3.2.1 Methodological approaches

Concerning the methodological approaches, 61 articles are purely numerical, while 9 are purely experimental. Of the experimental studies, eight feature wind-tunnel tests, and the remaining one reports tests performed in free flight. Additionally, three articles combine numerical and experimental approaches, using experimental tests to validate the results of preceding numerical analyses. Of these combined studies, two involved a wind tunnel, while the remaining one was conducted in free flight. This predominance of numerical approaches is largely attributed to their lower development costs, with many authors proposing experimental tests as part of their future work to further validate the proposed systems.

3.2.2 Aircraft parts

Regarding the aircraft parts modeled or tested, 31 articles focus on an aerofoil or a two-dimensional wing, 30 articles on a three-dimensional wing – including the engines in two cases, the fuel tanks in one case and an external store in another – and 12 articles on the entire aircraft. Among these, six consider a conventional aircraft – including one featuring a fuselage-tail ensemble for a light sport aircraft (LSA) – five address a flying wing, and one investigates a blended wing body (BWB). Once again, the main reason for aerofoil and wing models being more frequent than full aircraft models is the lower cost associated with analysing the problem at a smaller scale. Moreover, it is worth noting that out of the 12 full aircraft models, 6 feature unconventional configurations, highlighting the heightened interest in controlling flutter in these aircraft. This is particularly relevant, as flying wings and BWBs are prone to body-freedom flutter, which arises from the interaction between a flight dynamic mode and a low-frequency structural mode [Reference Zou, Huang, Mu, Hu, Fan and Liu120].

3.2.3 Flight conditions

With regard to the flight conditions studied in each paper, most works focus exclusively on AFS systems for the subsonic regime (60 articles), while only four, two and three studies address the transonic, supersonic and hypersonic regimes, respectively. Additionally, four studies consider more than one regime, with Ref. [Reference Brüderlin, Hosters and Behr82] standing out in this regard. Its objective was to design a robust controller capable of demonstrating adequate performance in both the subsonic and transonic regimes. However, this approach required a trade-off between the two regimes, whereas adaptive algorithms show greater potential. The higher incidence of subsonic studies can be attributed to the fact that most commercial aircraft operate in this regime. Two of the transonic studies also target commercial aircraft, analysing three-dimensional elastic swept-back wings [Reference Vepa and Kwon73, Reference Yang, Huang, Zhao and Hu77], whereas the remaining two feature a generic rectangular wing [Reference Micheli68] and a generic aerofoil [Reference Gong, Wang and Zhao99]. In contrast, the two supersonic studies apply to a missile fin [Reference Tian, Gu, Liu, Wang, Yang, Li and Li89, Reference Lu, Wu and Yang90], while two of the hypersonic studies focus on reentry vehicles [Reference Gao, Wang, Xu and Qu94, Reference Gao, Chen, Han and Yao118], and the remaining hypersonic study concerns a generic double-wedge aerofoil [Reference Chen and Zhao78].

3.2.4 Flutter types

Concerning the flutter types targeted by the AFS system, six main flutter mechanisms have been identified:

1. 1. Lifting surface flutter: This phenomenon is triggered by the dynamic coupling between two or more structural modes associated with lifting surfaces. It includes the classical wing torsion-bending flutter as well as other couplings such as wing–fuel tanks, wing–engines or horizontal stabiliser–vertical stabiliser. Lifting surface flutter is addressed in 51 articles, making it the most studied flutter type in the sample.

2. 2. Control surface flutter (CSF): This is the earliest identified flutter phenomenon [Reference Boo, Mansor and Abdul-Latif7]. It involves control surface deflection as one of the degrees of freedom whose coupling leads to flutter. Only three articles address this flutter type, likely because passive flutter control solutions, such as mass balancing, and improved hinge and actuator stiffness, which have low impact on the aircraft weight in the case of control surfaces [Reference Broadbent and Kirkby121], are commonly used. One of the three articles focuses on hysteresis nonlinearity in a wing–aileron system [Reference Dul95], another models the fuselage and tail of an LSA [Reference Kratochvíl and Valenta56], and the remaining study investigates CSF suppression in a missile fin–actuator system [Reference Lu, Wu and Yang90].

