Robust output tracking control of a class of non-minimum phase systems and application to VTOL aircraft

Abstract

In this article, we study the output tracking control of a class of MIMO nonlinear non-minimum phase systems in the presence of input disturbances. In order to attenuate the effects of disturbances, the method of uncertainty and disturbance estimator (UDE) is extended to the controller design for non-minimum phase systems. Due to the fact that the accumulated disturbances is composed of internal states and external disturbances, a different stability analysis is given, and the overall closed-loop system is proved to be semi-globally stable. The proposed state-feedback controller not only forces system outputs to asymptotically track desired trajectories, but also drives the unstable internal dynamics to follow bounded and causal ideal internal dynamics (IID) solved via stable system centre (SSC) method. Simulation results demonstrate that the proposed controller achieves excellent tracking and disturbance rejection performance via the example of VTOL aircraft which has been the benchmark of nonlinear non-minimum phase systems.

Keywords:

• robust control
• output tracking
• nonlinear system
• non-minimum phase
• VTOL aircraft

Acknowledgements

This work was supported by NSF of China under Grant 60874044 and Research Foundation for Key Disciplines of Beijing Municipal Commission of Education under Grant XK100060422.

Notes

Notes

1. Here, L _g and L _f are Lie derivative operators. denotes the k-th order Lie derivative of h _i (x) with respect to f, i.e. and

2. We use to denote the j-th time derivative of a variable y.

3. Matlab simulation codes can be obtained by Email: [email protected].