Modern Control Engineering

390 Chapter 6 / Control Systems Analysis and Design by the Root-Locus Method A–6–19. Consider the system shown in Figure 6–98(a) ...

Example Problems and Solutions 391 This system involves three poles and no zero. The three poles are at s=0, s=–3,ands=–6. A roo ...

392 Chapter 6 / Control Systems Analysis and Design by the Root-Locus Method Since the system involves two or more poles than ze ...

Example Problems and Solutions 393 Notice that the system has a zero at s=0and two poles at Since this system involves two poles ...

Problems 394 Chapter 6 / Control Systems Analysis and Design by the Root-Locus Method B–6–1.Plot the root loci for the closed-lo ...

Problems 395 K(s– 1) +– (s+ 2) (s+ 4) G 1 (s) (a) (b) K(1–s) +– (s+ 2) (s+ 4) G 2 (s) B–6–12.Plot root-locus diagrams for the no ...

396 Chapter 6 / Control Systems Analysis and Design by the Root-Locus Method B–6–19.Referring to the system shown in Figure 6–10 ...

Problems 397 B–6–25.Consider the system shown in Figure 6–115. The system involves velocity feedback. Determine the value of gai ...

7 398 Control Systems Analysis and Design by the Frequency-Response Method 7–1 Introduction By the term frequency response,we me ...

Section 7–1 / Introduction 399 Although the frequency response of a control system presents a qualitative picture of the transie ...

400 Chapter 7 / Control Systems Analysis and Design by the Frequency-Response Method whereaand the bi(wherei=1, 2,p,n)are consta ...

Section 7–1 / Introduction 401 X Y t Inputx(t)=Xsinvt Outputy(t)=Ysin (vt+f) Figure 7–2 Input and output sinusoidal signals. x y ...

402 Chapter 7 / Control Systems Analysis and Design by the Frequency-Response Method The amplitude ratio of the output to the in ...

Section 7–2 / Bode Diagrams 403 1.Bode diagram or logarithmic plot 2.Nyquist plot or polar plot 3.Log-magnitude-versus-phase plo ...

404 Chapter 7 / Control Systems Analysis and Design by the Frequency-Response Method Decibels (dB) Numbers 0.01 0.02 0.04 0.1 0. ...

Section 7–2 / Bode Diagrams 405 Note that, when expressed in decibels, the reciprocal of a number differs from its value only in ...

406 Chapter 7 / Control Systems Analysis and Design by the Frequency-Response Method First-Order Factors (1jVT)^1. The log mag ...

Section 7–2 / Bode Diagrams 407 10 0 10 20 0 ° 45 ° 90 ° f dB v 1 20 T 1 10 T 1 5 T 1 T 1 2 T 2 T 5 T 10 T 20 T Exact curve ...

408 Chapter 7 / Control Systems Analysis and Design by the Frequency-Response Method 0 1 2 3 4 dB Corner frequency 1 10 T 1 5 ...

Section 7–2 / Bode Diagrams 409 dB 40 20 0 40 20 v f 90 ° 0 ° 45 ° v Exact curve Asymptote 0.01 T 0.1 T 1 T 10 T 0.01 T 0.1 T ...