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Tham khảo tài liệu 'ogata - modern control engineering part 7', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 1 __ 5 ----- Eo s _ 7 2Ã4 1 _ R4C1 RịCỵ Eịịs R1R3 R2 2S 1 E3C2 1 kJ I 1 _ s y I I y K a ỉ K í 7-J 5 aT where T C aT R2C2 Kc -- Rz 2 Notice that K a _ 4 1 7 2C2 _ 2 4 a _ 2 2 R3C2 R C R RzR C1 This network has a de gain of Kca RiRtHRiRi . From Equation 7-1 we see that this network is a lead network if jRiCi R2C2 or Ct 1. It is a lag network if Al Cl R2C2. The pole-zero configurations of this network when A1C1 R2C2 and A1C1 R2C2 are shown in Figure 7-5 a and b respectively. Lead compensation techniques based on the root-locus approach. The root-locus approach to design is very powerful when the specifications are given in terms of time-domain quantities such as the damping ratio and undamped natural frequency of the desired dominant closed-loop poles maximum overshoot rise time and settling time. Consider a design problem in which the original system either is unstable for all val-ucsofgainorisstablebuthasundesirabletransient-responsecharacteristics.Insucha 410 Chapter 7 Control Systems Design by the Root-Locus Method case the reshaping of the root locus is necessary in the broad neighborhood of the j t axis and the origin in order that the dominant closed-loop poles be at desired locations in the complex plane.This problem may be solved by inserting an appropriate lead compensator in cascade with the feedforward transfer function. The procedures for designing a lead compensator for the system shown in Figure 7-6 by the root-locus method may be stated as follows 1. From the performance specifications determine the desired location for the dominant closed-loop poles. 2. By drawing the root-locus plot ascertain whether or not the gain adjustment alone can yield the desired closed-loop poles. If not calculate the angle deficiency 0. This angle must be contributed by the lead compensator if the new root locus is to pass through the desired locations for the dominant closed-loop poles. 3. Assume the lead compensator Gc s to be 1 Ti 1 s T GJs Ka X K------------- 0 a 1 7 c