Modern Control Engineering
330 Chapter 6 / Control Systems Analysis and Design by the Root-Locus Method Unit-Step Responses of Compensated and Uncompensate ...
Section 6–8 / Lag-Lead Compensation 331 function for this compensator may be obtained as follows: The complex impedance Z 1 is g ...
332 Chapter 6 / Control Systems Analysis and Design by the Root-Locus Method +– Gc(s) G(s) Figure 6–54 Control system. Then Equa ...
Section 6–8 / Lag-Lead Compensation 333 is approximately unity, where is one of the dominant closed-loop poles, choose the value ...
334 Chapter 6 / Control Systems Analysis and Design by the Root-Locus Method 2.The lag–lead compensator given by Equation (6–23) ...
Section 6–8 / Lag-Lead Compensation 335 EXAMPLE 6–8 Consider the control system shown in Figure 6–55. The feedforward transfer f ...
336 Chapter 6 / Control Systems Analysis and Design by the Root-Locus Method Thus Next we determine the value of Kcfrom the magn ...
Section 6–8 / Lag-Lead Compensation 337 The compensated system will have the open-loop transfer function Because of the cancella ...
338 Chapter 6 / Control Systems Analysis and Design by the Root-Locus Method t Sec 0 1 2 3 4 5 6 7 8 (a) Outputs 0.4 0.8 1.8 0 1 ...
Section 6–8 / Lag-Lead Compensation 339 Assuming the specifications are the same as those given in Example 6–8, design a compens ...
340 Chapter 6 / Control Systems Analysis and Design by the Root-Locus Method 0 jv s B A P 55 ° j 5 j 4 j 3 j 2 j 1 j 4 j 3 j 2 ...
Section 6–8 / Lag-Lead Compensation 341 The dominant closed-loop poles are located at The other closed-loop poles are located at ...
342 Chapter 6 / Control Systems Analysis and Design by the Root-Locus Method The maximum overshoot in the step response of the c ...
Section 6–9 / Parallel Compensation 343 The closed-loop transfer function for the system with parallel compensation [Figure 6–60 ...
344 Chapter 6 / Control Systems Analysis and Design by the Root-Locus Method Notice that the adjustable variable kdoes not appea ...
Section 6–9 / Parallel Compensation 345 At point Q, the value of Kis Hence Thus, we have two solutions for this problem. For k=0 ...
346 Chapter 6 / Control Systems Analysis and Design by the Root-Locus Method The open-loop zero at s=0was introduced in the proc ...
Example Problems and Solutions 347 From Figure 6–63 we notice that the response of the system with k=0.4490is oscillatory. (The ...
348 Chapter 6 / Control Systems Analysis and Design by the Root-Locus Method The breakaway and break-in points are determined fr ...
Example Problems and Solutions 349 4.Determine a sufficient number of points that satisfy the angle condition. (It can be found ...
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