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The piezoelectric smart structures, which can be labeled as the cream of the crop of smart structures without overstatement, are strongly impacted by a large number of uncertainties and disturbances during operation. The present paper reviews active disturbance rejection control (ADRC) technologies developed for application in piezoelectric smart structures, focusing on measurement, analysis, estimation, and attenuation of uncertainties/disturbances in systems. It first explained vast categories of uncertainties/disturbances with their adverse influences. Then, after a brief introduction to the application of basic ADRC in smart structures, a thorough review of recently modified forms of ADRC is analyzed and classified in terms of their improvement objectives and structural characteristics. The universal advantages of ADRC in dealing with uncertainties and its improvement on the particularity of smart structures show its broad application prospects. These improved ADRC methods are reviewed by classifying them as modified ADRC for specific problems, modified ADRC by nonlinear functions, composite control based on ADRC, and ADRC based on other models. In addition, the application of other types of active anti-disturbances technologies in smart structures is reviewed to expand horizons. The main features of this review paper are summarized as follows: 1) it can provide profound understanding and flexible approaches for researchers and practitioners in designing ADRC in the field and 2) light up future directions and unsolved problems.

This paper proposes a disturbance rejection method with extended state observer (ESO) and a tracking differentiator (TD) to realize vibration suppression of all-clamped plate structure in the presence of lumped disturbance, i.e. internal dynamic uncertainties, unknown external forces and accelerometer measurement noises. First, the structure is modeled as two degrees of freedom system based on vibration characteristics. Second, an ESO is employed to ensure the vibration suppression performance by estimating the lumped disturbances and compensating these disturbances via real-time feedforward mechanism. Meanwhile, a TD is introduced to eliminate the influence of the measurement noises. Moreover, the stability of the closed-loop system is discussed in detail. Finally, the proposed controller is verified on the hardware-in-loop plat-form based on NI PCIe-6343 data acquisition card. Theoretical analysis and experimental results show that the proposed method possesses good vibration suppression performance.

Considering the problems of model uncertainties, higher harmonics, uncertain boundary conditions, external excitations, and system time delay in practical vibration control system, a novel active vibration control method is proposed to suppress the vibration of a thin plate structure with acceleration sensor and piezoelectric bimorph actuator in this paper. First, a nonlinear extended state observer (NESO)-based controller is designed to ensure the anti-disturbance performance of the structural vibration control system. Then, an enhanced differentiator-based time delay compensation method is introduced to improve the vibration suppression performance of the NESO-based controller. A real time hardware-in-the-loop benchmark for an all-clamped piezoelectric thin plate is designed to verify and compare the performance of the developed controller against conventional ESO-based methods (linear ESO with/without time delay compensation, NESO without time compensation). The best vibration suppression and disturbance rejection performance of the proposed NESO-based controller with an enhanced time delay compensator is verified in the comparative experimental results. This work is able to provide practitioners with vital guidance in designing active vibration control system in the presence of disturbances and time delay.