### SOPDT – Second order plus dead-time model

Block SymbolLicensing group: STANDARD

Function Description
The SOPDT block is a discrete simulator of a second order continuous-time system with time delay, which can be described by one of the transfer functions below. The type of the model is selected by the itf parameter.

$\begin{array}{rcll}\mathtt{\text{itf}}=1:\phantom{\rule{1em}{0ex}}\phantom{\rule{1em}{0ex}}\phantom{\rule{1em}{0ex}}\phantom{\rule{1em}{0ex}}P\left(s\right)& =& \frac{\mathtt{\text{pb1}}\cdot s+\mathtt{\text{pb0}}}{{s}^{2}+\mathtt{\text{pa1}}\cdot s+\mathtt{\text{pa0}}}\cdot {e}^{-\mathtt{\text{del}}\cdot \mathit{\text{s}}}& \text{}\\ \mathtt{\text{itf}}=2:\phantom{\rule{1em}{0ex}}\phantom{\rule{1em}{0ex}}\phantom{\rule{1em}{0ex}}\phantom{\rule{1em}{0ex}}P\left(s\right)& =& \frac{\mathtt{\text{k0}}\left(\mathtt{\text{tau}}\cdot s+1\right)}{\left(\mathtt{\text{tau1}}\cdot s+1\right)\left(\mathtt{\text{tau2}}\cdot s+1\right)}\cdot {e}^{-\mathtt{\text{del}}\cdot \mathit{\text{s}}}& \text{}\\ \mathtt{\text{itf}}=3:\phantom{\rule{1em}{0ex}}\phantom{\rule{1em}{0ex}}\phantom{\rule{1em}{0ex}}\phantom{\rule{1em}{0ex}}P\left(s\right)& =& \frac{\mathtt{\text{k0}}\cdot {\mathtt{\text{om}}}^{2}\cdot \left(\mathtt{\text{tau}}∕\mathtt{\text{om}}\cdot s+1\right)}{\left({s}^{2}+2\cdot \mathtt{\text{xi}}\cdot \mathtt{\text{om}}\cdot s+{\mathtt{\text{om}}}^{2}\right)}\cdot {e}^{-\mathtt{\text{del}}\cdot \mathit{\text{s}}}& \text{}\\ \mathtt{\text{itf}}=4:\phantom{\rule{1em}{0ex}}\phantom{\rule{1em}{0ex}}\phantom{\rule{1em}{0ex}}\phantom{\rule{1em}{0ex}}P\left(s\right)& =& \frac{\mathtt{\text{k0}}\left(\mathtt{\text{tau}}\cdot s+1\right)}{\left(\mathtt{\text{tau1}}\cdot s+1\right)s}\cdot {e}^{-\mathtt{\text{del}}\cdot \mathit{\text{s}}}& \text{}\end{array}$

For simulation of first order plus dead time systems (FOPDT) use the LLC block with parameter a set to zero.

The exact discretization at the sampling instants is used for discretization of the $P\left(s\right)$ transfer function. The sampling period used for discretization is equivalent to the execution period of the SOPDT block.

Input

 u Analog input of the block  $\odot$0.0 Double (F64)

Output

 y Analog output of the block Double (F64)

Parameters

 itf Transfer function form  $\odot$1.00E+00 Long(I32) 1 .... A general form 2 .... A form with real poles 3 .... A form with complex poles 4 .... A form with integrator k0 Static gain  $\odot$1.0 Double (F64) tau Numerator time constant  $\odot$0.0 Double (F64) tau1 The first time constant  $\odot$1.0 Double (F64) tau2 The second time constant  $\odot$1.0 Double (F64) om Natural frequency  $\odot$1.0 Double (F64) xi Relative damping coefficient  $\odot$1.0 Double (F64) pb0 Numerator coefficient: ${s}^{0}$  $\odot$1.0 Double (F64) pb1 Numerator coefficient: ${s}^{1}$  $\odot$1.0 Double (F64) pa0 Denominator coefficient: ${s}^{0}$  $\odot$1.0 Double (F64) pa1 Denominator coefficient: ${s}^{1}$  $\odot$1.0 Double (F64) del Dead time [s]  $\odot$0.0 Double (F64) nmax Size of delay buffer (number of samples) for the time delay del. Used for internal memory allocation.  $↓$10 $↑$10000000 $\odot$1.00E+03 Long (I32)

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