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PID controller
Control engineering and signal processing
Michala Srnová2009/2010
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Content Compensator P compensator PI compensator Lead compensator Lag compensator PID controller
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PID controller Proportional + integral + derivative
Transfer function: KD – derivative gain Used in majority of closed-loop industrial processes
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PID controller Step response
Rise time Overshoot Settling Time Steady state Error
Effect of increasing the parameters:
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Tune Alter step response Find out parameter Kp, Ki, Kd Various methods
Manual Tuning Ziegler-Nichols Software Tools Cohen-Coon
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Manual Tuning No math required On-line method
1. What in characteristic need to be improved2. Kp – decrease the rise time3. Kd – reduce overshoot and settling time4. Ki – eliminate steady state error
Does not work in every time
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Ziegler-Nichols Rules for determine Kp, Ki, Kd Based on step response Proposed more methods First method – Step response method No integrators No dominant
complex-pairs Response:
s-shape, no overshoot Ʈ, a
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Ziegler-Nichols Parameters Ʈ and a – calculating
Drawbacks: lack robustness Improvement : K, Ʈ, T in model
From step response
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Ziegler Nichols Second method – frequency response
1. Ki and Kd =0, setting of Kp2. Starting of ocsillations → Kc, period – Tc3. These values used to calculate Kp,Ki,Kd
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Software Tuning Modern industrial facilities Online, offline method Software will
Gather data Develop process model Suggest optimal tuning
Principle Mathematical loops Frequency response to impulse Design PID loop values
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Thank you for your attention