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Root Locus Method
Published in Bogdan M. Wilamowski, J. David Irwin, Control and Mechatronics, 2018
Robert J. Veillette, J. Alexis De Abreu Garcia
Root locus analysis was first developed by Evans (1948) as a means of determining the set of positions (loci) of the poles of a closed-loop system transfer function as a scalar parameter of the system varies over the interval from –∞ to ∞. It constitutes a powerful tool in the design of a compensator for a feedback control system. The compensator poles and zeros are chosen to shape the branches of the root locus; then the compensator gain is chosen to place the closed-loop poles at the desired positions along the branches. By displaying the closed-loop poles, the root locus analysis complements the frequency-domain methods, which provide information on the magnitude and phase of the system frequency response. It is especially useful for systems that are unstable or marginally stable in open loop since the frequency-domain methods are more cumbersome for such systems.
Control Systems
Published in Keith L. Richards, Design Engineer's Sourcebook, 2017
This section is an introduction to the concept of root locus plots. Root locus analysis is a graphical method for examining how the roots of a system change with variation of a certain system parameter, commonly a gain within a feedback system. This section applies to a standard second-order system.
Control Theory Review
Published in Wayne Anderson, Controlling Electrohydraulic Systems, 2020
With more complex systems, it becomes difficult to directly calculate the closed-loop poles and zeros. The root-locus analysis lets us use a graphical technique to solve for the closed-loop poles and zeros with the open-loop variables of gain, poles, and zeros. The general closed-loop transfer function is
A novel fractional order proportional integral derivative plus second-order derivative controller for load frequency control
Published in International Journal of Sustainable Energy, 2021
Bhuvnesh Khokhar, Surender Dahiya, K. P. Singh Parmar
Growing complexity of power systems demand a fast and accurate tuning of the controller parameters for an improved LFC response. As a consequence, various metaheuristic optimisation algorithms have been proposed in the literature for the tuning process. Some of these include artificial bee colony (ABC) algorithm (Gozde, Taplamacioglu, and Kocaarslan 2012), grey wolf optimisation (GWO) algorithm (Guha, Roy, and Banerjee 2015), flower pollination algorithm (FPA) (Madasu, Kumar, and Singh 2016), differential evolution (DE) algorithm (Sahu, Panda, and Rout 2013) and multi-verse optimisation (MVO) algorithm (Guha, Roy, and Banerjee 2017). The advantage of these optimisation algorithms is that they are derivative free and independent of model of the plant. As per the ‘no-free-lunch’ (NFL) theorem, no optimisation algorithm is suitable for solving all the optimisation problems and scope of improvement always persists (Wolpert 1997). In this regard, a recently developed WWO algorithm (Jun Zheng 2015) has been implemented in this paper for the optimisation of various parameters of the proposed FOPID+DD controller. The powerful WWO algorithm takes inspiration from the shallow water wave theory based on propagation, refraction and breaking phenomena of water waves. The algorithm is very easy to implement and has been successfully implemented by researchers for solving various engineering optimisation problems (Wu, Liao, and Wang 2015; Zhao et al. 2018). To the best of the authors' knowledge, any LFC study implementing the WWO algorithm is unexampled in the literature. With reference to the above discussion, the salient features of this paper are presented below: A novel FOPID+DD controller is proposed for the LFC analysis of an hPS.A newly developed and powerful WWO algorithm is implemented for the first time to optimise the parameters of the proposed LFC controller.Potency of the proposed controller is established over the other controllers namely CC-TID (Guha and Roy 2018), I-TD (Kumari and Shankar 2018), FOPID, PID+DD (Raju, Saikia, and Sinha 2016) and PID that are well studied in the literature.Performance of the proposed controller is validated considering multiple disturbances and non-linearities (GRC, GDB and time delay (TD)) related with the hPS.Sensitivity analysis of the proposed controller is performed and justified considering ± 30% and ± 50% variations in the hPS parameters.Root locus analysis is performed in order to establish the operational stability of the proposed control scheme.