3. 3. Stall flutter: It arises from nonlinear dynamic coupling between the structural modes of a lifting surface and the unsteady aerodynamic forces generated by periodic flow separation and reattachment at high angles of attack. Three articles study this phenomenon [Reference Wu, Dai and Yang50, Reference Zheng, Pontillo, Chen and Whidborne106, Reference Li, Dai, Wu and Yang110].

4. 4. Whirl flutter: It appears in rotor systems, due to the coupling between the elastic deformation of the rotor support (wing, engine nacelle or pylon) and the rotor itself. Gyroscopic torques acting on the rotor induce changes in its orientation with respect to the airflow, thereby modifying aerodynamic loads and potentially leading to increasing amplitude oscillations. One article addressing whirl flutter has been included in the review. This work analyses a tiltrotor aircraft – defined as an aircraft with rotors mounted on rotating shafts capable of producing thrust, lift or a combination of both – in which the flutter mechanism results from the coupling between the aerodynamic forces induced by blade flapping and the bending and torsional deformation of the flexible wing [Reference Dong and Li63].

5. 5. Body freedom flutter (BFF): This flutter type involves the coupling of a rigid-body mode of the aircraft with other dynamic modes [Reference Niblett122, Reference Kaichun, Jinwu and Daochun123]. All six articles featuring BFF correspond to the works where either a flying wing or a BWB is analysed, due to the tendency of these aircraft to experience BFF caused by the coupling between the wing bending mode and the short period mode.

6. 6. Limit cycle oscillations (LCO): This phenomenon consists of non-attenuated oscillations whose amplitude remains bounded as airspeed increases [Reference Duncan1]. Unlike linear flutter, for which oscillation amplitudes grow indefinitely, LCOs arise due to the presence of aerodynamic and/or structural nonlinearities. Nine articles focus on this phenomenon.

In summary, six distinct flutter mechanisms, arising from different combinations of flight conditions and aircraft types, are studied in the articles included in this review. This underscores the complexity of designing AFS systems, as tailored analyses and control strategies are required for different aircraft configurations and operational regimes, discussed further in the Algorithms subsection.

3.2.5 Control strategies

The different active solutions employed by the control system to suppress flutter can be classified into four categories based on their physical mechanisms:

1. 1. Control surface: Flutter is suppressed through the deflection of a control surface governed by a deflection law defined by the AFS system. This is the most technologically mature AFS strategy [Reference Livne14]. Accordingly, research activity in the 52 articles employing this approach mainly focuses on the development, analysis and performance comparison of novel and less technologically mature algorithms, or on the application of classical and optimal control algorithms to suppress flutter in unconventional aircraft.

2. 2. Morphing technology: As mentioned in the Introduction section, this technology involves altering the wing’s external surface during flight. Although a wide variety of morphing concepts – including in-plane, out-of-plane and aerofoil morphing – have been proposed by many authors to adapt the wing’s aerodynamic performance to different flight conditions [Reference Sofla, Meguid, Tan and Yeo124], the five articles implementing morphing technology reviewed here exclusively use camber morphing. These articles explore so-called morphing flaps, which modify the wing camber in the trailing-edge section. This solution achieves a similar effect to that of a conventional trailing-edge flap, but without a hinge, as the surface deformation is continuous. All five works are numerical. In two cases [Reference Ouyang, Gu, Kou and Yang66, Reference Wang and Shoele103], the morphing behaviour is investigated at a theoretical level, since no real actuator is modeled. In Ref. [Reference Zhang, Shaw, Wang, Gu, Amoozgar, Friswell and Woods61], aerofoil deformation is achieved by means of a tendon-spooling pulley connected to two tendons attached to the upper and lower wing surfaces near the trailing edge, while Refs [Reference Wu, Dai and Yang50, Reference Li, Dai, Wu and Yang110] use the Fish Bone Active Camber structure proposed in Ref. [Reference Woods, Bilgen and Friswell125]. Moreover, the five articles focus on studying the interest in using morphing technologies for AFS. As a result, three of them use classical and optimal algorithms to simplify the study. In contrast, Ref. [Reference Li, Dai, Wu and Yang110] uses a nonlinear model inversion (NMI) controller to extend the investigation of the morphing aerofoil previously studied in Ref. [Reference Wu, Dai and Yang50] using a PD controller, while Ref. [Reference Wang and Shoele103] employs a model predictive control (MPC) approach. Additionally, active surface morphing is proposed as a potential AFS solution in another article [Reference Xia, Dai, Huang and Yang30] by the authors of Refs [Reference Wu, Dai and Yang50, Reference Li, Dai, Wu and Yang110]. These authors investigated the benefits of inducing harmonic oscillations of the wing’s flexible surface for stall flutter suppression. However, this concept has so far only been implemented using an open-loop strategy.

