• P never reaches setpoint.
• PID responds before PI does because
of the Derivative term.