DIFFERENTIAL FLATNESS ACTIVE DISTURBANCE REJECTION CONTROL APPROACH FOR A CLASS OF NONLINEAR UNCERTAIN SYSTEMS

A differential flatness active disturbance rejection control (ADRC) approach is proposed for a type of nonlinear systems with structured periodic and unstructured aperiodic uncertainties. Firstly, the system is proved to be a differential flat system by employing the differential flatness system theory, and its flat output is also pointed out. Following the idea of the ADRC approach, all the unmodelled dynamics, structured periodic and unstructured aperiodic uncertainties in the system are regarded as a total disturbance. The total disturbance, the flat output, and its finite-order time derivatives can all be estimated accurately with the aid of the proposed extended state observer if the observer bandwidth is appropriately selected. A simple linear feedback controller used to cancel the effect of the total disturbance is then designed to make the flat output track the desired output trajectory in the presence of all the uncertainties. The optimal tuning parameters of the control approach are obtained by using the diminishing step fruit fly optimization algorithm to achieve a minimum performance index, which is a weighted summation of the integral time of absolute error and the integration of the control input variable. Finally, the effectiveness and performance superiority over the present results of the proposed approach are validated by the extensive simulations through the examples of the van der Pol oscillator.