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## Lesson 9

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**Automatic control**2. Analysis Lesson 9 Root locus automatic control by meiling CHEN**Poles and zeros**zeros poles pole zero automatic control by meiling CHEN**Closed-loop transfer function :**automatic control by meiling CHEN**Negative damped**Undamped Underdamped Critically damped Overdamped automatic control by meiling CHEN**Root locus**k G(s) ＋ － H(s) poles automatic control by meiling CHEN**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 CHEN**Root locus properties:**• The locus segments are symmetrical about the real axis. • (iii) automatic control by meiling CHEN**each locus from poles to zeros**for excess zeros or poles, locus segments extend from infinity. if Root locus construction (i) Loci Branches (1) (2) automatic control by meiling CHEN**(ii) Real axis segments**Poles + zeros = odd Poles + zeros = even automatic control by meiling CHEN**(iii) Asymptotic angles**automatic control by meiling CHEN**(iv) Centroid of the asymptotes**example Zero : 0 Poles: -2, -3+j3, -3-j3 automatic control by meiling CHEN**(v) Breakaway and entry points**example The characteristic function of closed loop system automatic control by meiling CHEN**(vi) Angle of departure and approach**example Angle of departure from the pole: automatic control by meiling CHEN**example**Angle of approach to the zero: automatic control by meiling CHEN**(vii) The cross point of root locus and Im-axis**example The characteristic function of closed loop system: automatic control by meiling CHEN**+**- (i) (iii) (ii) automatic control by meiling CHEN**MATLAB method**gh=zpk([],[0 –2 -10],[1]) rltool(gh) n=[-3 -9] m=[1 –1 –1 –15 0] gh=tf(n,m) rltool(gh) automatic control by meiling CHEN