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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