3. 3. Flow control: Two experimental studies aimed at assessing the AFS capabilities of two flow control strategies through wind-tunnel tests are included in the review. In Ref. [Reference Chen, Shi, Chen, Tong and Dong98], trailing-edge circulation control is achieved by incorporating two blowing slots on the upper and lower wing surfaces. In Ref. [Reference Chen, Shi, Chen, Liao and Mei51], two additional leading-edge blowing slots are added to the previous configuration. Furthermore, one numerical study employs two zero-mass synthetic jets on the upper and lower surfaces, where the total flux of both jets is zero, thereby eliminating the need for additional air sources [Reference Gong, Wang and Zhao99]. In all three studies, control algorithms adjust jet intensity to suppress flutter.

4. 4. Vibration control: The remaining 13 articles propose different strategies aimed at suppressing flutter by controlling the structural vibrations of the aerofoil or wing. In Ref. [Reference Kassem, Yang, Gu, Wang and Safwat47], an innovative approach based on an active dynamic vibration absorber (ADVA) is introduced. This concept extends a traditional mass–spring–damper system by incorporating an active component that applies a control force to the mass, guided by feedback signals derived from the response of the aeroelastic system. The ADVA was constructed using a Macro Fiber Composite (MFC) actuator driving a mass located at the tip of a cantilever beam, and it was subsequently tested in a wind-tunnel. In Ref. [Reference Kassem, Yang, Gu and Wang54], this strategy is further explored, complementing the initial tests with numerical studies. In addition, in Ref. [Reference Fazelzadeh, Azadi and Azadi115], a piezoceramic wafer strut is incorporated in the pylon to suppress flutter in a wing–store ensemble. Other researchers have also employed piezoelectric actuators to suppress wing vibrations, placing them either on the wing box [Reference Asadi and Farsadi65, Reference Asadi, Farsadi and Kayran67], on the wing surface [Reference Tsushima and Su116] or on a cantilevered beam simulating the wing [Reference Kaneko and Yoshimura52, Reference Wang, Xia and Masarati53, Reference Versiani, Bertolin, Donadon and Silvestre55, Reference Li, Yang, Qi and Yuan104, Reference Wang and Xu112, Reference Wang, Xu and Li117]. A remarkable asset of piezoelectric actuators is their energy harvesting capacity, as they can retrieve energy from wing vibrations while simultaneously controlling flutter. This feature has the potential to reduce the energetic cost of vibration control AFS systems, as investigated in Refs [Reference Kaneko and Yoshimura52, Reference Tsushima and Su116]. Finally, in Ref. [Reference Ghasemikaram, Mazidi, Fazel and Fazelzadeh59], flutter suppression is achieved using an external store equipped with a magneto-rheological (MR) damper at its attachment to the wing. This MR damper relies on a fluid whose viscosity varies in response to an applied magnetic field, enabling real-time tuning of the damping force to suppress vibrations effectively. As in the case of morphing technologies, articles featuring vibration control strategies primarily focus on the strategy itself and therefore tend to employ classical and optimal control algorithms.

The analysis of the control strategies explored in the articles included in this review reveals a clear relationship between control strategies and algorithms. Studies on technologically mature solutions – such as control surface deflections – tend to focus on developing novel and complex algorithms, while those addressing less mature technologies prioritise the technology itself, often relying on more conventional algorithms. A notable exception is the case of flow control, for which two of the three reviewed studies employ reinforcement learning techniques, and whose positive results demonstrate the potential of artificial intelligence-based algorithms for this control strategy.

