USE OF LINEAR FEEDBACK TO CONTROL RELAXATION OSCILLATIONS IN A METAL-PASSIVATION MODEL

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.