Modern Control Engineering

370 Chapter 6 / Control Systems Analysis and Design by the Root-Locus Method Hence, the lead compensator will have the following ...

Example Problems and Solutions 371 Figures 6–82(a) and (b) show the unit-step response and unit-ramp response of the compensated ...

372 Chapter 6 / Control Systems Analysis and Design by the Root-Locus Method A–6–14. Consider a system with an unstable plant as ...

Example Problems and Solutions 373 (z=0.7 corresponds to a line having an angle of 45.573° with the negative real axis.) Hence, ...

374 Chapter 6 / Control Systems Analysis and Design by the Root-Locus Method Hence, we have (6–31) The value of is The value of ...

Example Problems and Solutions 375 SinceKvis specified as 50 sec–1, we have Thus Now choose Then ChooseT=10.Then the lag compens ...

376 Chapter 6 / Control Systems Analysis and Design by the Root-Locus Method t Sec 071 2 3 4 5 6 8 9 10 (a) Outputs 0.4 0.8 0 1. ...

Example Problems and Solutions 377 A–6–16. Consider a unity-feedback control system whose feedforward transfer function is given ...

The lead portion must satisfy the following conditions: and The first condition can be simplified as By using the same approach ...

Example Problems and Solutions 379 Then Noting that the angle contribution of the lag portion is –1.697° and the magnitude contr ...

To verify the improved system performance of the compensated system, see the unit-step responses and unit-ramp responses of the ...

Example Problems and Solutions 381 1 s(s+ 1) (s+ 5) + Gc(s) Figure 6–90 Control system. Solution.Let us employ the lag–lead ...

382 Chapter 6 / Control Systems Analysis and Design by the Root-Locus Method Then at , the following magnitude and angle conditi ...

Example Problems and Solutions 383 With the choice of we find (6–36) and (6–37) Since our choice of is acceptable. Then the lag– ...

384 Chapter 6 / Control Systems Analysis and Design by the Root-Locus Method Real Axis 20 – 15 – 10 – 5 0 5 10 (a) Imag Axis ...

Example Problems and Solutions 385 A–6–18. Figure 6–93(a) is a block diagram of a model for an attitude-rate control system. The ...

386 Chapter 6 / Control Systems Analysis and Design by the Root-Locus Method Time (sec) 0 50 100 150 200 250 300 (b) Amplitude 0 ...

Example Problems and Solutions 387 We now choose the compensator in the following form: Then the open-loop transfer function of ...

388 Chapter 6 / Control Systems Analysis and Design by the Root-Locus Method The entire compensator for the system becomes The v ...

Example Problems and Solutions 389 are as follows: Now that the compensator has been designed, we shall examine the transient-re ...