Finally, the distribution of the reviewed control strategies is illustrated in Fig. 2. Nearly three-quarters of the studies employ traditional control surfaces for AFS, reflecting their technological maturity and suitability for advanced algorithm development. In contrast, only 21 articles explore non-conventional control methods, among which vibration control is the most common. Morphing flaps are addressed in five studies, while flow control is investigated in three.

Figure 2.

Frequency of control strategies in the reviewed works.

3.2.6 Algorithms

The study of the control algorithms employed in the papers included in this review has enabled the development of an exhaustive classification of algorithms used for AFS. This classification encompasses both well-established methods – such as PID – and more recent approaches, including those based on artificial intelligence. The classification, summarised in Fig. 3, is accompanied by a brief note on each algorithm’s operation, properties and most suitable applications, which is included below. This classification constitutes one of the main contributions of the present review, and it is intended to support future AFS researchers in selecting the most appropriate algorithm for their specific applications.

Figure 3.

Classification of the algorithms used for AFS.

Figure 3. Long description

A diagram classifying various algorithms used for Active Flutter Suppression. The diagram is organized into several categories: Classical, Optimal, Robust, Adaptive, Intelligent, Modern, Frequency-Domain, State-Space, and Hybrid. Each category lists specific algorithms or methods relevant to flutter suppression. The Classical category includes PID and DVFB. The Optimal category includes LQR, LQG, H2 Control, and H-infinity Control. The Robust category includes mu-Synthesis, Loop Shaping, ADRC, LPV, and LPV Observer Based State Feedback Control. The Adaptive category includes MRAC, L1 Adaptive Control, SAC, GS-fPID, PPF-FxLMS, I&I, and LHS-GA. The Intelligent category includes Neural Networks, Fuzzy Logic Control, MFRL, and ADP. The Modern category includes MPC, SMC, INDI, Robust Integral of the Sign of the Error, Ridge Regression, and NMI. The Frequency-Domain category includes Nyquist/Bode Techniques. The State-Space category includes Pole Placement. The Hybrid category includes Hybrid Methods.

Classical control: These methods were used in the earliest AFS systems, dating back to the 1970s [Reference Shomber and Holloway15, Reference Schoenman and Shomber16]. They are characterised by being simple and intuitive, as they are based on feedback loops. Consequently, they represent a suitable option for simple systems that are not significantly affected by uncertainties or external disturbances. However, they are less suited for complex systems.

• • PID: It is a simple form of feedback control, consisting of three feedback loops with their corresponding gains – proportional, integral and derivative – aiming to correct the error between the desired and the actual output of the system [Reference Bardera, Crespo, Rodríguez-Sevillano, Muñoz-Campillejo, Barroso and Cobo-González126]. For AFS purposes, it may be insufficient when the system’s complexity is moderate to high. Therefore, it is sometimes combined with other algorithms within hybrid control strategies.

• • Direct velocity feedback (DVFB): It constitutes an even simpler form of feedback control when compared to PID, as it relies on a single derivative term. Its main advantage lies in its low control cost, but in most cases, it is insufficient to suppress flutter.

Optimal control: These methods are based on optimising a performance function defined by the programmer. As a result, they are best suited for applications in which the minimisation of the energetic cost is a key requirement. In addition, they have the advantage of being able to handle disturbances and uncertainties. Optimal control approaches have been used for AFS purposes since the 1980s [Reference Gupta17], and, together with the classical methods, they represent the most widely implemented and technologically mature class of AFS algorithms.

• • LQR: It is based on the minimisation of a quadratic cost function designed to provide the best balance between control effort and performance. It is used for linear systems.

• • LQG: It extends the LQR algorithm by incorporating a Kalman filter, which enables state estimation in the presence of measurement noise [Reference Gupta17]. Therefore, it is well suited for stochastic systems.

