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}{rcl} itf = 1 : P (s) & = & \frac{pb1 \cdot s + pb0}{s^{2} + pa1 \cdot s + pa0} \cdot e^{- del \cdot s} \\ itf = 2 : P (s) & = & \frac{k0 (tau \cdot s + 1)}{(tau1 \cdot s + 1) (tau2 \cdot s + 1)} \cdot e^{- del \cdot s} \\ itf = 3 : P (s) & = & \frac{k0 \cdot {om}^{2} \cdot (tau ∕ om \cdot s + 1)}{(s^{2} + 2 \cdot xi \cdot om \cdot s + {om}^{2})} \cdot e^{- del \cdot s} \\ itf = 4 : P (s) & = & \frac{k0 (tau \cdot s + 1)}{(tau1 \cdot s + 1) s} \cdot e^{- del \cdot s} \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 $P (s)$ transfer function. The sampling period used for discretization is equivalent to the execution period of the SOPDT block.

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

Input

u	Analog input of the block	Double (F64)

Parameter

itf	Transfer function form $⊙$ 1	Long (I32)
	1 .... General 2 .... Real poles 3 .... Complex poles 4 .... Integrating
k0	Static gain $⊙$ 1.0	Double (F64)
tau	Numerator time constant	Double (F64)
tau1	The first time constant $⊙$ 1.0	Double (F64)
tau2	The second time constant $⊙$ 1.0	Double (F64)
om	Natural frequency $⊙$ 1.0	Double (F64)
xi	Relative damping coefficient $⊙$ 1.0	Double (F64)
pb0	Numerator coefficient: s^0 $⊙$ 1.0	Double (F64)
pb1	Numerator coefficient: s^1 $⊙$ 1.0	Double (F64)
pa0	Denominator coefficient: s^0 $⊙$ 1.0	Double (F64)
pa1	Denominator coefficient: s^1 $⊙$ 1.0	Double (F64)
del	Dead time [s]	Double (F64)
nmax	Allocated size of array $↓$ 10 $↑$ 10000000 $⊙$ 1000	Long (I32)

Output

y	Analog output of the block	Double (F64)

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