A Composite Controller Design Method For Non-minimum Phase Nonlinear Systems

Where the non-minimum phase nonlinear systems differ from general nonlinear systems is the existence of unstable zero dynamics, it is a hot topic in the research on this kind of system in recent years, especially for the processing of unstable zero dynamics. Because this kind of system is common in the engineering practice, in-depth study and analysis of this kind of system is of important value and profound significance.In this paper, considering the characteristic of non-minimum phase nonlinear systems, a composite control scheme is proposed based on feedback linearization. First of all, the system is transformed into a regular standard form by using feedback linearization method, through selecting the appropriate control law, we can obtain the chain structure of the nonlinear system, and at the same time the internal subsystem(zero dynamic subsystem) and the external subsystem are also acquired. After that, a quadratic optimal controller and a high gain feedback controller are designed respectively for the unstable zero dynamic subsystem and the external subsystem. And the optimal signals produced by the optimal controller are treated as the reference signals of the external subsystem. Sequentially, the composite control of the whole system was realized. The time scales separation caused by the introduction of high gain feedback control changes the system into singular perturbation form which contains the fast states and slow states. Therefore, we can use the singular perturbation theory to analyze the stability of the system. The main content of this paper are as follows:Firstly, using the proposed composite control scheme to realize the stabilization and tracking control of a SISO nonlinear non-minimum phase system. The simulation results of a car inverted pendulum verified the effectiveness of this composite control scheme.Secondly, the proposed composite control method expanded to MIMO non-minimum phase nonlinear systems, and realized the stabilization and tracking control of the MIMO non-minimum phase nonlinear system. The simulation results of a two input two output aircraft model showed the effectiveness and good anti-jamming capability of the composite control scheme.