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20 EE481-W00708-Lecture December 2007
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Classical Control Theory
Open Loop Control Provide a command to a system Trust that it does what it should
Set Point Output
Plant
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Plant Characteristics
Most modelsuntil recently models Linear s-domain (frequency) Inaccurate Newer developments NonNon-linear Discrete (z-domain) (z-
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Closed Loop Control
Feedback is important Make sure the output is acceptable
Set Point Error + Plant Output
Feedback
Sensor Gain
2000-2007 by Henry L. Welch
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EE481-W00708-Lecture 12
20 December 2007
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Normalized Closed Loop Control
Unity feedback simplifies the computations Often an artificial modification
Error Set Point + Feedback Command Output Compensator Plant
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Compensator Design
One of the key areas of controls Desired characteristics Minimize error Allow for variations in operating point Insensitivity to plant variations Fast, stable response to set point changes
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On/Off Compensator
Sometimes called Bang-bang control BangSimple strategy If the output is too high, turn the system off p g y otherwise turn the system on Hysteresis is common Problems On Off Excessive thrashing Inefficient
2000-2007 by Henry L. Welch
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EE481-W00708-Lecture 12
20 December 2007
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Proportional Control (P)
Set the command on based the magnitude of the error Command = kpError Limitations SteadySteady-state error Poor high-speed response high-
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Integral Control (PI)
Keep proportional elements Examine long term error trends i.e. Take note of steady-state error ie steadyCommand = k p Error + k I Error
Limitations Removes steady state error Slows response time
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Derivative Control (PID)
Keep proportional and integral terms Anticipate trends
Command = k p Error + k I Error + k D dError dt
Limitations Compromises steady-state error with steadyrapid response time
2000-2007 by Henry L. Welch
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EE481-W00708-Lecture 12
20 December 2007
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PID Observations
Advantages Well understood mathematically Simple and popular p p p Disadvantages No model of transport lag Depends...