Tham khảo tài liệu 'crc press mechatronics handbook 2002 by laxxuss episode 3 part 8', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 5 Complete Root Locus for - K - -4 -2 0 2 4 6 8 Real Axis FIGURE Complementary and usual root loci for Example 4. Example 4 revisited In this example if K increases from x to the closed-loop system poles move along the complementary root locus and then the usual root locus as illustrated in Fig. . Root Locus for Systems with Time Delays The standard feedback control system considered in this section is shown in Fig. where the controller C and plant P are in the form C s N s Dc s and -hs p P s e Po s where Po s D-s with Nc Dc and Np Dp being coprime pairs of polynomials with real The term e h is the transfer function of a pure delay element in Fig. the plant input is delayed by h seconds . In general time delays enter into the plant model when there is a sensor or actuator processing delay and or a software delay in the controller and or a transport delay in the process. In this case the open-loop transfer function is G s Gh s e-hsG0 s where G0 s P0 s C s corresponds to the no delay case h 0. Note that magnitude and phase of G jW are determined from the identities G jw Go j w ZG jco - ho ZG0 ja 2A pair of polynomials is said to be coprime pair if they do not have common roots. 2002 CRC Press LLC 5 Complete Root Locus for - K - -4 -2 0 2 4 6 8 Real Axis FIGURE Complementary and usual root loci for Example 4. Example 4 revisited In this example if K increases from x to the closed-loop system poles move along the complementary root locus and then the usual root locus as illustrated in Fig. . Root Locus for Systems with Time Delays The standard feedback control system considered in this section is shown in Fig. where the controller C and plant P are in the form C s N s Dc s and -hs p P s e Po s where Po s D-s with Nc Dc and Np Dp being coprime pairs of polynomials with real The term e h is the transfer function of a pure delay element in Fig. the plant input is delayed by h
