Modern Control Engineering

350 Chapter 6 / Control Systems Analysis and Design by the Root-Locus Method Since the characteristic equation is we have The br ...

Example Problems and Solutions 351 The breakaway and break-in points are found from from which we get or Thus, the breakaway or ...

352 Chapter 6 / Control Systems Analysis and Design by the Root-Locus Method Hence, three root-locus branches meet at point s=–1 ...

Example Problems and Solutions 353 or which can be further simplified to For sZ–1.6,we may write this last equation as which giv ...

354 Chapter 6 / Control Systems Analysis and Design by the Root-Locus Method we have Now we set which yields Since these points ...

Example Problems and Solutions 355 Root-locus branches cross the imaginary axis at and The root-locus branch on the real axis to ...

356 Chapter 6 / Control Systems Analysis and Design by the Root-Locus Method The intersection of the asymptotes and the real axi ...

Example Problems and Solutions 357 A–6–7. Sketch the root loci of the control system shown in Figure 6–69(a). Determine the rang ...

358 Chapter 6 / Control Systems Analysis and Design by the Root-Locus Method Thus the equation dKds=0has a double root at s=–1. ...

Example Problems and Solutions 359 Taking tangents of both sides of this last equation, we obtain or which can be simplified to ...

360 Chapter 6 / Control Systems Analysis and Design by the Root-Locus Method Hence, for the system we have num = [1] den = [1 3 ...

Example Problems and Solutions 361 Drawing two or more plots in one diagram can also be accomplished by using the holdcom- mand. ...

362 Chapter 6 / Control Systems Analysis and Design by the Root-Locus Method A–6–9. Plot the root loci and asymptotes for a unit ...

Example Problems and Solutions 363 The MATLAB program to plot the root loci of G(s)and the asymptotes is given in MATLAB Program ...

364 Chapter 6 / Control Systems Analysis and Design by the Root-Locus Method the points where the root loci cross the imaginary ...

Example Problems and Solutions 365 A–6–11. Obtain the transfer function of the mechanical system shown in Figure 6–74. Assume th ...

366 Chapter 6 / Control Systems Analysis and Design by the Root-Locus Method A–6–12. Obtain the transfer function of the mechani ...

Example Problems and Solutions 367 A–6–13. Consider the model for a space-vehicle control system shown in Figure 6–76. Design a ...

368 Chapter 6 / Control Systems Analysis and Design by the Root-Locus Method or Hence, The value of can be determined from the m ...

Example Problems and Solutions 369 The closed-loop transfer function for the compensated system becomes Figure 6–79 shows the un ...