This paper proposes a novel method to approximate the ideal internal dynamics state trajectories which coincide with accurate output tracking for known non-minimum phase nonlinear systems. The proposed approach resembles the stable system centre method, but uses a lower order dynamic system than the stable system centre to generate an approximation of the ideal internal dynamics state trajectories. This approximate stable system centre is used to construct a sliding mode based output tracking controller which can achieve improved transient response at the cost of some tracking accuracy in comparison to the use of the stable system centre. The effectiveness of the proposed approach has been demonstrated considering the position control of a two-wheeled robot and has been found to be promising.