## 1 Introduction  
In the last decades, the demand for helicopter performance indicators, such as lower required power, greater cargo capacity, lower vibration, higher speed, and lower noise, has been increasing. With the rapid growth of environmental issues and economic needs, aerodynamic performance and efficiency have become the most prominent challenge for helicopter design in the near future. Active control techniques have been investigated for advanced rotor design. Morphing techniques with variable parameters were utilized in order to enhance the rotor performance [1, 2]. Extendable-chord rotors [3, 4], variable-span rotors [5, 6], and variable-speed rotors [7, 8, 9] have been examined in order to alleviate the dynamic stall and drag divergence by optimizing the trim states. Higher Harmonic Control (HHC) was originally used for reducing vibration and noise [10, 11]. As an improved form of HHC, the Individual Blade Control (IBC) showed significant potential in rotor performance improvement [12, 13]. When compared with HHC or IBC, the on-blade control (OBC) requires less power for actuation, and it has less impact on airworthiness. There has been a distinguished progress in OBC with various concepts [14, 15]. Active leading-edge slat [16], active control trailing-edge flags (ACF) [17, 18], active twist rotor (ATR) [19, 20, 21], active gurney flap [22], active camber [23, 24], etc. have been studied. The mechanism of OBC is to change the dynamic response of the rotor and refine the distribution of aerodynamic loads along the circumferential direction. With the development of active materials and structures, ATR has been studied as an emerging approach for enhancing the helicopter performance and reducing vibration and noise. An illustration of the active twist rotor concept is shown in Figure 1. The lack of independent mechanical parts is the most obvious advantage of ATR. The actuators embedded into the composite skin induce strain to twist the blades. Therefore, the ATR is aerodynamically clean and friendly for manufacture. [PERSON] and [PERSON] conductedearlier research on ATR [25; 26]. A 1/8-th Froude-scale bearingless helicopter rotor with embedded piezoceramic elements as sensors and actuators was tested for minimizing the rotor vibrations. Tip twist amplitudes of 0.5\({}^{\circ}\) were achieved, which results in maximally 9% thrust changes and 3% and 8% reductions in pitching and rolling moments. The most representative study is the NASA/Army/MIT Active Twist Rotor program, which contains tests in hover and forward flight while using both open-loop and closed-loop control [27]. Vibratory loads were clearly reduced using the 3/rev, 4/rev, and 5/rev active twist control [28]. The benefits from ATR on performance improvement were investigated while using the CFD-CSD approach proposed by [PERSON] et al. [29; 30]. Active twist actuations produce additional lift from reducing the negative loads on the advancing side, which increases the performance. The L/D ratio improves by 3.2%, 3.1%, and 8.6% with the 1/rev harmonic twist, 2/rev harmonic twist, and advancing-side-only twist, respectively. In addition to the piezoelectric actuation concept, the novel concept using shape memory alloy has also been studied [31]. The precursory studies show the considerable potential of OBC approaches. However, the procurable gain in performance is limited since the actuation concepts were simplified and unoptimized. Because the aerodynamic loads vary along the circumferential direction and spanwise direction, the optimal control deployment schedules and multi-device configurations have been increasingly concerned. [PERSON] and [PERSON] [32] investigated several input scenarios of active twist rotor for performance improvement and vibration reduction. Single-harmonic inputs, multi-harmonic inputs, and non-harmonic inputs are optimized with a multi-objective optimization framework. The reduction of both the required power and vibration index can be simultaneously achieved when a suitable twist control input is adopted [33].