Ch6 The Root Locus Method

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Ch6 The Root Locus Method
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6.3 Generalized root locus

• Parameter root locus
• Zero-degree root locus

Equivalent unity feedback transform An example
(refer to Script 4-12)
System contains inner positive-feedback- loop
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6.4 Parameter design by RL

• Root locus is a single-parameter method
• An example Welding head control

How to design two or more parameter by RL?
Refer to P354-356
Control system design by RL according to
performance specification.
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6.5 PID controllers

• Three-term or PID controller (P366)

• Transfer function in frequency domain

• Controller in the time domain

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Mechanism of PID

• PID controller provides a proportional term, an
  integration term and a derivative term. It is
  widely applied to many industrial process. Its
  popularity can be attributed partly to its good
  control performance and to the simplicity of
  design manner.
• PID controller introduces a TF with one pole at
  the origin and two zeros that can be located
  arbitrarily in the LH s-plane.

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PID explanation by RL
The TF of PID controller
If a high dynamic performance is desired, then
designers can select zeros of to
lie further left in the LHP and set K to drive
the roots near the complex zeros.
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6.6 Design example and simulation

• Laser manipulator control system
• The Root locus using Matlab

• The requirement for steady performance
• The requirement for stability
• The requirement for dynamic performance

Self-learning after class P373-380
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Summary

• The relationship between performance and roots
  location
• The concept of Root Locus
• The RL procedure
• The generalized RL and parameter RL
• A powerful tool for the analysis and design of
  modern control system

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Assignment

• E7.17
• P7.3