Experimental Investigation of Controlling Chaos using Pole Assignment in the Forced BVP Oscillator

Abstract

In previous work⁽¹⁾, we proposed a control method of the chaotic attractor in the non-autonomous systems and stabilized the unstable periodic orbits observed in the Duffing’s equation. Our method can be used as a general technique for controlling chaos, however, the control function was not demonstrated in the laboratory experiments. With this in mind, in this paper, we consider the experimental control of the chaotic behavior in the circuit model, called the forced BVP oscillator. The pole assignment for the corresponding discrete system derived from such a non-autonomous system via Poincaré mapping works effectively, and the control unit is easily realized by the window comparator, sample-hold circuits, and so on. In particular, we try to stabilize the unstable 1 and 3-periodic orbits in the chaotic attractor in the numerical and experimental simulations.