Feedback control systems characteristics Solutionschapter 4

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Feedback control systems characteristics
Solutions-chapter 4

T1S 044 - Spring 2009

• Prof. Marian S. Stachowicz
• Laboratory for Intelligent Systems
• ECE Department, University of Minnesota
  Duluth
• May 20, 2009

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References for reading

• R.C. Dorf and R.H. Bishop, Modern Control
  Systems,
• 11th Edition, Prentice Hall, 2008,
• Chapter 4.1 - 4.11
• 2. J.J. DiStefano, A. R. Stubberud, I. J.
  Williams, Feeedback and Control Systems,
  Schaum's Outline Series, McGraw-Hill, Inc., 1990
• Chapter 9

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Outline

• Introduction
• Error signal analysis
• Sensitivity of control systems to parameter
  variations
• Disturbance signals in a feedback control system

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Introduction
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Advantages of the closed-loop feedback control

• Decreased sensitivity of the system to variations
  in the parameters of the process
• Improved rejection of the disturbances
• Improved measurement noise attenuation
• Improved reduction of the steady-state error of
  the system
• Easy control and adjustment of the transient
  response

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System sensitivity
System sensitivity is the ratio of the change in
the system transfer function to the change of a
process transfer function (or parameter) for a
small incremental change.
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System sensitivity
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Sensitivity of the open-loop system
T(s) Gc(s) G(s)
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Open-loop system with a disturbance input
Y(s) R(s) G(s) Td(s) G(s)
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The sensitivity of the feedback system to change
in the G(s)
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The sensitivity of the feedback system to change
in the H(s)
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Sensitivity of the closed-loop system
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Closed-loop control system
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Closed-loop control system
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Loop gain
Sensitivity function
Complementary sensitivity function
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E 4.1 Tracking the sun
Gc(s) 1
H(s) 1
N(s) 0
G(s) 100/(? s 1)
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Sensitivity
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Time-constant
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Step responses
O L
C L
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E 4.9 Closed-loop system with non-unity
H(s) 14/(s2 5s 6)
G(s) K / (s 10)
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The transfer function
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Tracking error
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The steady-state error
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Sensitivity
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P 4.17 A robot gripper control
Km 30 Rf 1 ohm Kf Ki 1 J 0.1, b 1
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Transfer function
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Disturbance
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Final value
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AP 4.3 The machine tool
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Error plot
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AP 4.6 A lead network
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CP 4.3 Family of step responses
T(s) 5 K /(s2 15 s K)
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AP 4.1 Tank level regulator
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P 4.3 Thermal control system
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Open-loop response of the system
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