Performance analysis of 2‐DOF tracking control for a class of nonlinear uncertain systems with discontinuous disturbances

Abstract

Summary In this paper, the tracking control problem is considered for a class of uncertain nonlinear systems with infinite discontinuous points in the external disturbance. The extended state observer–based 2‐degree‐of‐freedom control is used with one degree to estimate and cancel the “total disturbance” and the other to force the closed‐loop system to have desired characteristics. The tracking error between the state vector and its ideal trajectory in the entire transient process is adequately discussed to illuminate the performance of resulting control systems. The quantitative analysis shows that the tracking error can be small enough by tuning the bandwidth of the extended state observer. Moreover, the necessary and sufficient condition for the tracking error and the estimation error of the “total disturbance” to converge to zero is presented. The simulation results of a motion test demonstrate that the desired performance of the control system can be achieved despite discontinuous disturbance and nonlinear uncertainties.

On active disturbance rejection control for nonlinear systems with multiple uncertainties and nonlinear measurement

“…By comparing the integrator chain form (8) with the nominal one (22), the total disturbance is revealed as follows:…”

A novel event‐triggered extended state observer for networked control systems subjected to external disturbances

“…Among the varieties of control methods coping with nonlinearity and disturbances, the active disturbance rejection control (ADRC) method has been well recognized to be very effective, which uses a composite control involving of a feedforward term and a feedback term . In the context of ADRC, the extended state observer (ESO) is critical which could estimate the aggregated effect of nonlinearity and disturbances only by system outputs and inputs . A literature survey shows that the ESO scheme has been implemented in almost all domains of control systems, such as spacecraft formation, tank gun, and magnetic rodless cylinders .…”

“…24,25 In the context of ADRC, the extended state observer (ESO) is critical which could estimate the aggregated effect of nonlinearity and disturbances only by system outputs and inputs. 26,27 A literature survey shows that the ESO scheme has been implemented in almost all domains of control systems, such as spacecraft formation, 28 tank gun, 29 and magnetic rodless cylinders. 30 In particular, in the work of Xia et al, 31 the ESO has been used to estimate the system uncertainties and states of the missile systems.…”

Sustained oscillations in MIMO nonlinear systems through limit cycle shaping

“…Motivated by this, a variety of approaches have been developed in the literature to achieve stable outputs with periodic behaviors . Most of the existing approaches are based on restating the dynamic equations of system in terms of tracking error and solving the stabilizing problem for the error dynamic system .…”

“…Motivated by this, a variety of approaches have been developed in the literature to achieve stable outputs with periodic behaviors. [8][9][10][11] Most of the existing approaches are based on restating the dynamic equations of system in terms of tracking error and solving the stabilizing problem for the error dynamic system. 12 Another solution for creating sustained oscillations in system's outputs is based on choosing a proper limit cycle according to the desired periodic response of the system's output (ie, its shape, amplitude, and frequency).…”