FIWR – Frequence Identification With Reconstructor

Block SymbolLicensing group: ADVANCED

Function Description
The FIWR block performs the identification experiment of the process frequency characteristics. The system is excited by a harmonic signal with a static component ubias, amplitude uampb and frequency $\omega$ passing through the interval $⟨$wb, wf$⟩$. If the adaptive amplitude change is enabled (adaptive_amp = on), then the excitation signal takes such values that the output amplitude is close to dy_max/2. The frequency sweep rate is determined by the cp state (unless it’s not adaptively adjusted, in which case cpb exclusively determines it), outlining:

• For logarithmic mode (mode = 1), it signifies the proportional reduction of the initial period $T_b=\frac{2\pi }{w_b}$ of the excitation sine wave over time $T_b$. Hence, the equation is as follows:
  $$cp=\frac{w_b}{\omega \left(T_b\right)}=\frac{w_b}{w_b{e}^{\gamma T_b}}=e^{-\gamma T_b}.$$

• For linear mode (mode = 2), it represents the frequency increase per unit of time.

The value of the cp state is usually in the interval $⟨0.7;1)$ in logarithmic mode. For the linear mode, the parameter must be chosen with respect to the specified frequency range and the desired frequency change. If the adaptive change of the sweeping rate is enabled (adaptive_cp = on), then the cp state is recalculated depending on the "wrong" position of the frequency characteristic point before its convergence at each scheduled stop of the sweeping (given by the vector PHI). The current value of the cp parameter is copied to the output cp, its initial value cpb can be selected. The minimum and maximum values of cp cp_min and cp_max are taken into account only in adaptive_cp = on mode, otherwise the value cpb is copied to the output cp. In the combined mode (mode = 3), cpb is the sweeping rate in logarithmic segments and the linear segments including the sweeping rates are defined by the matrix WL. This matrix can be defined:

• 1: Explicitly: [$w{b}_1$ $w{f}_1$ $c{p}_1$, $w{b}_2$ $w{f}_2$ $c{p}_2$, ..., $w{b}_N$ $w{f}_N$ $c{p}_N$], where the matrix size is [1x3N].
• 2: Alternatively: [$w{b}_1$ $w{b}_2$ ... $w{b}_N$; $w{f}_1$ $w{f}_2$ ... $w{f}_N$; $c{p}_1$ $c{p}_2$ ... $c{p}_N$], where $w{b}_i$ is the start of the i-th linear interval, $w{f}_i$ is the end of the i-th linear interval. The matrix size is [3xN].

The system identification is triggered by setting the input TUNE = on. After rmi seconds (estimated transient duration), the calculation of the current point of the frequency characteristic starts. Its real and imaginary parts are repeatedly copied to the outputs xre and xim, the phase delay at a given frequency is copied to the output phase. During the identification process, the sweeping stops whenever the phase delay points PHI are reached. The stopping time is related to the values of the parameters q_crit $\in ⟨0.001;0.1⟩$ and np. The smaller the parameter q_crit is, the more accurately the frequency characteristic point will be determined, and the sweeping stop time will be longer. For a shorter evaluation window given by the number of seconds np (usually chosen identically to rmi) the stopping time will be shorter. It is possible to select the maximum number of evaluation windows cmi, the common value is cmi = 10. By input HLD = on it is possible to manually stop the frequency sweeping, setting HLD = off again causes the sweeping to continue. If necessary, the identification process can be stopped by input BRK = on.

During the identification, the output TBSY = 1. It is set to 0 when finished. During an error-free experiment, the output IDE = off. If the identification ends in an error, then IDE = on and the output iIDE specifies the associated error.

The vector PHI can be inserted:

• 1: Explicitly: [${\varphi }_1,{\varphi }_2,...,{\varphi }_M$], where ${\varphi }_i>{\varphi }_{i+1}$ and the vector size is [1xM].
• 2: Alternatively: [$0,0,{\varphi }_{start},{\varphi }_{step},{\varphi }_{end}$], where ${\varphi }_{start}>{\varphi }_{end}$, ${\varphi }_{start}$ is the initial phase, ${\varphi }_{step}$ is the step between phases, and ${\varphi }_{end}$ is the final phase. The vector size is [1x5].

The nmax parameter specifies the maximum number of elements of the vector PHI that can be inserted. At the same time, this is the maximum width of the pmpRef matrix, thus the maximum number of accurately measured points that can be stored.

This block propagates the signal quality. More information can be found in the 1.4 section.

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