Adaptive anti-control of chaos of permanent magnet DC motor system

In this paper, an adaptive feedback control method is proposed for the anti-control of chaos of linear controllable systems with unknown parameters based on model matching. First, an anti-control method is designed for the known linear systems. Then, the parameters of the linear controllable system in canonical form are assumed to be unknown. The chaotification is achieved choosing an appropriate control law and a parametric updating law using adaptive control theory. The stability of the resulting error dynamics and the convergence of the tracking errors to zero are proved by Lyapunov stability theory, which guarantees that the unknown linear system tracks the reference chaotic system asymptotically. The methods are applied to anti-control of chaos of the permanent magnet DC motor system to generate chaotic motion for vibratory compactors, while the Rössler chaotic system is considered as the reference model. The numerical simulation results show the effectiveness of the proposed method.