**4. Control Implementation**

Regarding the considerations presented in [34,40,41], the implementation of the above control proposition (20) and (22)–(24) may be as follows: the boundary value problem (1)(3)(9)÷(11) may be solved in every sampling step of the real-time control, while the horizon of the optimisation may be assumed as one integration step to cope with the large computational load. A numerical implementation of such a nonlinear optimal control for a structure equipped with either an MR-TVA (a standard TVA featuring an MR damper instead of a passive one) [40] or an H-TVA [34] was realised recently using MAT-LAB/Simulink level-2 s-function and *bvp4c* iterative scheme [57]; it was shown numerically (for the MR-TVA system also experimentally [41]) that the iteration procedure yielding high computational load may be omitted, adopting a short time horizon optimal problem task and zero initial conditions for co-state integrators. It was proved that the influence of the terminal condition (11) error was negligible for the considered control applications. In the present research, both the active electric actuator optimal-based control and the

MR damper optimal-based control were implemented simultaneously in the TVA system (Figure 1)—this solution will be designated hereinafter by *OPT*.

A modified two-level displacement ground-hook control (hereinafter designated by *GH*)—the optimal control direct implementation for the case when the protected structure deflection minimisation is the single objective—was additionally regarded during this study. The *GH* control law changes the actuator force between −*Fnom* and +*Fnom* with regard to *x*1 sign changes and varies the MR damper control current between 0 and *imax*th regard to *x*1 and *Fmr* signs [34,40].

On the experimental ground, the *OPT* approach was compared with the *GH* technique for different levels of the nominal actuator force and maximum MR damper current, adopting the 1 ms sampling step.

#### **5. The Experimental Setup**

The regarded wind turbine tower-nacelle scaled laboratory model fulfilled a dynamic similarity condition of motions of tower tips with a real-world full-scale wind turbine Vensys82 structure [49,50,53,54].

The test rig (Figure 4) consisted of a vertically oriented Ti-Gr5 circular rod (no. 1, modelling the wind turbine tower) and a complex of steel plates (no. 2, modelling the nacelle unit, including the turbine) fastened to the top of the rod, with the H-MR-TVA system built-in. The Ti-Gr5 rod was fixed to a section steel foundation frame (no. 3). The H-MR-TVA (no. 4) consisted of an additional mass moving horizontally along linear bearing guides, joined to the nacelle-unit (no. 2) via springs (no. 5), Lord RD-1097-1 MR damper (no. 6) [45], and Festo EGSC-BS-KF-32-50-8P mini slide actuator of linear stroke (powered by Festo EMME-AS-40-S-LV-AS servo motor) (no. 7) [58] in parallel. The H-MR-TVA operated along the same direction as the force excitation applied. The structure was excited by the TMS2060E modal shaker (no. 8 [59]), whose force was transferred to the nacelle-unit (no. 2) with the use of the drive train system (no. 9) of the changeable leverage.

**Figure 4.** The laboratory test rig: (**a**) a general view, (**b**) the H-MR-TVA.

The data acquisition and control system used a laser sensor for the nacelle-unit absolute displacement (i.e., the tower tip deflection) *x*1 measurement, a laser vibrometer for the H-MR-TVA mass absolute displacement *x*2 measurement, the MR damper force sensor (no. 10), the shaker force sensor, the MR damper coil current Hall sensor, power supply and conditioning circuits for the sensors and actuators, and a measuring-control PC embedded

with Inteco I/O board of the RT-DAC4 series [60] and MATLAB/Simulink/RT-CON applications. The RT-CON software ensured the fulfilment of real-time regimes using the 1 kHz sampling rate. The RT-DAC4 analogue input channels and RT-CON analogue input drivers mediated measurement data transfer to the Simulink control environment, where the demanded MR damper current/actuator force was calculated in each sample step. The RT-CON/RT-DAC4 analogue output drivers/channels were used for control output mediation. The MR damper current output was conditioned with the dedicated amplifier and PID controller to force the required electric current through the MR damper coil. The demanded actuator force was fed to the Festo CMMT-AS-C2-3A-EC-S1 servo controller connected with the EMME-AS-40-S-LV-AS motor. The shaker control output was generated using the TMS2060E force measurement signal compared with the demanded excitation pattern and conditioned with the PI controller implemented in the MATLAB/Simulink/RT-CON environment [36].

