basics of control
DESCRIPTION
Basics of control. Lin Zhong ELEC424, Fall 2010. How can we set the room temperature at 78°?. Room: the system Temperature: the state of the system or the process variable. Sensor to measure the system state. Actuator to change the system state. Feedback system. Controller. - PowerPoint PPT PresentationTRANSCRIPT
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Basics of control
Lin ZhongELEC424, Fall 2010
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How can we set the room temperature at 78°?
Room: the systemTemperature: the state of the system or the process variable
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Sensor to measure the system state Actuator to change the system state
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Actuator SensorController
Feedback system
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Actuator SensorController
Feedback system
Setpoint: r Output: y
Control: u
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ProcessController
Feedback system (Contd.)
Setpoint: r Output: y
Control: u
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ProcessController
Feedback system (Contd.)
Setpoint: r
Error: e=r-y
- Output: y
Control: u
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On-off control
• If e>0, u=1 (On); if (e<=0), u=0 (Off)
ProcessControllerSetpoint: r
Error: e=r-y
- Output: y
Control: u
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On-off control (Contd.)
e
u On
Off
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On-off control with hysteresis
e
u On
Off
Reduction in switching frequency
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Targeted state
Starting state
How is a controller evaluated?
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Targeted state
Starting state
Rise time
10%
Time for the state to rise to within 10% of the desired level for the first time
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Targeted state
Starting state
OvershootDifference between peak and the targeted state
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Targeted state
Starting state
Settling time
time it takes the system to converge to the steady state
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Targeted state
Starting state
Steady-state error
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Targeted state
Starting state
In practice
Settling time
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Proportional control
• u=K×e
ProcessControllerSetpoint: r
Error: e=r-y
- Output: y
Control: u
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Proportional control
• u=K×e
ProcessControllerSetpoint: r
Error: e=r-y
- Output: y
Control: u
Heat dissipated at (100 Joules/s)
Heat generated at 10*e (Joules/s)
Steady-state error: 10°
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Proportional control
• Larger K Smaller steady-state error• Longer settling time• Danger of oscillation
http://www.cds.caltech.edu/~murray/courses/cds101/fa02/caltech/astrom.html
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Proportion/Integral (PI) control
ProcessControllerSetpoint: r
Error: e=r-y
- Output: y
Control: u
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PI control
• Smaller Ti Danger of oscillation
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Proportion/Integral/Derivative (PID) control
ProcessControllerSetpoint: r
Error: e=r-y
- Output: y
Control: u
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Derivative
• Larger Td Reduced danger of oscillation
• Too large Td Danger of oscillation increases again
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PID control
• Developed early 20th century– Nicolas Minorsky (1922): automatic steering
system for US Navy
• Extremely widely used– 97% of regulatory controllers in refining, chemical,
and pulp & paper industries• Very often PI control is used