IndustrialControlSystems.LinearSystems.Discrete

Discretised linear systems

Information

  

Description

Discrete time blocks

Extends from Modelica.Icons.Package (Icon for standard packages).

Package Content

NameDescription
IndustrialControlSystems.LinearSystems.Discrete.Integrator Integrator Integrator: mu/s
IndustrialControlSystems.LinearSystems.Discrete.FirstOrder FirstOrder First order process: mu/(1+tau*s)
IndustrialControlSystems.LinearSystems.Discrete.LeadLag LeadLag Lead lag process: mu(1+T1*s)/(1+T2*s)
IndustrialControlSystems.LinearSystems.Discrete.ComplexPoles ComplexPoles Process with complex poles
IndustrialControlSystems.LinearSystems.Discrete.TwoPolesTwoZeroes TwoPolesTwoZeroes Process with an integrator, 1 pole and 2 zeroes: mu(1+sT1)(1+sT2)/(1+sT3)s
IndustrialControlSystems.LinearSystems.Discrete.TransferFunction TransferFunction Model of a generic rational transfer function [a(m)*s^m + a(m-1)*s^(m-1) + ... + a(1)*s + a(0) ]/[b(n)*s^n + b(n-1)*s^(n-1) + ... + b(1)*s + b(0) ]
IndustrialControlSystems.LinearSystems.Discrete.Delay Delay Unitary time delay
IndustrialControlSystems.LinearSystems.Discrete.MultiStepsDelay MultiStepsDelay Multistep time delay
IndustrialControlSystems.LinearSystems.Discrete.Functions Functions Functions
IndustrialControlSystems.LinearSystems.Discrete.Types Types New types definition

IndustrialControlSystems.LinearSystems.Discrete.Integrator IndustrialControlSystems.LinearSystems.Discrete.Integrator

Integrator: mu/s

Information

  

Description

Discretised version of the continuous time transfer function of an integrating process.

   Y(s)      mu
   ----  = ------
   U(s)      s
  

Discretisation

The discretisation of the continuos time transfer function has been performed with the bilinear transformation formula
                 z - 1 
  s = ------------------------------
        z*alpha*Ts - (alpha - 1)*Ts
  
that is equivalent to

Extends from Interfaces.DiscreteBaseBlock (Partial discrete time block interfaces).

Parameters

NameDescription
Discretisation
Ts Sampling time [s]
method Discretisation method
Block parameters
mu Gain
Initial conditions
y_start Output initial value

Connectors

NameDescription
uinput
youtput

IndustrialControlSystems.LinearSystems.Discrete.FirstOrder IndustrialControlSystems.LinearSystems.Discrete.FirstOrder

First order process: mu/(1+tau*s)

Information

  

Description

Discretised version of the continuous time transfer function of first order process.

   Y(s)         mu
   ----  = ------------
   U(s)      (1+s*tau)
  

Discretisation

The discretisation of the continuos time transfer function has been performed with the bilinear transformation formula
                 z - 1 
  s = ------------------------------
        z*alpha*Ts - (alpha - 1)*Ts
  
that is equivalent to

Extends from Interfaces.DiscreteBaseBlock (Partial discrete time block interfaces).

Parameters

NameDescription
Discretisation
Ts Sampling time [s]
method Discretisation method
Block parameters
mu Gain
tau Time constant
Initial conditions
y_start Output initial value

Connectors

NameDescription
uinput
youtput

IndustrialControlSystems.LinearSystems.Discrete.LeadLag IndustrialControlSystems.LinearSystems.Discrete.LeadLag

Lead lag process: mu(1+T1*s)/(1+T2*s)

Information

  

Description

Discretised version of the continuous time transfer function of a lead lag process.

   Y(s)        (1 + s*T1)
   ----  = mu ------------
   U(s)        (1 + s*T2)
  

The time constant T1 must be different from T2.

Discretisation

The discretisation of the continuos time transfer function has been performed with the bilinear transformation formula
                 z - 1 
  s = ------------------------------
        z*alpha*Ts - (alpha - 1)*Ts
  
that is equivalent to

Extends from Interfaces.DiscreteBaseBlock (Partial discrete time block interfaces).

Parameters

NameDescription
Discretisation
Ts Sampling time [s]
method Discretisation method
Block parameters
mu Gain
T1 Costante di tempo dello zero
T2 Costante di tempo del polo
Initial conditions
y_start Output initial value

Connectors

NameDescription
uinput
youtput

IndustrialControlSystems.LinearSystems.Discrete.ComplexPoles IndustrialControlSystems.LinearSystems.Discrete.ComplexPoles

Process with complex poles

Information

  

Description

Discretised version of the continuous time transfer function of a process with complex poles.

   Y(s)                      1
   ----  = mu ------------------------------------
   U(s)        (1 + s*2*xi/omegan + (s/omegan)^2)
  

The damping coefficient xi must be between [0,1].

