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Definition of Root Locus
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This lesson includes the topics: characteristic equation, Feedback system, Root Locus definition, previous year GATE problem with solution.

AKHILESH PANDEY
B.Tech. in EC, GATE 2017 AIR 18, YouTuber (channel name - STUDENT MODULATOR), 5 years Teaching Experience

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1. Root Locus (Lesson 1) Subject: Control System By- AKHILESH PANDEY

2. About Me B.Tech. in Electronics & Communication GATE 2017 AIR 18 (EC) 5 Years Teaching Experience Youtuber (channel-STUDENT MODULATOR)

3. Target Audience GATE EC/EE/IN aspirants ESE EC/EE aspirants , Useful for all Graduate/Diploma level technical exams (ECEE): ISRO. DRDO, BARC, DMRC, SSC-JE, RRB-SSE/JE, Electricity boards, and all other PSUs conducting their own exams Note: This course covers only the topic on which questions asked in GATE exam

4. Course Overview 1. Root locus definition 2. Magnitude and phase angle of loop gain, Value of k on root locus 3. Basic rules for sketching root locus 4. Asymptote, angle of asymptote, Centroid 5. Break-away and break-in point Note: In each lesson, relevant previous year GATE problems will be discussed

5. Feedback System Forward Gain Positive feedback system Input + Output G (s) CLTFG 1-G(s)H(s) It leads to unstability H(s) Feedback Factor Negative feedback system CLTF-G(S) G (s) 1 F G(s)H(s) Closed Loop Transfer Function Input Output 1+G(S)H(S) Negative feedback system is characterized in control sys.

6. Characteristic Equation For a negative feedback system, CLTF-G(s) 1+G(s)H(s) Characteristic equation: 1 G(s) H(s) 0 where G(s) open loop forward gain H(s) feedback Solving the characteristic equation, we get different values of s which is called the roots of characteristic equation.

7. What is Root Locus? Graph showing how the roots of characteristic equation move around the s-plane as single parameter varies. Loop gain of system G(s) H(s)(s + P,)(s + P2Ps . zeros-Z1,Z2, Z3, .. poles- -PI -p2, -p3 kis the variable parameter for root locus

8. How to plot Root Locus? Root Locus: Roots of Characteristic equation 1 G(s) H(s) 0 plotted on s-plane for parameter k varying from 0 to oo Complementary Root Locus: Roots of Characteristic equation 1 + G(s) H(s) = 0 plotted on s-plane for parameter k varying from -oo to 0

9. GATE 2017 - 2 Marks (Question) A unity feedback control system has an open loop transfer function G(s) = s(s2+7s+12) The gain k for which s =-1 +jl will lie on the root locus of this system is (a) 4 (b) 5.5 (c) 6.5 (d) 10

10. GATE 2017- 2 Marks (Solution) and s=-1+j1 = s(s2+7s+12) G(s) For unity feedback system, CL.TF. So, characteristic equation, 1G(s) 0 Put s1 +j1, Solving, or, 1 + = 0 s(s2+7s+12) 1 + =0 k = 10