ABE 463 Electrohydraulic Systems

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ABE 463 Electrohydraulic Systems

• Tuning a PID Controller

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Structure of a Typical PID Controller
PID controller stands for Proportional-integral-
derivative controller.
PID controller is a most common form of
feedback controller.
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Performance Specifications
Performance specifications are considered with
respect to the closed loop response of the
compensated system to unit step input.
The specifications are chosen as (i)  Overshoot
                 3 (ii) Settling time
              3 s (iii) Steady state error    
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PID Controller Tuning
A well-functioned PID controller must be tuned to
ensure the stability and to meet other
performance requirements.
Normally, tuning criteria include five
performance measures of stability response
rate noise ratio disturbance rejection
capability, and parameter sensitivity.
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General Tuning Methods
Controller tuning process, in general, first
searches for proper gains to ensure a desired
stability and response, then calculates
disturbance rejection and parameter
sensitivities.
A typical PID controller can be described by one
of the following transfer functions in s-domain
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Ziegler-Nichols (ZN) Tuning Methods
The ZN PID controller tuning process can be
completed in one of the two approaches Open-loop
system step response based tuning or
Closed-loop system frequency response based
tuning.
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ZN Step Response Tuning
An earliest design method for PID controller
based on open-loop step response for tuning the
controller.
ZN PID Step Response Tuning Parameters
Controller KP TI TD
P 1/?
PI 0.9/? 3L
PID 1.2/? 2L L/2
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ZN Frequency Response Tuning
Frequency response test is also called relay
test It starts tuning the proportional gain
until the closed-loop controller becomes
critically stable, and set this gain as the
ultimate gain Ku, and the corresponding
oscillation frequency is set as the ultimate time
period Tu.
ZN PID Frequency Response Tuning Parameters
Controller KP TI TD
P 0.5ku
PI 0.4ku 0.8Tu
PID 0.6ku 0.5Tu 0.12Tu
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Practical Procedures of ZN Tuning
One of most commonly used methods for tuning PID
controllers in engineering practices.

• PID gains are determined in such a way that
• first sets the set-point value to a typical value
  for representative uses and turns both I and D
  gains to zero as if it is a P controller.
• Progressively increase the P gain from a
  reasonable low level slowly until it will
  inducing oscillations of just self-sustaining.
• Set the P gain at this point as the critical gain
  Ku, and the oscillation period at this point as
  the critical period Tu for the controller.

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Example of PID Control Performance
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Kappa-Tau Tuning
An automatic tuning method.
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Pole Placement Tuning
An analytical tuning method.
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A PID May Have To Be Tuned When

• Careful consideration was not given to the units
  of gains and other parameters.
• The process dynamics were not well-understood
  when the gains were first set, or the dynamics
  have (for any reason) changed.
• Some characteristics of the control system are
  direction-dependent (e.g. actuator piston area,
  heat-up/cool-down of powerful heaters).
• You (as designer or operator) think the
  controller can perform better.

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A PID May Not Have To Be Tuned When

• A control valve sticks. (You may be able to spot
  this without leaving the control room.) Valves
  must be able to respond to commands.
• A control valve is stripped out from
  high-pressure flow. A valves response to a
  command must have some effect on the system.
• Measurement taps are plugged, or sensors are
  disconnected. Bad measurements may have you
  correcting for errors that dont exist.