## 2 A Smart Base Restraint for High Wind Turbines to Mitigate Structural Demand  
[PERSON] et al. [4] proposed their new idea of base restraint, able to reduce the structural demand on high-rise wind turbine towers induced by wind. It is an SA rocking system including devices based on controllable fluid, as reported in the scheme of Figure 1: the uncontrolled wind turbine is fully restrained at the base and a single degree of freedom dynamic system with top mass \(m\), stiffness \(k_{T}\) and inherent damping \(c_{T}\), can be used to simulate it. Figure 1 evidences the proposed smart restraint at the base: its stiffness can be instantaneously varied during the motion by installing a smooth hinge at the base of the tower, two vertical linear springs (\(k_{\mathrm{s}}\)) mounted at a distance \(l_{\mathrm{s}}\) from the hinge, and two vertical SA MR devices (\(c_{d}\)) at a distance \(l_{d}\) from the central hinge. The aforementioned control system can produce a real-time modification in the system's stiffness by modifying the MR devices' mechanical properties according to a properly formulated control logic. A simple physical approach was developed by the authors with the aim of reducing base stress and simultaneously restraining the increase in top displacements within certain limits to control second-order effects: the purpose was to produce a trade-off between the contradictory objectives to limit the base stress \(\sigma_{\mathrm{lim}}\) and the top displacement \(x_{\mathrm{lim}}\).  
A \"bang-bang\" control logic makes the base restraint \"stiffer\" (i.e., switching ON the MR devices by setting the intensity of current intensity to the maximum value, \(i_{\mathrm{max}}\)) as long as the limit value for base stress, \(\sigma_{\mathrm{lim}}\), is not exceeded. Conversely, it \"relaxes\" the base restraint (i.e., switching OFF the dampers feeding the minimum level of current, \(i_{\mathrm{min}}\), generally suitable to be 0) when such a limit for stress is overpassed and if the top displacement does not exceeds the acceptable value \(x_{\mathrm{lim}}\). Actually, in this way, the structure converts its potential energy into kinetic energy. The following equation describes how the control logic works in all the possible state combinations for the two indices for the instantaneous structural demand  
\[\begin{array}{ccccc}(a)&if&\left|\sigma(t)\right|<\sigma_{lim}\\ (b)&if&\left|\sigma(t)\right|\geq\sigma_{lim}\end{array}\begin{array}{ccccc} \rightarrow&i(t)=i_{max}\\ \rightarrow&i(t)=i_{min}\\ \rightarrow&i(t)=i_{min}\end{array} \tag{1}\] \[\begin{array}{ccccc}(c)&if&\left|\sigma(t)\right|\geq\sigma_{lim} \end{array}\begin{array}{ccccc}and&\left|x(t)\right|\geq x_{lim}&and&x(t) \cdot\dot{x}(t)>0&\rightarrow&i(t)=i_{max}\\ \rightarrow&i(t)\cdot\dot{x}(t)\leq 0&\rightarrow&i(t)=i_{min}\end{array}\]  
where \(\sigma(t)\), \(x(t)\) and \(\dot{x}(t)\) are, respectively, the value of stress at the base, top displacement and top velocity at the instant of time \(t\). When both stress and displacement are beyond their threshold values, the controller switches the dampers to an ON state if the displacement is moving towards a larger value (i.e., positive velocity), thus trying to damp or invert the displacement's trend; otherwise, it switches the MR devices to an OFF state to an OFF state so as to allow base rotation and energy dissipation, finally reducing demand for stress. The springs have also the role of inducing the recentering of the tower to the initial position at the end of a severe wind-induced excitation.