Problems of Extended State Observer and Proposal of Compensation Function Observer for Unknown Model and Application in UAV

The extended state observer (ESO) used to estimate the unknown model for nonlinear systems has been widely applied in model-free control. In the ESO, three factors: 1) nonderivative structure; 2) insufficient usage of innovation; and 3) no compensation of the unknown character of a nonlinear function, causing low type and low accuracy of observation are identified. The convergence problem of the ESO is also raised. A simple linear compensation function observer (CFO) is proposed. The CFO adopts the derivative form overcoming the structure problem of the ESO, fully uses the available innovation, and then introduces a compensator to replace the unknown function. The filtering compensator counteracts the effect of the time-varying nonlinear unknown model to make the error equation behave with desired poles. The convergence of the CFO is theoretically proved. The CFO is the Type-III system, whereas the ESO is a Type-I system; therefore, the CFO has a qualitative leap over the ESO in accuracy improvement of observation. The CFO can observe nonlinear functions, including lumped disturbances, uncertainties, and unmodeled parts for nonlinear systems. The CFO decouples the multi-input and multioutput (MIMO) systems. Five unknown typical nonlinear functions are tested and demonstrates that the CFO qualitatively prevails over the ESO. The MIMO chaotic attitude system of a small-scale unmanned aerial vehicle (UAV) helicopter is conducted with results that CFO performance of function observation is highly improved over that of ESO about 29 times.