The system parameters, as in Table 1, along with the identified MR damper unit (Table 2) [41] and electric drive (21) parameters, were assumed for the experiments.


**Table 2.** The identified MR damper unit parameters [41].

The electric drive ±15 N step response series was gathered (Figure 5) using the locked (with 0.9 A control current) MR damper, built-in parallel, and its force sensor (no. 10, Figure 4). The response was identified with a time-delayed transfer Function (21) of three poles and two zeros from MATLAB *System Identification App* (fit to estimation data 96%, data prefiltered, stability enforced):

$$G\_4(s) = \frac{32.6s^2 + 1.55c4s + 9.66c4}{s^3 + 140s^2 + 1.71c4s + 1.06c5}e^{-0.006s} \tag{25}$$

**Figure 5.** Electric drive force step response series: measurement vs. identification.

The actuator identification tests confirmed the considerable response delay of the used mini slide powered by a servo motor (the electro-hydraulic cylinder assumed in the previous numerical study [34] guaranteed a measurably faster response [61]), which was projected to be compensated by the MR damper output force (exhibiting a few-millisecond response time) while maintaining the simplicity of real-time hardware implementationthe electric drive response delay influenced state and co-state variables values, which in turn amended the *i*<sup>∗</sup>*mr* control current according to (20).

#### **6. The Test Conditions**

For the real-time vibration control of the wind turbine tower-nacelle model first bending mode, the approach described in Sections 3 and 4 was implemented using the damper control Formula (20) and the actuator control Formulas (22)–(24). Various *OPT* control *cases I*–*III* (see below) were regarded along with *GH* control, assuming different MR damper maximum currents and actuator nominal force values.

The test conditions parameters were as follows. The wind turbine tower-nacelle model was excited by a harmonic force of amplitude *A*(*Fe*(*t*)) = 45.4 N and a frequency range of [2.2, 4.5] Hz. The fixed sample step *ts* = 10−<sup>3</sup> s was adopted. The nominal actuator output force *Fnom* = 12.5 N (thus servo motor nominal driving torque *Mnom* = 17.2·10−<sup>3</sup> Nm) was assumed as a *baseline OPT*/*GH* configuration, along with *Fnom* = 6.25 N assumed as its more energy-efficient, *restricted force* alternative; the corresponding actuator control signal *Fa ctr* maximum value of 15 N for the *OPT* system (13.5 N for the *GH* system), or 7.5 N for the *OPT* system (6.75 N for the *GH* system) (see time responses in Section 7), were assumed accordingly, based on the identification (25). The maximum value of *Fa ctr* corresponding to the assumed *Fnom* value for the *GH* system was 10% lower than for the *OPT* system due to the 10% duty cycle of the *OPT* resetting function (zero initial conditions for co-state integrators are assumed). The MR damper maximum current *imax* = 1.0 as was assumed for the *baseline* configuration (*Fnom* = 12.5 N), while *imax* = 0.5 as was assumed for its *restricted force* counterpart (*Fnom* = 6.25 N)—see Table 3. The values of *imax* elding *Fmr* ranges were tuned to the assumed *Fnom* ranges, as the MR damper, due to its few-millisecond response time (see, e.g., Figure 12b in [41] p. 12), was activated ahead of the electric drive, while the electric actuator may have cancelled the detrimental MR damper remanent force.


**Table 3.** The test cases: nominal actuator force *Fnom*/maximum MR damper current *i*\_*max*.

The general weighting factors for the *OPT* control solution's quality index (8) were assumed as follows: *g*11 = 1018, *g*12 = 0, *g*13 = 1015, *g*14 = 0, *g*21 = 4, *g*222 = 4·10−12. A negligible but nonzero *g*222 value was selected to eliminate calculation problems for *<sup>z</sup>*2(*t*) = *<sup>z</sup>*4(*t*) in (21), (22)(23)(24); the electric drive force magnitude was tuned through the *Fnom* assumption (*baseline* or *restricted force* configuration) in the current research. The remaining weights were assumed to (*OPT cases I*–*III*, see Table 3):