• • H₂ control: It is based on minimising the H₂ norm of the transfer function, which measures the root-mean-square (RMS) of the system output in response to a unit energy input [Reference Moelja and Meinsma127]. This makes it a natural choice for optimising performance in terms of energy efficiency or disturbance attenuation.

• • H_∞ control: It minimises the H_∞ norm, which represents the maximum gain of the system transfer function over all frequencies [Reference Theis, Pfifer and Seiler18]. Consequently, it provides guaranteed performance in the worst-case scenario, making it a well-suited algorithm for systems subject to disturbances and model uncertainties.

Robust control: These methods have as their main advantage their ability to guarantee stability and performance in the presence of uncertainties and parameter variations. Therefore, they are used when the system is required to operate under a wide range of conditions. Consequently, they are well suited for the design of AFS systems capable of operating across different flight regimes.

• • μ-synthesis: It explicitly accounts for structured uncertainties, optimising system performance under the worst-case scenario associated with these uncertainties [Reference Fujimori and Nikiforuk128].

• • Loop shaping: It consists of designing the frequency-domain closed-loop gain of the system so that it verifies the control requirements. The controller transfer function is subsequently obtained, taking into account the plant transfer function and the desired closed-loop gain [Reference Kopsakis129].

• • ADRC: It compensates both external and internal disturbances in real time. Moreover, it does not require a precise system model, which makes it adaptable to different systems [Reference Liu and Tian22].

• • Linear parameter-varying (LPV) + anti-wind-up compensator: LPV control is specifically designed for systems whose dynamics vary smoothly depending on certain scheduling parameters. Thus, it is well suited for representing parameter variations across the flight envelope [Reference Tang, Wu and Shi130], allowing automatic gain scheduling as a function of these varying parameters, thereby improving robustness [Reference Barker and Balas131]. In this algorithm combination, the LPV formulation allows the controller to work under varying conditions, while the anti-wind-up compensator prevents actuator saturation, which could appear when implementing a basic LPV controller [Reference Tang, Wang, Gu and Sun80].

• • LPV observer-based state feedback control: The system state is estimated by the LPV observer and subsequently used in the feedback control strategy [Reference Takarics and Vanek81].

Adaptive control: This category includes all the algorithms whose distinctive feature is the ability to adjust their parameters according to real-time changes in either the environment or the system itself. Therefore, they are used to guarantee performance in systems with time-varying parameters, which is particularly relevant for AFS applications.

• • Model reference adaptive control (MRAC): It consists of controlling a system subject to uncertainties and disturbances by tracking the behaviour of a desired reference model. The controller parameters and gains are tuned in real time using the tracking error [Reference Cassaro, Battipede, Marzocca and Behal132].

• • L₁ adaptive control: Similar to MRAC, it is based on determining the system dynamics by tracking the desired reference model [Reference Cassaro, Battipede, Marzocca and Behal132]. However, it handles control and state estimation as separate tasks. Thus, its adaptability with respect to parameter variations is enhanced, making it better suited to fast-changing systems.

• • Simple adaptive control (SAC): It is a simplified adaptive algorithm conceived to guarantee and formally prove stability while keeping the qualities of classical MRAC [Reference Barkana133].

• • Gain scheduled filtered PID (GS-fPID): It is an improvement of conventional PID, incorporating both a filtering stage to reduce measurement noise and gain scheduling capabilities to tune the gain values according to varying conditions [Reference Vindigni, Esposito and Orlando88]. Its unfiltered version is denominated GS-PID (gain scheduled PID) [Reference Lhachemi, Chu, Saussié and Zhu87].

• • Positive position feedback – filtered-X least mean square (PPF-FxLMS): In this algorithm, positive position feedback is enhanced by the use of an adaptive filter that minimises error by modifying the control action in response to changing conditions [Reference Tian, Gu, Liu, Wang, Yang, Li and Li89].

• • Immersion and invariance (I&I): This method is based on immersing the system into a lower-dimensional manifold and ensuring that the system state remains invariant within it. This approach allows for adaptive control with strong stability properties, even in the presence of model uncertainties and external disturbances, and it is particularly well suited for nonlinear systems [Reference Lu, Wu and Yang90].

