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IEEE TRANSACTIONS ON AUTOMATIC CONTROL, VOL. 43, NO. 12, DECEMBER 1998 1745 "hysteresis," caused by the subcritical bifurcation. The bifurcation
 

Summary: IEEE TRANSACTIONS ON AUTOMATIC CONTROL, VOL. 43, NO. 12, DECEMBER 1998 1745
"hysteresis," caused by the subcritical bifurcation. The bifurcation
diagrams for the backstepping controller (57) are shown in Fig. 4 for
c0 = 6 and 2
k = 0:5. This controller "softens" the bifurcation from
subcritical to supercritical and eliminates the hysteresis. In addition,
it stabilizes all stall equilibria and prevents surge for all values of 0.
While all three designs in Table I soften the bifurcation, the
global design achieved with backstepping is due to a methodological
difference. The bifurcation designs in [14] and [7] are based on
local stability properties established by the center manifold theorem
because the maximum of the compressor characteristic is a bifurcation
point that is not linearly controllable. Hence stabilization is inherently
nonlinear and results in asymptotic but not exponential stability.
Our Lyapunov-based design incorporates the good features of a
bifurcation-based design. For 80 = 1, the term Vr(r) in the Lyapunov
function (49), becomes Vr(R) = R, so that the Lyapunov function
V2 = c0
2
c1 + 3

  

Source: Amir, Yair - Department of Computer Science, Johns Hopkins University

 

Collections: Computer Technologies and Information Sciences