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A Heuristic Approach for Modelling and Control of an Automatic Voltage Regulator (AVR)
Published in Suman Lata Tripathi, Parvej Ahmad Alvi, Umashankar Subramaniam, Electrical and Electronic Devices, Circuits and Materials, 2021
Rishabh Singhal, Abhimanyu Kumar, Souvik Ganguli
From Table 9.3 results, it is found that our method and the other heuristic methods used for comparison have either a very high value or infinite gain margin. This justifies the fact that the reduced models produced are all inherently stable and are quite different from the gain margin of the original test system considered in this chapter. The phase margin of the proposed approach is in close proximity to that of the original model. The results produced by DA and SSA methods are only near the actual value. Thus, it can be concluded that the suggested technique shows close resemblance with the original system in terms of frequency domain measures. Further, the pole–zero locations of the original test system and the proposed model are reported in Table 9.4. The pole–zero locations implicate two salient points: whether the systems have right-half s-plane zeros and poles. Right-half poles indicate the unstable nature of the system while right-half plane zeros imply a non-minimum phase. These two properties are verified through the outcomes reflected in Table 9.4. In addition to this, the closest pole and zero locations in comparison to the original model are also being identified.
Root Locus Method
Published in Bogdan M. Wilamowski, J. David Irwin, Control and Mechatronics, 2018
Robert J. Veillette, J. Alexis De Abreu Garcia
Adding left half-plane zeros to a system has a desirable effect on the root locus. Systems with low relative degree (i.e., n – m ≤ 1) can be stable for all values of the feedback gain. Even a system with some open-loop poles in the right half-plane can be stabilized using feedback if there are some zeros in the left half-plane. On the other hand, a zero that has a stabilizing effect on the system may cause a deterioration of the low-frequency performance of the system. Such an undesirable effect can be discerned by the use of frequency-domain analysis techniques.
The s-plane and transient response
Published in C.C. Bissell, Control Engineering, 2017
We now have a most important stability criterion, expressed in terms of the s- plane: for a system to be stable all its poles must lie in the left half plane. Even just one right half-plane pole means instability, since the growing exponential term associated with it will eventually dominate the system response. (Poles on the jw axis itself correspond to systems on the stability borderline: the corresponding time waveforms neither die away nor increase indefinitely with time.)
Evolution dynamics of fractal aggregates in continuously stirred tank aerosol reactors using generalized condensation exponents
Published in Aerosol Science and Technology, 2020
Jayant Krishan, S. Anand, Y. S. Mayya, Jyoti R. Seth
To illustrate the application of stability analysis for a fractal system, a linear stability analysis is performed for a typical case of ν = 4/5 (Figure 3). From this stability curve, it is evident that the eigenvalues approach the origin of the complex plane as the residence time () increases. This is observed in Figure 1; the oscillations of number density vanish as the residence time increases. Initially, the system is in an unstable state and tends toward the stable steady-state asymptotically as the eigenvalues approach origin of the complex plane. The present case () is different from the case of (Pratsinis, Friedlander, and Pearlstein 1986) as there is no crossover of the eigenvalues from Left Half Plane (LHP) to Right Half Plane (RHP) and it directly moves toward origin of the complex plane.
Adaptive distributed BLS-FONTSM formation control for uncertain networking heterogeneous omnidirectional mobile multirobots
Published in Journal of the Chinese Institute of Engineers, 2020
Ching-Chih Tsai, Chien-Cheng Yu, Chung-Wei Wu
Now, consider the overall multirobot team with n follower HOMRs and one physical or virtual leader HOMR, which is regarded as the (n + 1)-th HOMR. Figure 2 illustrates a directed graph of the multi-HOMR system that has the four follower HOMRs and one virtual leader as the fifth robot. Hence, the overall multi-HOMR team is indeed formulated as a directed graph , which is assumed connected and having a spanning tree with its root being the leader. As mentioned previously, the overall digraph has its Laplacian matrix in which . Let another matrix be a nonzero diagonal matrix that has at least one positive entry, meaning that at least one following robot can access the leader’s velocity and position. It is worth mentioning that under the previous assumptions, the matrix can be shown invertible, and all of its eigenvalues lie within the right-half plane of the complex plane.
Published in International Journal of Control, 2018
Kui Zou, Xingyu Gou, Yanwei Ding
In this paper, attention is restricted to the derivation of performance limitations for linear time-invariant (LTI) discrete-time systems in the presence of stochastic disturbance. Performance limitations resulting from plant non-minimum phase zeros and unstable poles have been known for a long time. For example, for a minimum phase plant with stationary random disturbance acted on the plant output, it is possible to reduce the variance of the output lower than any desired value by optimal Wiener-Hopf controller if the sensors and actuators are perfect (Youla, Bongiorno, & Jabr, 1976). However, for a non-minimum phase plant with perfect sensor and actuator, the output variance still suffers a nonzero infimum. The limitation can be characterised completely by the number and locations of the right half plane zeros of the complex plane (Foghahaayee, Menhaj, & Talebi, 2015; Qiu & Davison, 1993; Salgado & Silva, 2006). It is clear that non-minimum phase zeros, unstable poles and time delays of an open-loop plant impose fundamental constraints on achievable performance and control bandwidth, and such constraints make control system design difficult (Middleton, 1991). If the control effort is invalid at very high frequency and leads to the constraint on system bandwidth, limitation of output variance is a decreasing function of it (Davison, Kabamba, & Meerkov, 1999). Other results on limitations of disturbance rejection can be found in Goodwin, Salgado, and Yuz (2003) for the case of single-input single-output (SISO) against unit step output disturbance in the presence of plant uncertainty, and in Bakhtiar and Hara (2008) for the case of single-input multi-output (SIMO) against impulse input disturbance. Recent works on fundamental limitations of disturbance attenuation using information theory can be found in Li and Hovakimyan (2013), Martins, Dahleh, and Doyle (2008), Martins and Dahleh (2008), et al.