SOPDT – Second order plus dead-time model

Block SymbolLicensing group: STANDARD
PIC

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.

itf = 1 : P(s) = pb1 s + pb0 s2 + pa1 s + pa0 edels itf = 2 : P(s) = k0 tau s + 1 tau1 s + 1 tau2 s + 1 edels itf = 3 : P(s) = k0om2 tauom s + 1 s2 + 2 xiom s + om2 edels itf = 4 : P(s) = k0 tau s + 1 tau1 s + 1s edels

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

Output

y

Analog output of the block

double

Parameters

itf

Transfer function form  1

long

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

tau

Numerator time constant

double

tau1

The first time constant  1.0

double

tau2

The second time constant  1.0

double

om

Natural frequency  1.0

double

xi

Relative damping coefficient  1.0

double

pb0

Numerator coefficient: s0  1.0

double

pb1

Numerator coefficient: s1  1.0

double

pa0

Denominator coefficient: s0  1.0

double

pa1

Denominator coefficient: s1  1.0

double

del

Dead time [s]

double

nmax

Size (number of samples) of delay buffer (used for internal memory allocation)   1  10000000 10

long