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.

Input

u	Analog input of the block	Double (F64)

Output

y	Analog output of the block	Double (F64)

Parameters

itf	Transfer function form $⊙$ 1	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 $⊙$ 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	Size of delay buffer (number of samples) for the time delay del. Used for internal memory allocation. $↓$ 10 $↑$ 10000000 $⊙$ 1000	Long (I32)

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