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Advances in PID Control Part 3

Tham khảo tài liệu 'advances in pid control part 3', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 30 Advances in PID Control Fig. 2. Block diagram of the augmented system where GASPR s G s GPFC s A s Gaspr s -1 AGp s 46 AGp s Gp s - Gp s A s represents an uncertain part of the augmented system. The following lemma concerns the ASPR-ness of the resulting augmented system 45 Mizumoto Iwai 1996 . Lemma 1. The augmented system 45 is ASPR if 1 Gaspr s isASPR. 2 A s e RH . 3 A s H 1. Where IIA s denote the H norm of A s which is defined as IIA s supseC A s . Remark 3 Theoretically one can select any ASPR model as GASPR s . However performance of the control system may be influenced by the given ASPR model. For example if the time constant of the given GASPR s is small one can attain fast tracking of the augmented system with small input. However since the resulting PFC might have a large gain the tracking of the practical output y t has delay. One the centrally if the time constant of GASPR s is large one can attain quick tracking for the practical output y t . However large control input will be required Minami et al. 2010 . The overall block diagram of the augmented system for the system with an internal model filter Gim s can be shown as in Fig. 2. Thus introducing an internal model filter the PFC must be designed for a system Gim s Gp s . Unfortunately in the case where Gim s is not stable the PFC design conditions given in Theorem 1 are not satisfied even if the controlled system Gp s is originally stable. For such cases the PFC can be designed according to the following procedure. Step 1 Introduce a PFC as shown in Figure 3. Step 2 Consider designing a PFC Gpfc z so as to render the augmented system Gc s Gp s Gpfc s for the controlled system Gp z ASPR. Adaptive PID Control System Design Based on ASPR Property of Systems 31 Fig. 3. Block diagram of a modified augmented system ---------------G s ------------------- PFC Fig. 4. Equivalent augmented system Step 3 Design the desired ASPR model so that the obtained PFC Gpfc s has Dim s as a part of the numerator. .