## 5 Active Coating and its Control Algorithm
### The Control Algorithm for the Synthesis of DNOV
**Figure 7.** The shape of pulse of electric voltage \(\overline{\varphi}_{B}(t)\), which is applied to external layer of \(z\in(-h_{c},0)\) active piston (a); shape of pulses of electric voltage \(\overline{\overline{\varphi}}_{B}(t)\), which is applied to internal layer \(z\in\)\((-2h_{c},-h_{c})\) of active piston (b); shape of \"basic pulses\" \(\Psi_{B}(\mathbf{r},\mathbf{\rho}_{k};t)\) of normal displacement of outside surface \(S_{k}\) of piston, which was created by electric pulses above mentioned on a distance \(|\mathbf{r}-\mathbf{\rho}_{k}|<c_{w}t\),\(L_{V})\)) from the border of piston \(\overline{S}_{k}\) (or in the locally one-dimensional problem) (c). This double layer provides a bipolar pulse of media particles displacement of duration \(T_{B}=3\tau_{V}+\tau_{c}\). These pulses are moving through space (like wavelets [36], Figure 8) with speed \(c_{w}\). A wavelet (we will also call it a \"basic pulse\") is only radiated forwards (outside the surface \(S_{V}\)) and must always contain an interval of zero magnitude and of duration \(\tau_{V}\), between two pulses of mutually opposite polarity and same duration \(\tau_{V}\). At the back (\(z<\) -2\(h_{c}\)) the pulses, induced by both piezoelectric layers, move and add to mutually opposite phases giving a zero sum in the backspace (inside \(\overline{S}_{V}\), Figure 8). The main difference between of the suggested approach and traditional approaches is concerned with the following. Usually the desired trajectory (temporal) of the normal displacement of \(S_{V}\) can be achieved by the temporal sequence of pulses without their intersection and with nonzero mean value of each pulse (for instance - delta pulse). In the algorithm of the synthesis of desired trajectory, described below, we use bipolar pulses mutually intersecting with: zero mean value, duration \(T_{B}=3\tau_{V}+\tau_{c}\) (where \(\tau_{c}<<\tau_{V}\)), temporal period \(T_{V}=2\tau_{V}\) of sequence. Each main pulse consists of three consequent identical intervals \(\tau_{V}\). The first (left part) interval of the next basic pulse is covered by the third (right part) interval of the previous basic pulse. The absence of the source (one-dimensional [36]) and wave field in back-space means that we can generate forward radiation waves without any mechanical support of both piezoelectric layers, due to the special construction of the Huygens' source. Besides one-side radiation this Huygens' source is an acoustically transparent source. The wave, which was radiated by a Huygens' source, does not depend on impedance in back-space and can be simply added to any wave passing without any interaction with the source. In [36] we can see the same effect of the one side radiation without mechanical support for the monochromatic excitation (on some frequency  
Figure 8: “Huygens’ piston” of finite dimensions \(L_{V}+L_{V}\) in the homogeneous free compressible space and the instant spatial distributions of media particles displacements are represented by a running “basic pulses” \(\Psi_{B}(z,t)\) (at \(|\mathbf{r}-\mathbf{p}_{k}|<c_{w}t,L_{V}\))) (an external side of an active piston), induced by piezoelectric layers (and zero pulses at internal side of active piston). Darker pulses (waves) are produced by the electric voltage \(\overline{\psi}_{B}(t)\) layer of active piston. Less dark pulses (waves) are induced by the electric voltage \(\overline{\psi}_{B}(t)\). \(\omega\)) of two piezoelectric layers (with the phase difference \(\Delta\varphi=\omega h_{c}/c_{c}\) of excitation). A very small phase difference (necessary for one side radiation) is defined by stationary device tuning. This phase difference does not depend of acoustical field, measured by sensors.