This article presents a new method that employs the active disturbance rejection control (ADRC) paradigm to handle the control problem for a class of nonlinear systems with unknown disturbances and measurement noise. An improved extended state observer (ESO) is devised to separate disturbance estimation from state reconstruction and a new parameter is used to adjust disturbance-rejection performance independently. This increases the flexibility of system design and makes the gain of the improved ESO (IESO) small compared to that of a conventional ESO in the ADRC. A low-pass filter is added to the IESO. This changes the slope of the magnitude curve of the Bode diagram from $-20$ dB/dec to $-40$ dB/dec at high frequencies for measurement noise, which improves the noise-suppression performance. Comparison with a conventional ESO reveals the superiority of the IESO in disturbance rejection and noise suppression. The presented method is validated by simulation and experimental results.

This paper presents an improved equivalent-input-disturbance (EID) approach to deal with exogenous disturbances and system nonlinearities. The disturbances and nonlinearities are regarded as a lumped disturbance on the control input channel. The EID approach, which has a state observer and an EID estimator, is used to estimate the lumped disturbance. There is a constraint between the observer and the estimator on the design of the control system for the conventional EID approach. A stable ze-ro was added to the estimator to remove the constraint and to improve the stability of the system in this study. This ensures that the observer and the estimator can be designed independently. An analysis of the improved EID approach explains the mechanism of disturbance rejection. The simulation and experimental results of position control of a ball-and-beam system demonstrate the validity of the method.

This article presents an improved equivalent-input-disturbance (EID) approach to handle unknown disturbances and plant uncertainties. The disturbances and uncertainties are treated as a lumped disturbance in an EID-based control system. The effect of the lumped disturbance is compensated by an EID estimator. A constraint between design parameters and uncertainties is imposed on the design of the estimator. In addition, there are insufficient analyses of the influence of uncertainties on the control performance and the stability of the system. A new filter is devised for an improved EID estimator in this article to remove the constraint. This ensures that the sensitivity of the system to disturbances at low frequencies can be freely decreased. An analysis of the system reveals that uncertainties not only influence disturbance-rejection and reference-tracking performance but also affect system stability. A sufficient stability criterion is derived with consideration of uncertainties. The validity of the presented method is demonstrated by simulation and experimental results.

This paper addresses the control problem of an open-loop unstable linear time-invariant system with an input delay and an unknown disturbance. An observer-predictor-based control method is presented for such a system in which only output information is available. First, the system state is reconstructed and the disturbance is estimated using the equivalent-input-disturbance approach. Next, the future information on the state and the disturbance is predicted to reduce the effect of the input delay. Then, a new predictive control scheme is developed. The closed-loop system is simplified into two subsystems for analysis. Stability conditions are derived for each subsystem separately. Finally, a comparison with previous approaches through simulations shows the superiority of the presented method over others for disturbance rejection.

Disturbance rejection for industrial control systems with nonlinearities is a challenge. In this article, a disturbance-rejection control paradigm has been proposed to handle disturbances and nonlinearities by simply treating them as a total disturbance. However, this simplification has performance limitations as the characteristics of disturbances and nonlinearities are usually different. To this end, an extra degree of freedom is devised in this study to separate the estimation of an unknown disturbance and a system nonlinearity based on the equivalent-input-disturbance (EID) approach. Two scenarios, i.e., the nonlinearity with and without a known mathematical model, are considered. The information on the nonlinearity (for the scenario with the known model) or an extended state (for the scenario without the known model) is employed to design an observer and an EID estimator. The estimate of the nonlinearity is calculated using the mathematical model or the extended state, while the estimate of the disturbance is obtained from the EID estimator. An inner loop is then constructed to counteract the effect of them by using the estimates. A composite control law is devised to improve control performance by using feedforward control, feedback control, and inner-loop compensation. Stability criteria are derived using the small-gain theorem. The bounds of the errors in estimating the nonlinearity and the disturbance are analyzed. The simulation and experimental results demonstrate the validity of the method.

Rotate vector (RV) reducers have widely been used in high-performance precision drives for industrial robots. However, the current nonlinear dynamic studies on RV reducers are not extensive and require a deeper focus. To bridge this gap, a translational–torsional nonlinear dynamic model for an RV reducer transmission system is proposed. The gear backlash, time-varying mesh stiffness, and comprehensive meshing errors are taken into account in the model. The dimensionless vibration differential equations of the system were derived and solved numerically. By means of bifurcation diagrams, phase trajectories, Poincaré sections, and the power spectrum, the motion state of the system was studied with the bifurcation parameters’ variation, including excitation frequency and meshing damping. The results demonstrate that this system presents enriched nonlinear dynamic characteristics under different parameter combinations. The motion state of the system is more susceptible to change at lower frequencies. Increasing the meshing damping coefficient proves effective in suppressing the occurrence of chaos and reducing vibration amplitudes, significantly enhancing the stability of the transmission system.