Mini course at Danfoss A/S

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Auto-tuning of PID controllers

• Mini course at Danfoss A/S
• Henrik Rasmussen
• Department of Control Engineering
• Aalborg University

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Content

• The Satt Control auto-tuner in a distributed
  control system
• The Self-tuning Regulator concept
• PID-algorithm textbook and modifications
• Ziegler-Nichols frequency response method
• Relay tuning in closed loop
• Bump-less transfer and anti integrator windup
• Gain scheduling
• Choice of controller type

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References

• Automatic tuning of PID controllers, Åstrøm
  Hägglund
• Adaptive Control, Åstrøm Wittenmark
• Automatic tuning of PID-regulators, H. Rasmussen
  URL,
  http//www.control.auc.dk/hr

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Distributed control system
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SattControl Auto-tuner
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Self Tuning Regulator
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Textbook and modified PID-algorithm
The ''textbook'' version of the PID controller
can be described by the equation
Modification of ''textbook'' version
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Controller Parameters
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Ziegler-Nichols ultimate period method
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Auto Tuning based on relay feedback
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Nyquist plot
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Phase and amplitude margin
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1. Break
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Relay with hysteresis
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Stable limit cycle
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Offset
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Auto tuning of PID regulators
Ziegler-Nichols tuning
Spec. phase and amplitude margin
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Actuator Saturation
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Integrator windup
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Regulator modified to avoid windup
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Regulator modified to avoid windup
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Anti windup for PID controller
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Discrete time PI controller
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p and q operators
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Discrete Time PID-controller
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Integrator windup and bumpless transfer
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2. Break
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Open loop step response
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Closed loop with PI control ?!?
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Anti integrator windup
Measured actuator output
Estimated actuator output
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Observer A1-exp(-Ts/(0.1Ti))
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Observer A1-exp(-Ts/Ti))
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PI controller and a nonlinear valve
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Step response for different levels
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PI controller with gain scheduling
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Step response for different levels
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Gain scheduling principle
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Bumpless transfer between controllers
y
y
u
1 A1
ref
G
T1
A1-R1
-S1
1 A2
T2
A2-R2
-S2
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Choice of Controller
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Conclusions

• The Self-tuning Regulator concept
• Relay experiment gives ultimate period and gain
• Ziegler-Nichols tuning
• Tuning based on phase and amplitude margin
• Bump-less transfer and anti integrator windup
• PID-algorithm textbook and modifications
• Gain scheduling
• Choice of controller type