Discretisation

The discretisation of the continuos time transfer function has been performed with the bilinear transformation formula
                 z - 1 
  s = ------------------------------
        z*alpha*Ts - (alpha - 1)*Ts
  
that is equivalent to

Extends from Interfaces.DiscreteBaseBlock (Partial discrete time block interfaces).

Parameters

NameDescription
Discretisation
Ts Sampling time [s]
method Discretisation method
Block parameters
xi Damping coefficient
omegan Natural frequency
mu Gain
Initial conditions
y_start Output initial value
dy_start Slope initial value

Connectors

NameDescription
uinput
youtput

IndustrialControlSystems.LinearSystems.Discrete.TwoPolesTwoZeroes IndustrialControlSystems.LinearSystems.Discrete.TwoPolesTwoZeroes

Process with an integrator, 1 pole and 2 zeroes: mu(1+sT1)(1+sT2)/(1+sT3)s

Information

  

Description

Discretised version of the continuous time transfer function of a process with an integrator, one pole and two zeroes.

   Y(s)        (1 + s*T1)*(1 + s*T2)
   ----  = mu ----------------------
   U(s)            s*(1 + s*T3)
  

The time constants T1 and T2 must be different from T3.

Discretisation

The discretisation of the continuos time transfer function has been performed with the bilinear transformation formula
                 z - 1 
  s = ------------------------------
        z*alpha*Ts - (alpha - 1)*Ts
  
that is equivalent to

Extends from Interfaces.DiscreteBaseBlock (Partial discrete time block interfaces).

Parameters

NameDescription
Discretisation
Ts Sampling time [s]
method Discretisation method
Block parameters
mu Gain
T1 first zero's time constant
T2 second zero's time constant
T3 pole's time constant
Initial conditions
y_start Output initial value

Connectors

NameDescription
uinput
youtput

IndustrialControlSystems.LinearSystems.Discrete.TransferFunction IndustrialControlSystems.LinearSystems.Discrete.TransferFunction

Model of a generic rational transfer function [a(m)*s^m + a(m-1)*s^(m-1) + ... + a(1)*s + a(0) ]/[b(n)*s^n + b(n-1)*s^(n-1) + ... + b(1)*s + b(0) ]

Information

  

Description

Discretised version of the continuous time transfer function, defined by its numerator and denumerator.

   Y(s)     a(m)*s^m + a(m-1)*s^(m-1) + ... + a(1)*s + a(0) 
   ----  = -------------------------------------------------
   U(s)     b(n)*s^n + b(n-1)*s^(n-1) + ... + b(1)*s + b(0)
  

The order of the numerator cannot be higher than the denumerator one: m <= n.

Discretisation

The discretisation of the continuos time transfer function has been performed with the bilinear transformation formula
                 z - 1 
  s = ------------------------------
        z*alpha*Ts - (alpha - 1)*Ts
  
that is equivalent to

Extends from Interfaces.DiscreteBaseBlock (Partial discrete time block interfaces).

Parameters

NameDescription
Discretisation
Ts Sampling time [s]
method Discretisation method
Block parameters
num[:] Numerators coefficients (4*s + 2) is {4,2}
den[:] Denumerators coefficients (4*s + 2) is {4,2}
Initial conditions
y_start Output initial value
initOutput Initialise the output
initSteadyState Initialise at steady state
initSteadyOutput Initialise at steady output

Connectors

NameDescription
uinput
youtput

IndustrialControlSystems.LinearSystems.Discrete.Delay IndustrialControlSystems.LinearSystems.Discrete.Delay

Unitary time delay

Information

  

Description

Discrete version of the single step time delay.

   Y(s) = e^(-s*Ts)*U(s)
  

The delay must be positive T >= 0.

Extends from LinearSystems.Interfaces.DiscreteBaseBlock (Partial discrete time block interfaces).

Parameters

NameDescription
Discretisation
Ts Sampling time [s]
method Discretisation method
Initial conditions
y_start Output initial value

Connectors

NameDescription
uinput
youtput

IndustrialControlSystems.LinearSystems.Discrete.MultiStepsDelay IndustrialControlSystems.LinearSystems.Discrete.MultiStepsDelay

Multistep time delay

Information

  

Description

Discrete version of the multistep time delay.

   Y(s) = e^(-s*N*Ts)*U(s)
  

The delay must be positive T >= 0.

Extends from LinearSystems.Interfaces.DiscreteBaseBlock (Partial discrete time block interfaces).

Parameters

NameDescription
NFixed multi-step dalay
y_startInitial output value
Discretisation
Ts Sampling time [s]
method Discretisation method

Connectors

NameDescription
uinput
youtput

Automatically generated Mon May 21 13:34:15 2012.