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Design Methods
Published in William S. Levine, Control System Fundamentals, 2019
Jiann-Shiou Yang, William S. Levine, Richard C. Dorf, Robert H. Bishop, John J. D’Azzo, Constantine H. Houpis, Åström Karl J., Tore Hägglund, Katsuhiko Ogata, Richard D. Braatz, Z.J. Palmor
Example 10.12 demonstrates that, on one hand, the SP provides significant improvements in tracking properties over conventional controllers, but on the other hand its potential enhancements in regulatory capabilities are not as apparent. The reason for this has been pointed out in Section 10.8.3a, where it was shown that the open-loop poles are present in the transfer function Gd. These poles are excited by input disturbances but not by the reference. Depending on their locations relative to the closed-loop poles, these poles may dominate the response. The slower the open-loop poles are, the more sluggish the response to input disturbances will be. This is exactly the situation in Example 10.12: the closed-loop pole (the zero of 1 + CoPo) is s = −6, while the two open-loop poles are located at s = −1. The presence of the open-loop poles in Gd is a direct consequence of the structure of the SP, and many modifications aimed at improving that shortcoming of the SP were proposed. Several modifications are presented in Section 10.9. It is worthwhile noting, however, that the influence of the open-loop poles on the response to disturbances is less pronounced in cases with large DTs. In such a circumstance, the closed-loop poles cannot usually be shifted much to the left, mainly due to the effect of model uncertainties. Hence, in such situations the closed-loop poles do not differ significantly from the open-loop ones, and their influence on the response to disturbances is less prominent.
Introduction to Feedback Control Systems
Published in Ramin S. Esfandiari, Bei Lu, Modeling and Analysis of Dynamic Systems, 2018
As discussed in Section 10.2, the performance of a controlled system is associated with the closed-loop poles. If a feedback gain matrix K is determined based on desired pole locations, then the closed-loop system with the feedback control law u = −Kx will achieve the desired performance. This is the basic idea of pole placement. Assume that the desired locations of the closed-loop poles are s1, s2, …, and sn. Note that poles of a system are the roots of the characteristic equation of the system. Thus, the desired characteristic equation is () (s−s1)(s−s2)…(s−sn)=0
Design Methods
Published in William S. Levine, The Control Handbook: Control System Fundamentals, 2017
Jiann-Shiou Yang, William S. Levine, Richard C. Dorf, Robert H. Bishop, John J. D’Azzo, Constantine H. Houpis, Karl J. Åström, Tore Hägglund, Katsuhiko Ogata, Masako Kishida, Richard D. Braatz, Z. J. Palmor, Mario E. Salgado, Graham C. Goodwin
Example 9.14 demonstrates that, on the one hand, the SP provides significant improvements in tracking properties over conventional controllers, but on the other hand, its potential enhancements in regulatory capabilities are not as apparent. The reason for this has been pointed out in Section 9.8.3.1, where it was shown that the open-loop poles are present in the transfer function Gd. These poles are excited by input disturbances but not by the reference. Depending on their locations relative to the closed-loop poles, these poles may dominate the response. The slower the open-loop poles, the more sluggish the response to input disturbances. This is exactly the situation in Example 9.14: the closed-loop pole (the zero of 1 + C0P0)is s = −6, while the two open-loop poles are located at s = -1. The presence of the open-loop poles in Gd is a direct consequence of the structure of the SP, and many modifications aimed at improving that shortcoming of the SP were proposed. Several modifications are presented in Section 9.8.4. It is worth noting, however, that the influence of the open-loop poles on the response to disturbances is less pronounced in cases with large DTs. In such a circumstance, the closed-loop poles cannot usually be shifted much to the left, mainly due to the effect of model uncertainties. Hence, in such situations the closed-loop poles do not differ significantly from the open-loop ones, and their influence on the response to disturbances is less prominent.
Control of time-delay systems through modified Smith predictor using sliding mode controller
Published in International Journal of Systems Science, 2023
P. Princes Sindhuja, V. Vijayan, Rames C. Panda
The research progress and advancements made in SP and SMC are summarised in chronological order from 1951 to 2022 for a better understanding (of the state of the art) of the readers in this section. Smith, in 1957, proposed the ‘Smith predictor’ structure for compensating the dead time of processes (Smith, 1959). However, the structure was not applicable for integrating systems as it resulted in constant offset in IPDT processes subjected to load disturbance. Furthermore, in SP, the closed loop poles were derived from the open loop ones, which render stability of the overall system depending on the properties of the open loop poles. Chien and Fruehauf (1990) proposed an IMC-based PID design for integrating processes. Luyben (1996, 2000) suggested regular methods for identifying parameters of IPDT systems where a PI controller was used to validate the +2DB maximum closed-loop log modulus criteria. However, the performance of larger values from equation (1) needs improvement by compensating for the dead time. Though the SP provides a better response compared to the conventional PI for set point tracking, its performance deteriorated for disturbance rejection of IPDT systems with large values. Hence there is a need for the modification of the SP structure rather than the controller parameters.
Damping of Inter-Area Oscillations Using TCPS Based Delay Compensated Robust WADC
Published in Electric Power Components and Systems, 2023
Abhineet Prakash, Kundan Kumar, S. K. Parida
In order to guarantee a minimum damping ratio of ζ for the closed-loop poles, a well-known D-stability criteria is used in this article, in addition to the requirement D-stability involves moving relevant modes to left-half complex plane in D-space sub-region. To avoid asymptotic instability, a conic section with angle θ is defined, where (see Figure 5). This significantly reduces the settling time of closed-loop poles. Considering this, the objective function can be further modified to find the feedback controller K that satisfies