#### **7. Real-Time Control Results**

The efficiency of the adopted solutions was analysed using the frequency characteristics of the nacelle displacement (primary structure deflection) amplitude *<sup>A</sup>*(*x*1) (Figures 6–8), the TVA stroke amplitude *<sup>A</sup>*(*<sup>x</sup>*1 − *x*2) (Figures 9–11), the maximum MR damper force (Figures 12–14), and the mean actuator power (Figures 15–17), along with the

time patterns of *x*1, *x*1 − *x*2, *Fa ctr*, *Fa*, and *Fmr* (Figures 18–21). If omitted, *imax* = 0 d all weights as for control *case I* (Section 6) were assumed all over this section. Figures 6, 9, 12 and 15 present the frequency characteristics of *<sup>A</sup>*(*x*1), *<sup>A</sup>*(*<sup>x</sup>*1 − *<sup>x</sup>*2), the maximum MR damper force, and the mean actuator power, respectively, obtained for the *OPT* and *GH* systems with *Fnom* = 12.5 N, relative to the passive system with constant MR damper control current values of 0.0 A, 0.1 A, 0.2 A, 0.5 A, and idling electric actuator (passive system omitted in Figure 15). Similarly, Figures 7, 10, 13 and 16 present the frequency patterns of *<sup>A</sup>*(*x*1), *<sup>A</sup>*(*<sup>x</sup>*1 − *<sup>x</sup>*2), the maximum MR damper force, and the mean actuator power, respectively, obtained for the *OPT* solution with *Fnom* = 12.5 N, and different *imax*/*g*221 values (*imax* = 0, *imax* = 0.5 A or *imax* = 1.0; nonzero MR damper force weight *g*221 = 10<sup>6</sup> for *imax* = 1.0 case only), the *OPT* solution with *Fnom* = 6.25 N, and *imax* = 0 *imax* = 0.5 A, and *GH* solution with *Fnom* = 6.25 N, and *imax* = 0 or *imax* = 0.5 A. Additionally, Figures 8, 11, 14 and 17 present the frequency characteristics of *<sup>A</sup>*(*x*1), *<sup>A</sup>*(*<sup>x</sup>*1 − *<sup>x</sup>*2), the maximum MR damper force, and the mean actuator power, respectively, obtained for the *OPT* concept with *Fnom* = 12.5 N and different *imax*/*g*23 values (*imax* = 0, *imax* = 0.5 A or *imax* = 1.0; the actuator power weight *g*23 = 10<sup>10</sup> or *g*23 = 1011).

**Figure 6.** Nacelle horizontal displacement amplitude *<sup>A</sup>*(*x*1) frequency characteristics: passive system vs. *OPT* for *Fnom* = 12.5 N vs. *GH* for *Fnom* = 12.5 N.

**Figure 7.** Nacelle horizontal displacement amplitude *<sup>A</sup>*(*x*1) frequency characteristics: *OPT* for different control parameter values vs. *GH* for *Fnom* = 6.25 N.

**Figure 8.** Nacelle horizontal displacement amplitude *<sup>A</sup>*(*x*1) frequency characteristics: *OPT* for different *imax* d *g*23 values, and *Fnom* = 12.5 N.

**Figure 9.** The TVA stroke amplitude *<sup>A</sup>*(*<sup>x</sup>*1 − *x*2) frequency characteristics: passive system vs. *OPT* for *Fnom* = 12.5 N vs. *GH* for *Fnom* = 12.5 N.

**Figure 10.** The TVA stroke amplitude *<sup>A</sup>*(*<sup>x</sup>*1 − *x*2) frequency characteristics: *OPT* for different control parameter values vs. *GH* for *Fnom* = 6.25 N.

**Figure 11.** The TVA stroke amplitude *<sup>A</sup>*(*<sup>x</sup>*1 − *x*2) frequency characteristics: *OPT* for different *imax* an d *g*23 values, and *Fnom* = 12.5 N.

**Figure 12.** The maximum MR damper force frequency characteristics: passive system vs. *OPT* for *Fnom* = 12.5 N vs. *GH* for *Fnom* = 12.5 N.

**Figure 13.** The maximum MR damper force frequency characteristics: *OPT* for different control parameter values vs. *GH* for *Fnom* = 6.25 N.

**Figure 14.** The maximum MR damper force frequency characteristics: *OPT* for different *imax* and *g*23 values, and *Fnom* = 12.5 N.

**Figure 15.** The mean actuator power frequency characteristics: *OPT* for *Fnom* = 12.5 N vs. *GH* for *Fnom* = 12.5 N.

**Figure 16.** The mean actuator power frequency characteristics: *OPT* for different control parameter values vs. *GH* for *Fnom* = 6.25 N.

