Modern Control Engineering

490 Chapter 7 / Control Systems Analysis and Design by the Frequency-Response Method This transfer function is tentative because ...

Section 7–10 / Control Systems Design by Frequency-Response Approach 491 7–10 Control Systems Design by Frequency-Response Appro ...

A common approach to the design based on the Bode diagram is that we first adjust the open-loop gain so that the requirement on ...

Basic Characteristics of Lead, Lag, and Lag–Lead Compensation. Lead com- pensation essentially yields an appreciable improvement ...

the lead compensator. The minimum value of ais usually taken to be about 0.05. (This means that the maximum phase lead that may ...

Hence, (7–26) As seen from Figure 7–92, the lead compensator is basically a high-pass filter. (The high frequencies are passed, ...

lead compensator shifts the gain crossover frequency to the right and decreases the phase margin. 4.Determine the attenuation fa ...

The first step in the design is to adjust the gain Kto meet the steady-state performance spec- ification or to provide the requi ...

fm=38° corresponds to a=0.24.Once the attenuation factor ahas been determined on the basis of the required phase-lead angle, the ...

The solid curves in Figure 7–96 show the magnitude curve and phase-angle curve for the compen- sated system. Note that the bandw ...

Figure 7–98 shows the polar plots of the gain-adjusted but uncompensated open-loop trans- fer function G 1 (jv)=10 G(jv)and the ...

MATLAB programs for obtaining the unit-step response and unit-ramp response curves are given in MATLAB Program 7–13. Figure 7–99 ...

502 Chapter 7 / Control Systems Analysis and Design by the Frequency-Response Method 7–12 Lag Compensation In this section we fi ...

Section 7–12 / Lag Compensation 503 In the complex plane, a lag compensator has a zero at s=–1/Tand a pole at s=–1/(bT).The pole ...

Define Then The open-loop transfer function of the compensated system is where Determine gain Kto satisfy the requirement on the ...

Section 7–12 / Lag Compensation 505 EXAMPLE 7–27 Consider the system shown in Figure 7–103. The open-loop transfer function is g ...

The magnitude curve and phase-angle curve of G 1 (jv)are shown in Figure 7–104. From this plot, the phase margin is found to be ...

Section 7–12 / Lag Compensation 507 Thus, the transfer function of the lag compensator is Since the gain Kwas determined to be 5 ...

508 Chapter 7 / Control Systems Analysis and Design by the Frequency-Response Method Finally, we shall examine the unit-step res ...

Section 7–12 / Lag Compensation 509 Note that the zero and poles of the designed closed-loop system are as follows: The dominant ...