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 aims to investigate the disturbance estimation mechanism of extended state observer (ESO) from a new perspective: a time-delay estimation (TDE) interpretation. By drawing the concept of input-output linearization, ESO is transformed into an equivalent TDE form in frequency domain. The establishment of this relationship can lead to an improved understanding of ESO’s principle. In addition, ESO’s parameters for disturbance estimation are given with explicitly physical meanings. Furthermore, theoretical analysis from this perspective also results in a quantitative relationship between ESO estimation performance and its two tuning parameters including control gain $b_0$ and bandwidth $\omega _o$ . Theoretical results are evaluated by using an all-clamped plate structure with an inertial actuator, which is considered to be a typical benchmark for active vibration control. Extensive comparative experiments validate algorithm effectiveness. Note to Practitioners —This paper was focused on the ability of extended state observer (ESO) to estimate total disturbances. The controlled system is a typical benchmark for active vibration control consisting of an all-clamped plate structure with an inertial actuator. The model uncertainties and external disturbances that bothers the system is compensated by the real-time estimation of the ESO. In order to facilitate practical engineering applications, the distinct physical meanings of ESO parameters are expounded with the help of the relationship between ESO and time delay estimation (TDE) established in frequency domain. Moreover, the influence of parameters control gain $b_0$ and bandwidth $\omega _o$ on ESO is qualitatively established. Therefore, the engineer can avoid fall into a trial-and-error strategy that could be laborious and time-consuming. Thus, this paper proposed a convenient way for practitioners interested in developing anti-disturbance control strategies based on ESO. The simplicity and the partial-model-based characteristics are also profitable in practice. Potential applications include robotic systems, smart structures and electrical drives. In the future, the improvements of ESO based on the proposed method to deal with the intractable disturbances should be taken in an effort.

A novel control method of addressing coupling and disturbance influences for finite-time energy-saving robust control of active suspension systems (ASSs) is investigated. By elaborately constructing coupling and disturbance effect indicators, the pros and cons of coupling and disturbance influences on ASSs are discussed, and then a finite-time coupling and disturbance effects-triggered control method is designed via a second-order sliding mode control technique. Importantly, the good/bad coupling effects are assessed through a well-designed nonlinear function. By means of determining if the sign of disturbances conforms to the expected motion or not, the addition of beneficial disturbance effects or removal of detrimental disturbance effects is implemented. Noticeably, by employing a bioinspired nonlinear reference model, beneficial nonlinear stiffness and damping effects are thus utilized, leading to the possibility of energy-saving performance. As a result, the proposed control method exhibits a unique feature, i.e., fully employing potential contribution from the coupling and disturbance effects, and presents a totally new coupling and disturbance effects-triggered control framework, leading to obvious performance improvement. Benchmark experimental conclusions are devoted to distinguishing the advantages and effectiveness of the designed tracking method.

Considering the problems of total disturbances, i.e., higher harmonics, model uncertainties and external excitations in a practical vibration control system, a compound vibration suppression method is proposed for an all-clamped plate, which combines sliding mode control (SMC) with reduced-order extended state observer (RESO). First, a state space model of the all-clamped plate with inertial actuator is established. Second, a RESO is designed to estimate the system state variables and total disturbances in real time. In addition, the total disturbances can further be attenuated by RESO through a feedforward compensation part. Third, a sliding mode controller based on the estimation values is designed for a vibration control system. The Lyapunov stability theorem is further applied to prove the stability of the whole closed-loop vibration control system with the proposed controller. Finally, vibration control experiment equipment is built based on the NI-PCIe acquisition card, inertial actuator and acceleration sensor to verify the vibration suppression performances of the proposed method. The experimental results show that the amplitude value of vibration has been reduced by 75.2% with the proposed method, while the amplitude value is reduced by 54.5% with the traditional sliding mode control method based on an extended state observer (SMC-ESO). The comparative experimental results illustrate that the proposed method has excellent anti-disturbance and vibration suppression performances.

While augmenting the observer gain can diminish the estimation errors of the extended state observer (ESO), it inevitably leads to an amplification of the observing noise, thus creating the trade-off between high-gain observation and noise sensitivity. To address the trade-off, this paper introduces the disturbance-compression extended state observer (DC-ESO) from a frequency-domain perspective. By employing disturbance compression, the DC-ESO modifies the disturbance characteristics encountered by the observer, effectively diminishing the upper bounds of the disturbance and its derivative. Frequency-domain analysis indicates that the DC-ESO necessitates substantially lower observer gain than the ESO while maintaining the same estimation errors. The principles of disturbance compression and its effects on disturbance estimation and noise amplification are elucidated, revealing that the DC-ESO effectively alleviates the inherent conflict between high-gain observation and susceptibility to noise. The parameter tuning methodology and frequency-domain stability criteria are user-friendly for practicing engineers. The effectiveness of the proposed approach is empirically verified through its application to an electro-optical tracking system. Note to Practitioners—This work tackles the disturbance rejection problem in control systems, which encompasses disturbance including mechanical vibrations, friction, and parametric perturbations. Existing extended state observers (ESOs) rely on high gain (or high bandwidth) for disturbance suppression, which unfortunately results in substantial amplification of driving noise. In this research, we incorporate a disturbance compression channel that divides the compensation of disturbance into two separate stages. This approach effectively pre-compresses the disturbance, thus reducing the observational burden on the observer. We reconstruct the ESO in the frequency domain as a transfer function and present a frequency-domain disturbance compression ESO that is easily grasped by engineers. Accordingly, the proposed method is highly practical and effective according to experiments. Future research may consider expanding the targeted suppression to the specific harmonics disturbance and nonlinear system.