Control Systems

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Control Systems

• Part 8 Control System Design Techniques

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Learning objectives

• To understand different control
  strategies/configurations
• To design controllers using root locus technique
• To state the properties and structure of lead
  compensator
• To state the properties and structure of lag
  compensator
• To design controllers using frequency response
  techniques

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Different control system configurations
(a) Cascade controller
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Different control system configurations
(b) Feedback controller
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Different control system configurations
(c)
(c) Cascade and feedback controller (two degree
of freedom)
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Different control system configurations
(d)
(d) Forward and cascade controller
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Different control system configurations
(e)
(e) Feedforward and cascade controller
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Cascade controller design with root locus method
The original system does not have any integrator,
therefore, it will result a steady-state error
when a unit step input is applied.
Objective Design a cascade controller (in the
position of the gain K) to improve the
steady-state performance without inducing much
change to the transient behavior
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Cascade controller design with root locus method
(Cont.)
K 164.6
Uncompensated system
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Cascade controller design with root locus method
(Cont.)
The idea is to add an integrator to improve the
steady-state performance and also to add a zero
to cancel out the effect on the transient
behavior
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Cascade controller design with root locus method
(Cont.)
K 158.2
Compensated system
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Cascade controller design with root locus method
(Cont.)
Step responses of the compensated and
uncompensated systems
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Cascade controller design with root locus method
The original system response is too slow.
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Cascade controller design with root locus method
Uncompensated system
The design objective is to move the closed-loop
poles further to left along the constant damping
line.
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Cascade controller design with root locus method
(Cont.)
where
K47.45
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Cascade controller design with root locus method
(Cont.)
Compensated system
K47.45
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Cascade controller design with root locus method
(Cont.)
Time domain responses
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Lead and lag compensators
Lead compensator
Lag compensator
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Frequency response of a lead compensator
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Frequency response of a lag compensator
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Design example with a lead compensator
Plant
Controller


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Design example with a lead compensator (Cont.)
Unit step response of open-loop system
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Design example with a lead compensator (Cont)
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Design example with a lead compensator (Cont)
The compensator has the transfer function
The loop transfer function is then
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Design example with a lead compensator (Cont)
Unit step response of closed-loop system
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Design example with a lag compensator
Plant
Controller


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Design example with a lag compensator (Cont)
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Design example with a lag compensator (Cont)
The compensator has the transfer function
The loop transfer function is then
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Design example with a lag compensator (Cont)
Uncompensated system
Compensated system
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Summary

• Controller can interact with the system in
  several different ways cascade, feedback, and
  feedforward.
• The essence of the controller design is to change
  the dynamic characteristics of the system through
  the introduction of dynamic compensator.
• The compensated system should satisfy certain
  criteria in s-domain (Root Locus method) or in
  frequency domain (Frequency Response method).
• There are two commonly used controller
  structures, lead compensator, and lag
  compensator.