**Figure 17.** The mean actuator power frequency characteristics: *OPT* for different *imax* and *g*23 values, and *Fnom* = 12.5 N.

Figures 18–21 present the comparison of the primary structure deflection (i.e., nacelle horizontal displacement) *x*1, the TVA displacement *x*1 − *x*2, the actuator control signal *Fa ctr* and force *Fa*, and the MR damper force *Fmr* time patterns obtained at the specific frequency points: 3.2 Hz (Figure 18), 4.0 Hz (Figure 19), 3.4 Hz (Figure 20), 3.6 Hz, and 3.7 Hz (Figure 21). Figures 18 and 19 present the comparison of the time responses obtained for the *OPT* system with *Fnom* = 12.5 N, *imax* = 0/0.5/1.0 A, *g*221 = 0, the *OPT* system with *Fnom* = 12.5 N, *imax* = 1.0 A, *g*221 = 106, and the *GH* system with *Fnom* = 12.5 N, *imax* = 0/1.0 A. Fig. 20 presents the comparison of the time responses obtained for the *OPT* system with *Fnom* = 6.25 N, and *imax* = 0 or 0.5 A. Figure 21 compares the time responses determined for the *OPT* system with *Fnom* = 12.5 N, *imax* = 0/1.0 A, and *g*23 = 0/1010/1011.

As may be observed in Figures 6 and 7 for *Fnom* = 12.5 N (in Figure 7 for *Fnom* = 6.25 N), both *OPT* and *GH* solutions with an MR damper semi-active operation (i.e., with nonzero *<sup>i</sup>*max) exhibited significantly lower maximum *<sup>A</sup>*(*x*1) values within the regarded structure first bending mode frequency neighbourhood (especially in 4.0 Hz neighbourhood), than *OPT* and *GH* without the MR damper support (i.e., with *imax* = 0, omitted in the legends). The latter, however, presented slightly lower *<sup>A</sup>*(*x*1) values in the 3.2 Hz neighbourhood. These phenomena are illustrated in Figures 18 and 19 for *Fnom* = 12.5 N and various *imax*/*g*221 values. The additional force provided by the MR damper semi-active operation resulted in a slightly smaller TVA stroke (*<sup>x</sup>*1 − *x*2) amplitude (compared to Figures 9 and 10), which yielded somewhat lower TVA efficiency for nonzero *imax* at 3.2 Hz (Figure 18). At a higher frequency of 4.0 Hz (Figure 19), however, the other factor was dominant in relation to the electric servo activation delay time regarding the shorter vibration period; thus, the MR damper few-millisecond response time was greatly beneficial, as previously expected (Section 5). Similar phenomena for *Fnom* = 6.25 N are depicted in Figure 20a,b (for 3.6 Hz) and Figure 20c,d (for 3.7 Hz). Figure 6 clearly indicates the TVA excess damping with regard to the optimally tuned TVA [19]—the maximum *<sup>A</sup>*(*x*1) for the zero-control passive system was greater than 2.5 mm. In contrast, Figure 2 suggests a value of 2.1 mm for a 14.1% mass ratio.

**Figure 18.** Time responses at 3.2 Hz: (**a**) *OPT*, *imax* = 0 (**b**) *OPT*, *imax* = 0.5 A (**c**) *OPT*, *imax* = 1.0 A, (**d**) *OPT*, *imax* = 1.0 A, *g*221 = 106, (**e**) *GH*, *imax* = 0, (**f**) *GH*, *imax* = 1.0 A (*Fnom* = 12.5 N).

**Figure 19.** Time responses at 4.0 Hz: (**a**) *OPT*, *imax* = 0 (**b**) *OPT*, *imax* = 0.5 A (**c**) *OPT*, *imax* = 1.0 A, (**d**) *OPT*, *imax* = 1.0 A, *g*221 = 106, (**e**) *GH*, *imax* = 0, (**f**) *GH*, *imax* = 1.0 A (*Fnom* = 12.5 N).

**Figure 20.** *OPT* time responses at 3.6 Hz: (**a**) *imax* = 0, (**b**) *imax* = 0.5 A vs. *OPT* time responses at 3.7Hz: (**c**) *imax* = 0, (**d**) *imax* = 0.5 A (*Fnom* = 6.25 N).

