Feedback Control Roundup
• 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:
• 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?
Speed
SpeedSensor
Speed in km/h
SpeedError in km/h
Desired speed in km/h
-+
CruiseControl
DesiredThrottlePosition Throttle
Actuator
ActualThrottlePosition Engine,
Transmission,Wheels
Disturbances - wind, slope, bad fuel
1. The controlled variable is measured.
2. It is then compared to a desired value, or setpoint.
3. The difference between setpoint and measurement is called the error.
4. The controller calculates a control output depending on the error.
5. 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.
6. The process responds to the change made by the final control element.
7. or 1. The process response is measured
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
CruiseControl
Engine,Transmission,
Wheels
ThrottleActuator
SpeedSensor
Speed
Speed in km/h
Desired speed in km/h
SpeedError in km/h
-+
DesiredThrottlePosition
ActualThrottlePosition
Disturbances - wind, slope, bad fuel
Standard Nomenclature• 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
CruiseControl
Engine,Transmission,
Wheels
ThrottleActuator
SpeedSensor
Speed
Speed in km/h
Desired speed in km/h
SpeedError in km/h
-+
DesiredThrottlePosition
ActualThrottlePosition
Disturbances - wind, slope, bad fuel
ysp e y
ym
uGc Gv Gp
Gm
DisturbanceProcessGd or GL
dThe purpose of the C.L.T.F. is to describe the entire system with a single transfer function that can be analyzed.
Block Diagram
CruiseControl
Engine,Transmission,
Wheels
ThrottleActuator
SpeedSensor
Speed
Speed in km/h
Desired speed in km/h
SpeedError in km/h
-+
DesiredThrottlePosition
ActualThrottlePosition
Disturbances - wind, slope, bad fuel
ysp e y
ym
uGc Gv Gp
Gm
DisturbanceProcessGd or GL
d
Closed Loop System
Closed LoopSetpoint
Transfer Function
Closed LoopDisturbance
Transfer Function
Block Diagram
CruiseControl
Engine,Transmission,
Wheels
ThrottleActuator
Speed
Speed in km/h
Desired speed in km/h
SpeedError in km/h
-+
DesiredThrottlePosition
ActualThrottlePosition
Disturbances - wind, slope, bad fuel
ysp e y
ym
uGc Gv Gp
Gm
Gd or GL
d
•The block diagram is used to figure out the governing equations directly.
•Each transfer function is multiplied by its input to get its output:
u = Gc * eym = Gm * y
•Summers (circle with x inside) add inputs, or, if the input is marked with a - sign, that input is subtracted
e = ysp - ym
•These rules are applied around the block diagram:
y = Gd * d + Gp * Gv * uu = Gc * ee = ysp - ymym = Gm * y
y = Gd * d + Gp * Gv * u = Gd * d + Gp * Gv * Gc * e = Gd * d + Gp * Gv * Gc * (ysp - ym) = Gd * d + Gp * Gv * Gc * (ysp - Gm * y) = Gd * d + Gp * Gv * Gc * ysp - Gp * Gv * Gc * Gm * yy + Gp * Gv * Gc * Gm * y = Gd * d + Gp * Gv * Gc * yspy ( 1 + Gp * Gv * Gc * Gm) = Gd * d + Gp * Gv * Gc * yspy = (Gd/(1 + Gp Gv Gc Gm)) * d + ( Gp Gv Gv/(1 + Gp Gv Gc Gm)) * ysp
Block Diagram
CruiseControl
Engine,Transmission,
Wheels
ThrottleActuator
Speed
Speed in km/h
Desired speed in km/h
SpeedError in km/h
-+
DesiredThrottlePosition
ActualThrottlePosition
Disturbances - wind, slope, bad fuel
ysp e y
ym
uGc Gv Gp
Gm
Gd or GL
d
Closed Loop System
Closed LoopSetpoint
Transfer Function
Closed LoopDisturbance
Transfer Function
Gp Gv Gc 1 + Gp Gv Gc Gm
Gd 1 + Gp Gv Gc Gm
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 aMPEG-4 Video decompressor
are needed to see this picture.
PI animation
QuickTime™ and aMPEG-4 Video decompressor
are needed to see this picture.
Animation
QuickTime™ and aMPEG-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.