Modern Control Engineering

450 Chapter 7 / Control Systems Analysis and Design by the Frequency-Response Method Im (^01) Re 1 +G(jv)H(jv) Im (^0) Re 1 1 ...

Section 7–5 / Nyquist Stability Criterion 451 Im 1 0 Re GH Plane Figure 7–49 Region enclosed by a Nyquist plot. Remarks on the ...

452 Chapter 7 / Control Systems Analysis and Design by the Frequency-Response Method jv jv 0 ss s Plane s Plane j 0 + j 0 – ` s= ...

Section 7–5 / Nyquist Stability Criterion 453 jv s D s Plane C A B E F j 0 + j 0 – +j` j` ` ` (e 1) v = 0 + – (^1) D,E,F v ...

454 Chapter 7 / Control Systems Analysis and Design by the Frequency-Response Method Note that a similar analysis can be made if ...

Section 7–6 / Stability Analysis 455 Im 1 Re GH Plane G(jv)H(jv) v = –` v =^0 v =` Figure 7–53 Polar plot of G(jv)H(jv) consid ...

456 Chapter 7 / Control Systems Analysis and Design by the Frequency-Response Method Im Re GH Plane v = 0 – v = 0 + v =– v = I ...

Section 7–6 / Stability Analysis 457 Im Re GH Plane v = 0 – v = 0 + 1 v =` v =–` Figure 7–56 Polar plot of the system consider ...

458 Chapter 7 / Control Systems Analysis and Design by the Frequency-Response Method R(s) C(s) G(s) G 1 (s) G 2 (s) H 1 (s) H 2 ...

Section 7–6 / Stability Analysis 459 Figure 7–60 Control system. IfG(s)is unstable, the effects of instability are to produce a ...

460 Chapter 7 / Control Systems Analysis and Design by the Frequency-Response Method Im v = 0.8 v = 0.7 j1.5 G KPlane v = 0.6 v ...

Section 7–6 / Stability Analysis 461 Nyquist Stability Criterion Applied to Inverse Polar Plots. In the previous analyses, the N ...

462 Chapter 7 / Control Systems Analysis and Design by the Frequency-Response Method Depending on whether the data are graphical ...

Section 7–7 / Relative Stability Analysis 463 s Plane jv G(jv) 0 s jv 4 jv 3 jv 2 jv 1 s 4 – s 3 – s 2 – s 1 GPlane Im – (^10) ...

464 Chapter 7 / Control Systems Analysis and Design by the Frequency-Response Method Phase and Gain Margins. Figure 7–66 shows t ...

Section 7–7 / Relative Stability Analysis 465 |G | in dB |G | in dB 0 + 0 + |G | in dB + |G | in dB + 90 ° 180 ° ...

466 Chapter 7 / Control Systems Analysis and Design by the Frequency-Response Method anglegis positive (negative). The angle fro ...

Section 7–7 / Relative Stability Analysis 467 v =` v =` v Im Im Re Re 0 v 0 v 1 v 1 v 2 v 2 v 3 v 3 Phase crossover frequencies ...

468 Chapter 7 / Control Systems Analysis and Design by the Frequency-Response Method The phase and gain margins can easily be ob ...

Section 7–7 / Relative Stability Analysis 469 G(s) 20(s+ 1) s(s+ 5)(s^2 + 2 s+ 10) +– Figure 7–71 Closed-loop system. Frequency ...