Tham khảo tài liệu 'ogata - modern control engineering part 4', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Consequently the amplitude four cycles later becomes ----------------------------------------x 4T x 0 e fr 4r x 0 e- 10 4 ------------------------------------ X m A-4-13. Consider a system whose closed-loop poles and closed-loop zero are located in the 5 plane on a line parallel to the jd axis as shown in Figure 4- 47. Show that the impulse response of such a sys--------------tern is a damped cosine X jo jod -Ơ 0 a Y -jod Figure 4-47 Closed-loop pole-zero configuration A of system whose impulse response is a damped cosine function. Solution. The closed-loop transfer function is C s __K s Ơ Jỉ s 0 Ơ ja d s ơ- ja d For a unit-impulse input R s 1 and K s 5 Ơ 2 O2d The inverse Laplace transform of C s is c i Ke at cos O dt for Í a 0 which is a damped cosine function. the liquid-level control system shown in Figure 4-48. The controller is of the propor-tional type. The set point of the controller is fixed. Draw a block diagram of the system assuming that changes in the variables are small. Obtain the transfer function between the level of the second tank and the disturbance input qd- Obtain the steady-state error when the disturbance qd is a unit-step function. Solution. Figure 4-49 a is a block diagram of this system when changes in the variables are small. Since the set point of the controller is fixed r 0. Note that r is the change in set point. To investigate the response of the level of the second tank subjected to a unit-step disturbance qd we find it convenient to modify the block diagram of Figure 4-49 a to the one shown in Figure 4-49 b . The transfer function between ỉhís and Qd s can be obtained as 200 Chapter 4 Transient-Response Analysis Proportional controller system. c2 b a Figure 4-49 a Block diagram of the system shown in Figure 4-48 b modified block diagram. H2 s _ Ổdơ R s 1 7 2C2s 1