The combined electric drive and MR damper operation in the H-MR-TVA system (control *case I*, *baseline* configuration), i.e., with *Fnom* = 12.5 N, *imax* = 1.0 A led to a 35% maximum *<sup>A</sup>*(*x*1) reduction in relation to the H-MR-TVA operation without MR damper semi-active support (i.e., with *imax* = 0 a and 52% reduction with regard to the previous research with an MR-TVA system of a lower (7.7%) mass ratio, but less TVA excess damping [41]. This is regarded as a satisfactory result for such a real-time implementation, considering the nonlinearity of Figure 2 characteristics and the expected 23% *<sup>A</sup>*(*x*1) reduction only (Section 2). Both *GH* and *OPT* (control *case I*, *baseline* configuration) provided maximum *<sup>A</sup>*(*x*1) values close to 1.1 mm (i.e., 57% reduction concerning the 0.0 A passive configuration exhibiting the lowest *<sup>A</sup>*(*x*1) values, and 87% reduction regarding the 0.5 A passive configuration, see Figure 6). This result was obtained at ca. 4 mm TVA stroke amplitude (*OPT* configuration, Figure 9), ca. 32 N maximum MR damper force (Figure 12), and ca. 0.76 W maximum actuator power (Figure 15). The configurations without the MR damper semi-active support were characterised by more than 4.5 mm TVA stroke amplitude, only 4 N maximum MR damper force, and as much as 0.95 W maximum actuator power, while being significantly less efficient in primary structure deflection minimisation.

**Figure 21.** *OPT* time responses at 3.4 Hz: (**a**) *imax* = 0 (**b**) *imax* = 0, *g*23 = 10<sup>10</sup> (**c**) *imax* = 0, *g*23 = 10<sup>11</sup> (**d**) *imax* = 1.0 A (**e**) *imax* = 1.0 A, *g*23 = 1010, (**f**) *imax* = 1.0 A, *g*23 = 10<sup>11</sup> (*Fnom* = 12.5 N).

As presented in Figures 6, 9, 12 and 15 for *Fnom* = 12.5 N (in Figures 7, 10, 13 and 16 for *Fnom* = 6.25 N), the results of *OPT* and *GH* operation were similar, with minor differences noticeable concerning *<sup>A</sup>*(*x*1), *<sup>A</sup>*(*<sup>x</sup>*1 − *x*2), the maximum MR damper force, and the mean actuator power, especially for *Fnom* = 12.5 N. In Figure 18a,c vs. Figure 18e,f as well as in Figure 19a,c vs. Figure 19e,f, disparities in the time patterns may be spotted with *Fa ctr* differences coming to the forefront, as explained in the final paragraph of Section 6.

The interesting alternative to the *baseline* configuration (*Fnom* = 12.5 N, *imax* = 1.0 A with *g*221 = 0 (control *case I*) was a configuration with a lower *imax* = 0.5 A value (control *case I*), and with *imax* = 1.0 A and nonzero MR damper force weight *g*221 = 10<sup>6</sup> (control *case II*); *Fnom* = 12.5 N for both these configurations. In Figures 7, 10, 13 and 16, the respective frequency characteristics are included, while in Figure 18b,d as well as in Figure 19b,d, the time patterns are presented. It may be observed that these two solutions exhibited higher *x*1 deflection amplitudes, similar *x*1 − *x*2 strokes, and lower MR damper forces (as intended, especially for the *imax* = 1.0 A, *g*221 = 10<sup>6</sup> configuration) than the *baseline* configuration. The maximum actuator power used in the *imax* = 1.0 A, *g*221 = 10<sup>6</sup> configuration was actually slightly higher, being also less efficient in *<sup>A</sup>*(*x*1) minimisation than the *imax* = 0.5 A, *g*221 = 0 configuration. In Figure 18c vs. Figure 18d as well as in Figure 19c vs. Figure 19d, the differences in the *Fmr* patterns resulting from the different *g*221 (MR damper force) weights may be spotted. Due to the MR damper millisecond response time, its control signal *imr* patterns were omitted in the time characteristics Figures 18–21 (details may be found in [41] pp. 12–13).