• • Latin hypercube sampling – genetic algorithm (LHS-GA): This approach integrates Latin hypercube sampling for an efficient representation of the design space, combined with genetic algorithms for optimisation. It is particularly effective for control problems requiring robust solutions under uncertain or fluctuating conditions, striking a balance between exploring different possibilities and exploiting known solutions to optimise control parameters [Reference Rekik, Khaled, Grigoriadis and Franchek91].

Intelligent control: These methods are based on the use of artificial intelligence, being specifically appropriate for complex systems that are difficult to model. They rely on analysing the available data and learning from it, and therefore do not need a precise model of the system subject to control.

• • Neural networks: This control strategy can be applied in cases where the availability of complete control data is not guaranteed, as the control law is learned using available data while predicting unavailable information [Reference Voitcu and Wong134]. It is best suited for complex and nonlinear systems.

• • Fuzzy logic control: It is based on the use of fuzzy set theory to learn a control strategy that must be robust in the presence of uncertainties. It is best suited for systems characterised by vague input data, such as incomplete, delayed or time-varying systems, as it does not require a precise model of the system [Reference Zhang, Han and Ma135].

• • Model-free reinforcement learning (MFRL): The data used by this algorithm to design the control laws are obtained directly from the interaction with the environment. Thus, no explicit model of the controlled system is required [Reference Dong, Shi, Chen and Yao136]. Deep reinforcement learning (DRL) is a subtype of MFRL that employs deep neural networks to approximate policies or value functions. DRL extends the capabilities of MFRL by enabling the agent to handle high-dimensional input spaces. As a result, more complex behaviours can be learned through its neural network-based architecture [Reference Gong, Wang and Zhao99].

• • Adaptive dynamic programming (ADP): It approximates an optimal control law by using artificial intelligence and dynamic programming, without requiring an explicit model of the controlled system [Reference Jia, Tang, Sun and Ding100].

Modern control: These methods involve nonlinear control strategies, predictive models, and state estimation techniques to address complex systems that cannot be controlled using simpler alternatives.

• • MPC: It is based on predicting the future states of a dynamic plant model and optimising the control law that leads the model from the initial state to the desired state. The resulting law is then applied to the actual plant [Reference Wang and Shoele103].

• • SMC: It relies on switching between different control laws depending on the conditions [Reference Li, Yang, Qi and Yuan104]. As a result, it is well suited for systems subject to disturbances and for aircraft flying across different regimes.

• • Incremental nonlinear dynamic inversion (INDI): It handles nonlinear systems by linearising the dynamics around the desired trajectory and then adjusting them with incremental changes [Reference Schildkamp, Chang, Sodja, De Breuker and Wang107]. Therefore, it is used when an exact linearisation of the system is computationally expensive.

• • Robust integral of the sign of error (RISE)-based partial feedback linearised controller: The use of the RISE formulation allows this algorithm to better reject nonlinearities and disturbances [Reference Sharma, Agrawal and Misra108].

• • Ridge regression: This algorithm is based on minimising the sum of squared errors by adding a penalty proportional to the coefficients. It has the advantage of being able to be implemented on a model-free controller [Reference Yu, Qi, Du, Wang and Guo109].

• • Nonlinear model inversion (NMI): This control strategy directly inverts the nonlinear system dynamics to compute the required control inputs, effectively transforming a nonlinear system into an approximately linear one. It is best suited for applications in which nonlinearities significantly affect performance. However, a major limitation of this method is the need for an accurate system model, as any discrepancies in the model can lead to suboptimal control performance [Reference Li, Dai, Wu and Yang110].

Frequency-domain control: These methods are based on analysing the frequency-domain behaviour of the system, and they are usually applied to linear systems.

• • Nyquist and Bode techniques: The desired system performance is achieved by establishing the necessary stability margins. Their limited robustness and adaptability make them generally not well suited for AFS purposes.

State-space control: These algorithms represent system dynamics in a multidimensional state-space model. They are mainly used for multi-variable or complex systems.

