Root locus
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Root Locus. Closed-loop control system with a variable parameter K. Unity feedback control system. The gain K is a variable parameter. Root locus for a second-order system when K e <K 1 <K 2 . The locus is shown in color. Evaluation of the angle and gain at s 1 ,for gain K=K 1.

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Root Locus

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Root locus

Root Locus


Root locus

Closed-loop control system with a variable parameter K.


Root locus

Unity feedback control system. The gain K is a variable parameter.


Root locus

Root locus for a second-order system when Ke<K1<K2. The locus is shown in color.


Root locus

Evaluation of the angle and gain at s1,for gain K=K1.


Root locus

(a) Single-loop system. (b) Root locus as a function of the parameter a.


Root locus

(a) The zero and poles of a second-order system,(b) the root locus segments,and (c) the magnitude of each vector at s1.


Root locus

A fourth-order system with (a) a zero and (b) root locus.


Root locus

Illustration of the breakaway point (a) for a simple second-order system and (b) for a fourth-order system.


Root locus

A graphical evaluation of the breakaway point.


Root locus

Closed-loop system.


Root locus

Evaluation of the (a) asymptotes and (b) breakaway point.


Root locus

Illustration of the angle of departure:(a) Test point infinitesimal distance from p1;(b) actual departure vector at p1


Root locus

Evaluation of the angle of departure.


Root locus

The root locus for Example 7.4:locating (a) the poles and (b) the asymptotes.


Root locus

1.Write the characteristic equation in pole-zero form so that the parameter of interest k appears as 1+kF(s)=O.

2.Locate the open-loop poles and zeros of F(s) in the s-plane.

3.Locate the segments of the real axis that are root loci.

4.Determinethenumberofseparateloci.

5.Locate the angles of the asymptotes and the center of the asymptotes.

6.Determine the break away point on the real axis(if any).

7.By utilizing the Routh-Hurwitz criterion, determine the point at which the locus crosses the imaginary axis(if it does so).

8.Estimate the angle of locus departure from complex poles and the angle locus arrival at complex zeros.


Root locus

Root loci as a function of α and β:(a) loci as α varies; (b) loci as β varies for one value of α = α1


Root locus

A region in the s-plane for desired root location.


Root locus

A feedback control system.


Root locus

Closed-loop system with a controller.


Root locus

Root locus for plant with a PID controller with complex zeros.


Root locus

Laser manipulator control system.


Root locus

Root locus for a laser control system.


Root locus

The response to a ramp input for a laser control system.


Root locus

Proposed configuration for control of the lightweight robot arm.


Root locus

Root locus of the system if K2=0,and K1 is variedfrom K1=0 to K1=∞,and Gc(s)=K1.


Root locus

Root locus for the robot controller with a zero inserted at s=-0.2 with Gc(s) = K1.


Root locus

Using the rlocus function.


Root locus

Disk drive control system with a PD controller.


Root locus

Sketch of the root locus.


Root locus

Root Locus Plots for Typical Transfer Functions (continued).


Root locus

Root Locus Plots for Typical Transfer Functions (continued).


Root locus

Root Locus Plots for Typical Transfer Functions (continued).


Root locus

Root Locus Plots for Typical Transfer Functions (continued).


Root locus

Root Locus Plots for Typical Transfer Functions (continued).


Root locus

Root Locus Plots for Typical Transfer Functions (continued).


Root locus

Root Locus Plots for Typical Transfer Functions (continued).


Root locus

Root Locus Plots for Typical Transfer Functions (continued).


Root locus

Root Locus Plots for Typical Transfer Functions (continued).


Root locus

Root Locus Plots for Typical Transfer Functions (continued).


Root locus

Root Locus Plots for Typical Transfer Functions (continued).


Root locus

Root Locus Plots for Typical Transfer Functions (continued).


Root locus

Root Locus Plots for Typical Transfer Functions (continued).


Root locus

Root Locus Plots for Typical Transfer Functions (continued).


Root locus

Root Locus Plots for Typical Transfer Functions (continued).


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