In Figure 8, Figure 11, Figure 14, and Figure 17, the frequency characteristics determined for the *OPT* system with nonzero actuator power weights *g*23 (control *case III*) and different *imax* values are presented. Figure 21 depicts time patterns obtained for zero and nonzero *g*23 values with the MR damper in passive mode (*imax* = 0) and semi-active mode (*imax* = 1.0 A) Due to lowering actuator power (Figure 17) (and so its mean force, see Figure 21), the maximum *<sup>A</sup>*(*<sup>x</sup>*1) values may be observed within the (3.3, 3.4)Hz neighbourhood (Figure 8), contrary to the configurations with *g*23 = 0 (Figures 6 and 7), for which *<sup>A</sup>*(*<sup>x</sup>*1) elevation may be observed at higher frequencies due to the more detrimental actuator response delay in the situation of its higher output force. However, for the (3.3, 3.4)Hz range, MR damper support was not beneficial (see Figures 8 and 21), as was discussed earlier (i.e., the MR damper semi-active operation resulted in a slightly smaller TVA stroke amplitude, while the actuator response delay was not that meaningful as for the higher frequencies). The influence of the actuator power weight on its operation is apparent in Figure 21—the actuator control signal *Fa ctr* (and so its output force *Fa*) was clearly lowered for *g*23 = 1010, and particularly for *g*23 = 1011. This yielded significant actuator power reduction, i.e., below 0.19 W, regarding the control *case I* (*g*23 = 0), as shown in Figure 17 vs. Figures 15 and 16.

Three of the regarded control options deserve a special note: the *restricted force OPT* configuration, control *case I* (*Fnom* = 6.25 N, *imax* = 0.5 A, *g*23 = 0) vs. the *restricted force GH* configuration (*Fnom* = 6.25 N, *imax* = 0.5 A) vs. the *baseline* configuration, control *case III* (*Fnom* = 12.5 N, *imax* = 1.0 A, *g*23 = 1010). All three configurations yielded maximum *x*1 deflection amplitudes of ca. 1.78 mm (Figures 7 and 8), which was more than a 30% reduction regarding the 0.0 A passive system (Figure 6), while the maximum TVA stroke amplitudes were close to those of the 0.0 A passive system. To obtain the primary structure deflection minimisation, both noted *restricted force OPT*/*GH* configurations required the MR damper of ca. 16 N maximum force and the actuator of 0.35 W nominal power, while the latter approach (*baseline* configuration, control *case III*) required the damper of 3.3 N maximum force and the actuator of 0.17 W nominal power, which is by far a preferable solution. Here comes forth the advantage of the properly tuned *OPT* solution (over the simple *GH* control with changeable *Fnom* and *imax* values only) with its various optimisation fields (quality function components) to obtain a significantly better efficiency concerning the important aspect of the energy demand, associated with the *g*23 weight use, while the vibration attenuation efficiency was the same as for the *GH* configuration considered here. Recapitulating, the control solutions that are particularly recommended are:


For higher actuator force solutions (as the former), the MR damper semi-active support with millisecond response time was greatly beneficial due to the substantial actuator response time delay related to the oscillation period at frequencies above 3.6 Hz (see Figures 5, 6 and 19). On the other hand, it may also be observed that the electric actuator cancelled the unwanted MR damper remanent force, as assumed previously—see Figures 17, 18, 19 and 20a,b,d.

Using a nonzero *g*221 value led to 40% MR damper force reduction (*Fnom* = 12.5 N, *imax* = 1.0 see Figure 13); however, the cost was a 24% increased maximum structure deflection, and a 7.5% increased maximum actuator power, which rendered this solution aimless. The influence of the other weighting factors (*g*11, *g*13, *g*21) was studied within the scope of the previous research [34,41]. The operation of the regarded system with MR damper control only (idling electric drive) was also studied before; in current research, it was regarded as aimless, as the already embedded electric actuator adds undesirable excess damping to the TVA system.

With the help of the dynamical similarity analysis that includes previously determined time and length scale factors (*sT* = 0.135 and *sL* = 0.0176, respectively) [53] in combination with force scale factor *sF* = 1.75·10−<sup>3</sup> [54], the results obtained in the current study may be used as the indicators of the demanded control forces (with regard to actual mass ratio) that have to be generated in the H-MR-TVA (H-TVA) system attached to the real-world Vensys82-class wind turbine structure. Full-scale implementation of the two exemplary control solutions (1) and (2) recommended above will require: (1) an actuator of 7.1 kN nominal force and 3.33 kW nominal power, plus an MR damper of 18.2 kN maximum force, (2) an actuator of 7.1 kN nominal force and 0.74 kW nominal power, plus a passive damper of 1.9 kN maximum force.
