An Augmented Automatic Choosing Control Designed by Extremizing a Combination of Hamiltonian and Lyapunov Functions for Nonlinear Systems with Constrained Input

Authors: Toshinori Nawata, Hitoshi Takata

Abstract:

In this paper we consider a nonlinear feedback control called augmented automatic choosing control (AACC) for nonlinear systems with constrained input. Constant terms which arise from section wise linearization of a given nonlinear system are treated as coefficients of a stable zero dynamics.Parameters included in the control are suboptimally selectedby extremizing a combination of Hamiltonian and Lyapunov functions with the aid of the genetic algorithm. This approach is applied to a field excitation control problem of power system to demonstrate the splendidness of the AACC. Simulation results show that the new controller can improve performance remarkably well.

Keywords: Augmented Automatic Choosing Control, NonlinearControl, Genetic Algorithm, Hamiltonian, Lyapunovfunction

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1085557

References:

[1] Y. N. Yu, K. Vongsuriya and L. N. Wedman, Application of an Optimal Control Theory to a Power System, IEEE Trans. Power Apparatus and Systems, 89(1), 1970, 55-62.
[2] A. P. Sage and C. C. White III, Optimum Systems Control (2nd edition) (Prentice-Hall, Inc., 1977).
[3] M. Vidyasagar, Nonlinear Systems Analysis (Prentice-Hall, Inc., 1978).
[4] A.Isidori, Nonlinear Control Systems : An Introduction (2nd edition) (Springer-Verlag, 1989).
[5] Y.Takagi and T.Shigemasa, An Application of State-Space Linearization to a Power System Stabilizer, Proc. 29th CDC, TA8-1, 1990, 1553-1558.
[6] H.Takata, An Automatic Choosing Control for Nonlinear Systems, Proc. 35th CDC, FA10-5, 1996, 3453-3458.
[7] Z.Xi, G.Feng, D.Cheng and Q.Lu, Nonlinear Dicentralized Saturated Controller Design for Power Systems, IEEE Trans. on Control Systems Technology, 11(4), 2003, 539-547.
[8] T.Nawata and H.Takata, An Augmented Automatic Choosing Control Using Zero Dynamics for Nonlinear Systems and Its Application to a Power System, Proc. 22nd IASTED MIC, 2003, 191-196.
[9] D. E. Goldberg, Genetic Algorithms in Search, Optimization, and Machine Learnings (Addison-Wesley Pub. Co. Inc., 1989).