Aj. Markworth et Am. Bloch, USE OF LINEAR FEEDBACK TO CONTROL RELAXATION OSCILLATIONS IN A METAL-PASSIVATION MODEL, Modelling and simulation in materials science and engineering, 4(6), 1996, pp. 641-653
A method of linear feedback is shown to be applicable to the control o
r suppression of spontaneously occurring relaxation oscillations in a
two-dimensional model for the passivation of a metal surface exposed t
o an aqueous medium. For the operating conditions selected, these osci
llations are characterized by a large limit cycle within the state spa
ce of the electrochemical system. A physically plausible control is us
ed, involving feedback of a linear combination of two measurable quant
ities to a controllable parameter. The control acts to stabilize an ot
herwise unstable fixed point without changing its state space coordina
tes. Addition of the control to the system's dynamics also results in
the appearance of two new fixed points, one of which is stable, the ot
her unstable. The control is found to be extremely robust; when applie
d, even when the system is far from a fixed point, stabilization onto
one or the other of the two stable fixed points occurs quickly. Which
of the two it approaches depends upon the state space coordinates of t
he system on the limit cycle at the time the control is initiated. Sta
bilization onto the fixed point of the free system, from any point on
the limit cycle, can be achieved using a combination of free and contr
olled dynamics. Release of the control causes the system to return to
its oscillatory dynamics. Other linear-feedback-based approaches to co
ntrol also are briefly considered, such as feeding back the time deriv
ative of a measurable quantity to a controllable parameter.