This article develops an improved equivalent-input-disturbance (EID) approach that rejects disturbances for a plant. A control system based on the approach includes an improved EID estimator, which is newly devised using a $\lbrace 1\rbrace$ inverse of the plant input matrix. Compared with a conventional EID estimator, the improved EID estimator has an additional free matrix. This free matrix enables the control system to improve the disturbance rejection performance but not increase the configuration complexity. An analysis of the control system explains how the free matrix improves the disturbance rejection performance. The experiments of a posture control system for a Stewart platform demonstrate the validity of the approach.

This article presents a nonlinear-state-observer-based equivalent-input-disturbance approach that rejects unknown exogenous disturbances while preserving intrinsic nonlinearities. First, a nonlinearity in a plant is decomposed into four parts in four subsystems based on controllability and observability. This system decomposition derives the intrinsic part of a nonlinearity. Second, the intrinsic nonlinearities are embedded in a nonlinear state observer to reconstruct. This strategy has a significant advantage because it separates intrinsic nonlinearities from disturbances. Then, a stability condition that ensures uniform ultimate boundedness for the closed-loop system is derived and gains of state feedback and observer are obtained in terms of a linear matrix inequality. After that, a method is presented to evaluate the overall effect of nonlinearity preservation and disturbance compensation. Finally, simulation results and a comparison study demonstrate the validity of the developed method and its superiority over the conventional equivalent-input- disturbance approach and the generalized extended state observer method.

This paper presents an improved equivalent-input-disturbance (EID) approach of actively rejecting exogenous disturbances for a plant. A control system based on the approach includes a new EID estimator constructed by embedding extra integrals to the conventional EID estimator. These integrals enable the estimator to improve the disturbance-estimation precision without amplifying the effect of the measurement noise. Stability conditions of the control system are obtained using Separation Theorem. The system design ensures that the control system satisfies the stability conditions. Experiments of a rotational control system demonstrate the validity of the approach.

This article carries out an inside observation of a disturbance-compensation error in the equivalent-input-disturbance (EID) approach and divides the causes of the compensation error into two types: disturbance- and state-estimation errors. A modified EID (MEID) approach precisely deals with each type separately. Considering that the disturbance-estimation error cannot be measured, we use a high-gain observer to ensure the rapid convergence of the disturbance-estimation error. Unlike the conventional EID approach, the MEID approach newly introduces a weighted output-estimation error, which is produced by a state observer, to compensate for the state-estimation error in a prescribed frequency range. A stability condition is devised for an MEID-based control system. The parameters of a filter and an observer are optimized simultaneously based on a time-domain performance index with a constraint in the frequency domain. An experimental comparison with other EID approaches demonstrates the superiority of the MEID approach.

This article presents a sliding-mode-control-based-equivalent-input-disturbance (SMCEID) approach that enhances the disturbance-rejection performance of a plant. The control scheme includes a conventional equivalent-input-disturbance (EID) estimator and a newly added sliding-mode controller (SMC). While the EID estimator estimates and compensates for disturbances, there is a disturbance-rejection error caused by the filter in the EID estimator. This error is determined by the state-observation error. The SMC set the state-observation error as a sliding-mode surface. A binary-search algorithm is devised to select the gain of the SMC. The selected gain ensures the sliding-mode surface converges to the origin, thus eliminating the error and enhancing the disturbance-rejection performance. Employing the SMCEID approach for a Stewart-platform control system demonstrates its validity.