## 5 Semi-Active Structural Control
### Semi-Active Controller Based on the Amplitude of Tower Vibrations  
A semi-active control strategy based on a Tuned Mass Damper (TMD) is proposed. The parameters of the TMD--spring stiffness \(k_{TMD}\) and damping coefficient \(d_{TMD}\)--were optimized using the Transfer Time Domain (TTD) method. During the simulation, these parameters are adaptively adjusted based on the standard deviation of the TTD using a gain scheduling approach. \begin{table}
\begin{tabular}{c c} \hline \hline
**Initial Range [Min; Max]** & **[3000, 1000; 7000, 10,000]** \\ \hline Selection & Stochastic and uniform \\ Crossover & Scattered \\ \hline \hline \end{tabular}
\end{table} 
Table 2: GA configuration. Figure 4: Passive TMD execution scheme. Figure 3: Passive TMD optimization scheme. To design the gain scheduling strategy, the amplitude of oscillations at the top of the tower, as depicted in Figure 5, was analyzed. The initial oscillation amplitude exceeded 1 m, gradually decreasing throughout the simulation, reaching values as low as 0.2 m (Figure 5, blue line, without TMD). As a result, the TMD parameters were adjusted through an optimization process that considers this range of amplitudes. The system response is segmented into three distinct phases, based on the standard deviation of the tower top displacement:  
* Section 1: \(\sigma_{TTDFA}<\frac{1}{3}*\sigma_{TTDFA\ MAX}\)
* Section 2: \(\frac{1}{3}*\sigma_{TTDFA\ MAX}\leq\sigma_{TTDFA}<\frac{2}{3}*\sigma_{TTDFA\ MAX}\)
* Section 3: \(\frac{3}{3}*\sigma_{TTDFA\ MAX}\leq\sigma_{TTDFA}\)  
It is important to note that the optimization was performed independently for each segment, under the assumption that the selection of optimal parameters for one segment does not affect the optimization process for the other segments. Consequently, three separate optimization processes were conducted. Figure 5 illustrates the optimization scheme for the amplitude-based semi-active TMD. The color of the arrows indicates the type of signal and its source. Signals shown in black are generated during each iteration of the simulation. Signals depicted in blue are produced by the Genetic Algorithm (GA) at the start or end of each simulation. Finally, signals in orange are generated by the scheduler upon completion of the GA optimization process, triggered by the condition \(op_{end}=1\). The scheduler initializes with \(sec_{s}=1\), indicating the amplitude section to be optimized. The scheduler (represented by the orange block in Figure 6) resets the Genetic Algorithm (GA) with \(ga_{reset}=1\), and subsequently begins the optimization process. The GA then generates the tuning parameters \(\left(k_{gTMD},\ d_{gTMD}\right)\). The Genetic Algorithm (GA) initiates the simulation with the signal \(run_{sim}=1\). During the simulation, the standard deviation of the TTD, \(\sigma_{sTTD}\), is analyzed at each simulation control period. This variable is used to determine the amplitude section of the signal, \(\sec_{s}\). If the current amplitude section \(\sec_{d}\) matches the section set by the scheduler, \(\sec_{s}\) (i.e., \(\sec_{d}=\sec_{s}\)), the switch for the TMD input changes its state, and the TMD input signals \(\left(k_{TMD},\ d_{TMD}\right)\) are updated with the new parameters provided by the GA \(\left(k_{gTMD},\ d_{gTMD}\right)\), corresponding to the second position of the switch in Figure 5. If the sections do not  
Figure 5: Amplitude-based semi-active TMD optimization scheme. match, the input signals default to the optimal parameters obtained for the passive TMD \((k_{pTMD},\ d_{pTMD})\), represented by the first position of the switch. Upon completion of the simulation, the standard deviation of the TTD for the entire simulation, \(\sigma_{gTTD}\) is calculated. This value serves as the fitness function for the GA. If the fitness value is better than the best recorded fitness value up to that point, the new parameters \(\left(k_{gTMD},\ d_{gTMD}\right)\) are stored in the lookup table _sec2 par_ (row indicated as _secs_).