automatic control by meiling CHEN1 Lesson 9 Root locus Automatic control 2. Analysis

automatic control by meiling CHEN2 Poles and zeros zeros poles pole zero

automatic control by meiling CHEN3 Closed-loop transfer function :

automatic control by meiling CHEN4

5

6 Overdamped Critically damped Underdamped Undamped Negative damped

automatic control by meiling CHEN7 Root locus kG(s) H(s) ＋ － poles

automatic control by meiling CHEN8 Open loop transfer function Using open loop transfer function + system parameters to analyze the closed-loop system response Draw the s-plan root locus

automatic control by meiling CHEN9 Root locus properties: (i)The locus segments are symmetrical about the real axis. (ii) (iii)

automatic control by meiling CHEN10 Root locus construction (i) Loci Brancheseach locus from poles to zeros if for excess zeros or poles, locus segments extend from infinity. (1) (2)

automatic control by meiling CHEN11 (ii) Real axis segments Poles + zeros = odd Poles + zeros = even

automatic control by meiling CHEN12 (iii) Asymptotic angles

automatic control by meiling CHEN13 (iv) Centroid of the asymptotes Zero : 0 Poles: -2, -3+j3, -3-j3 example

automatic control by meiling CHEN14 (v) Breakaway and entry points example The characteristic function of closed loop system

automatic control by meiling CHEN15 (vi) Angle of departure and approach example Angle of departure from the pole:

automatic control by meiling CHEN16 Angle of approach to the zero: example

automatic control by meiling CHEN17 (vii) The cross point of root locus and Im-axis example The characteristic function of closed loop system:

automatic control by meiling CHEN (i) (ii) (iii)

automatic control by meiling CHEN19

automatic control by meiling CHEN20 MATLAB method n=[-3 -9] m=[1 –1 –1 –15 0] gh=tf(n,m) rltool(gh) gh=zpk([],[0 –2 -10],[1]) rltool(gh)