• • Pole placement: It consists of placing the closed-loop system poles at the desired locations by using a state feedback strategy. Therefore, it allows selecting the desired response speed and stability. Different methods can be selected to place the poles. Among these, the receptance method is particularly suitable for AFS systems, as it determines the pole placement gains by using the relationship between the system’s inputs and outputs, thereby eliminating the need for explicit knowledge of the system model [Reference Mokrani, Palazzo, Mottershead and Fichera114].

Hybrid control: These algorithms combine two or more of the previously mentioned strategies, in order to enhance the flexibility and robustness of the control system.

Furthermore, the incidence of the aforementioned algorithm types is represented in Fig. 4 with the aim of studying the relevance of each category in current research. In the cases where the articles aim to compare the performance of different algorithms, the most complex one has been considered for classification purposes, since simpler algorithms are generally included as benchmarks or reference methods in such comparisons.

Figure 4.

Frequency of algorithm types in the reviewed works.

First, it is remarkable that none of the reviewed works employ frequency-domain strategies, even though they constitute one of the most basic techniques to design control systems. This absence is likely related to their inability to adapt to changes or disturbances, which constitutes an important drawback for AFS applications.

By contrast, optimal algorithms form the most frequent category, with almost 25% of the articles employing one of these strategies. Moreover, when classical and optimal algorithms are considered together, this proportion increases to nearly 40%. It has previously been mentioned that these algorithms, which are the most technologically mature, are employed in works focusing on studying new control strategies differing from the deflection of aerodynamic surfaces. However, this explanation alone does not account for all papers employing classical and optimal methods, as fewer than 30% of the articles deal with alternative control strategies. The remaining works, concerning the use of technologically mature algorithms applied to control surfaces, focus on specific cases of application, comparisons with other methods, and particular properties of the algorithms to make their contribution to the state of the art. For instance, concerning specific cases of application, Refs [Reference Micheli68, Reference Vepa and Kwon73] focus on the application of optimal control in the transonic regime, while Ref. [Reference Muñoz and García-Fogeda71] considers the subsonic, transonic and supersonic regimes. Additionally, Refs [Reference Shi, Liu, Gu and Yang48, Reference Liu, Niu, Li and Lu72] cover BFF, while Ref. [Reference Wu, Dai and Yang50] studies stall flutter, Ref. [Reference Dong and Li63] discusses whirl flutter and Ref. [Reference Kratochvíl and Valenta56] covers CSF. Concerning comparisons with other methods, Refs [Reference Martins, De Paula, Carneiro and Rade49, Reference Li, Wang, Da Ronch and Chen64] compare the performance of passive control methods alone against hybrid methods combining those passive methods with a classical or optimal active strategy, respectively. Finally, regarding particular properties of the algorithms, Ref. [Reference Sinou62] studies the critical time delay, Ref. [Reference Bueno, Gonsalez Bueno and Dowell60] focuses on the use of a modal approach to synthesise the optimal controller, Ref. [Reference Zhou, Yu and Cai58] studies the reduction in the number of states in the plant to design a sub-optimal controller and Ref. [Reference Micheli68] discusses the performance loss due to actuator saturation.

Robust controllers form the next group in terms of algorithm maturity. All 11 articles featuring one of these algorithms apply them to the deflection of control surfaces. However, while some focus exclusively on the algorithms themselves by considering the baseline case of lifting surface flutter in the subsonic regime, others apply the algorithms to different conditions in order to better test their robustness. In line with this, Refs [Reference Yang, Huang, Zhao and Hu77, Reference Brüderlin, Hosters and Behr82] apply them to the transonic regime, while Ref. [Reference Chen and Zhao78] considers the hypersonic regime. In addition, Refs [Reference Tang, Wang, Gu and Sun80, Reference Zou, Mu, Li, Huang and Hu83] focus on controlling BFF, while Ref. [Reference Xu, Gao, Lv, Yang and Fu79] applies the algorithm to a system comprising both wings and fuel tanks.

Adaptive algorithms are featured in ten works, mainly focusing on testing the AFS capabilities of the algorithms, as they are applied to control surfaces in the subsonic regime. An exception is Ref. [Reference Gao, Wang, Xu and Qu94], which analyses the application of an adaptive fault-tolerant controller to a reentry vehicle in the hypersonic regime.

