LINEAR CONTROL SYSTEMS

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LINEAR CONTROL SYSTEMS

• Ali Karimpour
• Assistant Professor
• Ferdowsi University of Mashhad

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Lecture 16
Root Locus Technique

• Topics to be covered include
• Root locus criterion.
• Root loci (RL).
• Complement root loci (CRL).
• Complete root loci.
• Property and construction of complete root loci.

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Root locus
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Root loci (RL)
Complement root loci (CRL)
Complete root loci
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Example 1? Draw the complete root loci of
following system.
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The Root Locus procedure
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It is
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The Root Locus procedure
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The Root Locus procedure
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The Root Locus procedure
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The Root Locus procedure
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The Root Locus procedure
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Rule 4 Find the asymptotes and centered of
asymptotes for positive and negative values of k.
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Example 2? Draw the complete root loci of the
following system.
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Clearly it is ok
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The Root Locus procedure
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The Root Locus procedure
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????? 6 ???? ????? ?? ???? ??????
Rule 6 Find the cross of root locus with
imaginary axis
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rlocus(1,1 15 50 0)
hold on rlocus(-1,1 15 50 0)
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Example 3? Draw the complete root loci of
following system.
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Example 4
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Example 4
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Example 4
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Example 4
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????? 6 ???? ????? ?? ???? ??????
Rule 6 Find the cross of root locus with
imaginary axis
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Exercises
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1 The transfer function of a single-loop control
system are given as
Construct the root loci of the Zeros of
1G(s)K(s) for -8ltTdlt8
2 The open loop transfer function of a
unity-feedback (negative sign) system is
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Constract the complete root loci of the
characteristic equation.
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Exercises
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3 The open loop transfer function of a
unity-feedback (negative sign) system is
Construct the complete root loci of the
characteristic equation for Let n1, n2 , n3
and n4
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Exercises
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6 Consider following system Construct the
root loci for 0ltk1lt8
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Exercises
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7 Consider following system For k10, k11
1nd k110 construct the root loci for 0ltk2lt8 .
8 Construct the root loci of the closed loop
poles of the following system for 0ltalt8(Midterm
spring 2008).