Ray, Goshaidas; Dey, Sitansu; Bhattacharyya, T. K. Design of reaching phase for variable structure controller based on Householder transformation. (English) Zbl 1249.93032 Kybernetika 41, No. 5, 601-622 (2005). Summary: The paper presents control signals generation methods, preventing the excitation of residual vibration in slightly damped oscillational systems. It is focused on the feedforward methods, as most of the vibrations in examined processes are induced by the control, while the influence of disturbances is mostly negligible. Application of these methods involves ensuring of the insensitivity to natural frequency change, which can be reached in classical approach only by considerable increase of transient response duration. Genetic algorithms can be effectively applied for the numerical optimization of developed shaper while maintaining the insensitivity to parameter change and short time delay. MSC: 93B12 Variable structure systems 93C42 Fuzzy control/observation systems 93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory 93D15 Stabilization of systems by feedback Keywords:switching function; reachability; Householder transformation; variable structure control; fuzzy logic; interconnected power systems; Lyapunov function × Cite Format Result Cite Review PDF Full Text: EuDML Link References: [1] Chen C. L., Chang M. H.: Optimal design of fuzzy sliding mode control: A comparative study. Fuzzy Sets and Systems 93 (1998), 37-48 [2] Chen C. G., Lin M. H., Hsiao J. M.: Sliding mode controllers design for linear discrete-time systems with matching perturbations. Automatica 36 (2000), 1205-1211 · Zbl 0954.93501 · doi:10.1016/S0005-1098(00)00030-3 [3] DeCarlo R. A., Zak S. H., Matthews G. P.: Variable structure control of nonlinear multivariable systems: A tutorial. Proc. IEEE 76 (1988), 212-232 [4] Edwarda C., Spurgeon S. K.: Sliding Mode Control: Theory and Applications. Taylor and Francis, London 1998 [5] Fosha C. E., Elgerd O. I.: The megawatt-frequency control problem: A new approach via optimal control theory. IEEE Trans. Power Apparatus Systems 89 (1970), 563-577 · doi:10.1109/TPAS.1970.292603 [6] Gutman S.: Uncertain dynamical systems: a Lyapunov min-max approach. IEEE Trans. Automat. Control 24 (1979), 437-443 · Zbl 0416.93076 · doi:10.1109/TAC.1979.1102073 [7] Hung J. Y., Gao, W., Hung J. C.: Variable structure control: a survey. IEEE Trans. Industrial Electronics 40 (1993), 2-22 · doi:10.1109/41.184817 [8] Nobel N., Daniel J. W.: Applied Linear Algebra. Prentice-Hall, Englewood Cliffs, NJ 1988 [9] Slotine J. J. E., Li W.: Applied Non-Linear Control. Prentice-Hall, Englewood Cliffs, NJ 1991 · Zbl 0753.93036 [10] Utkin V. I.: Variable structure systems with sliding modes. IEEE Trans. Automat. Control 22 (1977), 212-222 · Zbl 0382.93036 · doi:10.1109/TAC.1977.1101446 [11] White B. A., Silson P. M.: Reachability in variable structure control systems. Proc. IEE-D (Control Theory and Applications) 131 (1984), 3, 85-91 · Zbl 0541.93004 · doi:10.1049/ip-d.1984.0015 [12] Yoo D. S., Chung M. J.: A variable structure control with simple adaptation laws for upper bounds on the norm of the uncertainties. IEEE Trans. Automat. Control 37 (1992), 860-864 · Zbl 0760.93014 · doi:10.1109/9.256348 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.