Intelligent algorithms are relatively less represented in the reviewed literature, with only six articles addressing this category. This limited presence is likely attributed to the emerging stage of this kind of technology. However, as mentioned later in the Discussion section, results are highly promising in terms of performance and cost. Refs. [Reference Chen, Shi, Chen, Tong and Dong98, Reference Gong, Wang and Zhao99] apply MFRL and DRL, respectively, to suppress flutter using flow control; Ref. [Reference Mu, Huang, Zou and Hu97] applies reinforcement learning (RL) to control BFF; and Ref. [Reference Dul95] uses both neural network (NN) and RL to suppress CSF.

Concerning the 11 articles featuring modern algorithms, 6 focus on their application to the baseline case, while the remaining ones extend their study to particular flutter mechanisms and alternative control technologies. Regarding the suppression of particular flutter phenomena, Ref. [Reference Zheng, Pontillo, Chen and Whidborne106] applies SMC to control stall flutter, while Ref. [Reference Schmidt, Danowsky, Kotikalpudi, Theis, Regan, Seiler and Kapania111] compares the performance of both modal isolation and damping for adaptive aeroelastic suppression (MIDAAS) and identically located acceleration and force (ILAF) algorithms to that of robust H_∞ when suppressing BFF. Regarding alternative control technologies, Ref. [Reference Wang and Shoele103] designs an MPC strategy for a morphing flap, while Ref. [Reference Li, Yang, Qi and Yuan104] applies SMC to vibration control. Additionally, combining both of the aforementioned purposes, Ref. [Reference Li, Dai, Wu and Yang110] synthesises an NMI controller to suppress stall flutter using a morphing flap and compares its performance with that of a PID controller.

Moreover, only three articles focus on state-space algorithms. This is likely due to two main reasons. First, the pole placement strategy is not well suited for AFS purposes due to its lack of adaptability and robustness. Second, the technology is well studied, so new research can only focus either on refining the method to place the poles in order to improve controller performance or on studying the control strategy itself. Concerning the first research focus, Refs [Reference Singh, Black and Kolonay113, Reference Mokrani, Palazzo, Mottershead and Fichera114] investigate the receptance method, which has the advantage of not requiring a precise model of the system. In contrast, Ref. [Reference Wang and Xu112] aligns with the second research focus, presenting an improved self-sensing circuit manufactured using MFC.

Finally, five articles employ hybrid strategies. The low number of works opting for this line of research is due to the higher complexity of hybrid controller synthesis and the need to properly study the properties and performance of the integrating algorithms separately beforehand. However, the promising results shown in Refs. [Reference Gao, Chen, Han and Yao118, Reference Vindigni and Orlando119] indicate that this research path needs to be extensively explored in the near future. Moreover, it is remarkable that three of the articles featuring hybrid algorithms apply them to vibration control strategies, even if the complexity of such controllers may hinder the evaluation of the control strategy performance [Reference Fazelzadeh, Azadi and Azadi115–Reference Wang, Xu and Li117].

In summary, with the exception of state-space, frequency-domain and hybrid control, all categories are well represented in the reviewed literature, highlighting their research interest in the field of AFS. The absence of works on frequency-domain algorithms and the scarcity of works featuring state-space solutions are justified by their inability to adapt to disturbances, uncertainties and changes in the conditions, which is a key aspect of AFS system performance. By contrast, the low number of works featuring hybrid algorithms is due to the complexity of this solution, although their positive results indicate that hybrid algorithms constitute a promising area of research. Classical and optimal algorithms remain well represented in the sample, mainly due to their use in studies testing alternative control strategies. Finally, intelligent algorithms are featured less often than other solutions due to their novelty. However, their results are also promising, showing better performance and lower energetic cost when compared with more traditional solutions.

3.2.7 Tabular summary of features and findings

To conclude the Results section, Table 1 provides a consolidated summary of the main features and findings of the 73 articles included in this review. The works are organised according to the taxonomy introduced in Fig. 3.