Transient tracking performance improvement for nonlinear nonminimum phase systems: an additive-state-decomposition-based control method

To study the problem of improving transient tracking performance for nonlinear systems, this paper proposes an additive-state-decomposition-based control method for a class of nonlinear nonminimum phase (NMP) systems. This method ‘additively’ decomposes the original problem into two more tractable problems, namely a tracking problem for a linear time-invariant NMP ‘primary’ system and a state stabilisation problem for a certain nonlinear ‘secondary’ system. Then, controller for each system is designed respectively by employing existing methods, i.e. the linear quadratic regulator (LQR) method for the primary system and the backstepping method for the secondary system. Next, these two controllers are combined together to achieve the original tracking goal. Furthermore, the adjustment of weighting matrix Q in the LQR regulates the transient response of the closed-loop nonlinear system. Finally, two illustrative examples are provided to demonstrate the effectiveness of the proposed method.