Tham khảo tài liệu 'ogata - modern control engineering part 10', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | cl x1 t step num den t c2 x2 t step numc denc t plot t d . t c2 - grid titlei Unit-Step Responses of Compensated and Uncompensated Systems xlabei t Sec ylabel Outputs text Compensated system text Uncompensated system Unit-ramp responses num1 fo 0 0 41 deni 1 2 4 01 num1c 0 0 0 denies 1 0 t 0 5 y1 z1 t Step num1 den1 t y2 z2 t Step num1c den1 c t plot t y1 . t y2 - t t - grid title Unit-Ramp Responses of Compensated and Uncompensated Systems xlabel t Sec ylabelf Outputs text Compensated system text Uncompensated system Figure 9-11 Unit-step response curves of the compensated and uncompensated systems. Unit-Step Responses of Compensated and Uncompensated Systems tSec 620 Chapter 9 Control Systems Design by Frequency Response Figure 9-12 Unit-ramp response curves of the compensated and uncompensated systems. Unit-Ramp Responses of Compensated and Uncompensated Systems 5 Ỗ o compensated system Uncompensatedsystem 0 77 i----rt i i----------------------- 0 1 2 3 4 5 Í Sec It is noted that the closed-loop poles for the compensated system are located as follows 3 3 Because the dominant closed-loop poles are located far from the ja axis the response damps out quickly. 9-3 LAG COMPENSATION In this section we first discuss the Nyquist plot and Bode diagram of the lag compensator. Then we present lag compensation techniques based on the frequency-response approach. Characteristics of lag compensators. Consider a lag compensator having the following transfer function In the complex plane a lag compensator has a zero at 3 - 1 T and a pole at 5 -l T .The pole is located to the right of the zero. Figure 9-13 shows a polar plot of the lag compensator. Figure 9-14 shows a Bode di agram of the compensator where Kc 1 and 10. The corner frequencies of the lag compensator are at co l T and 0 As seen from Figure 9-14 where the val- ues of Kc and ft are set equal to 1