Design of an Augmented Automatic Choosing Control by Lyapunov Functions Using Gradient Optimization Automatic Choosing Functions

In this paper we consider a nonlinear feedback control called augmented automatic choosing control (AACC) using the gradient optimization automatic choosing functions for nonlinear systems. Constant terms which arise from sectionwise linearization of a given nonlinear system are treated as coefficients of a stable zero dynamics. Parameters included in the control are suboptimally selected by expanding a stable region in the sense of Lyapunov 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.

Authors:

• Toshinori Nawata

Keywords:

• augmented automatic choosing control
• nonlinear control
• genetic algorithm
• zero dynamics.

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, pp.55-62, 1970.
[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] K.Glover and J.C.Doyle, "State-Space Formula for All Stabilizing Controllers
that Satisfy and H∞-norm Bound and Relations to Risk Sensitivity",
System & Letters, Vol.11-2, pp.167-172, 1988.
[5] A.Isidori, "Nonlinear Control Systems : An Introduction (2nd edition)",
Springer-Verlag, 1989.
[6] H.Takata, "Automatic Choosing Control Design via GA for Nonlinear
Systems", Proc.38th IEEE CDC, pp.5301-5306, 1999.
[7] 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, pp.191-196, 2003.
[8] T.Nawata, "Computer Simulations of an Augmented Automatic Choosing
Control Using Automatic Choosing Functions of Gradient Optimization
Type", Proc. WASET, Issue 71, pp.578-583, 2010.
[9] D. E. Goldberg, "Genetic Algorithms in Search, Optimization, and
Machine Learnings", Addison-Wesley Pub. Co. Inc., 1989.