Modelica.Blocks.Nonlinear

Library of discontinuous or non-differentiable algebraic control blocks

Information

This package contains discontinuous and non-differentiable, algebraic input/output blocks.

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

Package Content

Name	Description
Limiter	Limit the range of a signal
VariableLimiter	Limit the range of a signal with variable limits
SlewRateLimiter	Limits the slew rate of a signal
DeadZone	Provide a region of zero output
FixedDelay	Delay block with fixed DelayTime
PadeDelay	Pade approximation of delay block with fixed DelayTime
VariableDelay	Delay block with variable DelayTime

Modelica.Blocks.Nonlinear.Limiter

Limit the range of a signal

Information

The Limiter block passes its input signal as output signal as long as the input is within the specified upper and lower limits. If this is not the case, the corresponding limits are passed as output.

Extends from Interfaces.SISO (Single Input Single Output continuous control block).

Parameters

Name Description

uMax Upper limits of input signals

uMin Lower limits of input signals

Advanced

strict = true, if strict limits with noEvent(..)

limitsAtInit = false, if limits are ignored during initialization (i.e., y=u)

Name	Description
uMax	Upper limits of input signals
uMin	Lower limits of input signals
Advanced
strict	= true, if strict limits with noEvent(..)
limitsAtInit	= false, if limits are ignored during initialization (i.e., y=u)

Connectors

Name Description

u Connector of Real input signal

y Connector of Real output signal

Name	Description
u	Connector of Real input signal
y	Connector of Real output signal

Modelica.Blocks.Nonlinear.VariableLimiter

Limit the range of a signal with variable limits

Information

The Limiter block passes its input signal as output signal as long as the input is within the upper and lower limits specified by the two additional inputs limit1 and limit2. If this is not the case, the corresponding limit is passed as output.

Extends from Interfaces.SISO (Single Input Single Output continuous control block).

Parameters

Name Description

strict = true, if strict limits with noEvent(..)

limitsAtInit = false, if limits are ignored during initialization (i.e., y=u)

Name	Description
strict	= true, if strict limits with noEvent(..)
limitsAtInit	= false, if limits are ignored during initialization (i.e., y=u)

Connectors

Name Description

u Connector of Real input signal

y Connector of Real output signal

limit1 Connector of Real input signal used as maximum of input u

limit2 Connector of Real input signal used as minimum of input u

Name	Description
u	Connector of Real input signal
y	Connector of Real output signal
limit1	Connector of Real input signal used as maximum of input u
limit2	Connector of Real input signal used as minimum of input u

Modelica.Blocks.Nonlinear.SlewRateLimiter

Limits the slew rate of a signal

Information

The SlewRateLimiter block limits the slew rate of its input signal in the range of [Falling, Rising].

To ensure this for arbitrary inputs and in order to produce a differential output, the input is numerically differentiated with derivative time constant Td. Smaller time constant Td means nearer ideal derivative.

Note: The user has to choose the derivative time constant according to the nature of the input signal.

Extends from Modelica.Blocks.Interfaces.SISO (Single Input Single Output continuous control block).

Parameters

Name Description

Rising Maximum rising slew rate [+small..+inf) [s-1]

Falling Maximum falling slew rate (-inf..-small] [s-1]

Td Derivative time constant [s]

Advanced

strict = true, if strict limits with noEvent(..)

Name	Description
Rising	Maximum rising slew rate [+small..+inf) [s-1]
Falling	Maximum falling slew rate (-inf..-small] [s-1]
Td	Derivative time constant [s]
Advanced
strict	= true, if strict limits with noEvent(..)

Connectors

Name Description

u Connector of Real input signal

y Connector of Real output signal

Name	Description
u	Connector of Real input signal
y	Connector of Real output signal

Modelica.Blocks.Nonlinear.DeadZone

Provide a region of zero output

Information

The DeadZone block defines a region of zero output.

If the input is within uMin ... uMax, the output is zero. Outside of this zone, the output is a linear function of the input with a slope of 1.

Extends from Interfaces.SISO (Single Input Single Output continuous control block).

Parameters

Name Description

uMax Upper limits of dead zones

uMin Lower limits of dead zones

deadZoneAtInit = false, if dead zone is ignored during initialization (i.e., y=u)

Name	Description
uMax	Upper limits of dead zones
uMin	Lower limits of dead zones
deadZoneAtInit	= false, if dead zone is ignored during initialization (i.e., y=u)

Connectors

Name Description

u Connector of Real input signal

y Connector of Real output signal

Name	Description
u	Connector of Real input signal
y	Connector of Real output signal

Modelica.Blocks.Nonlinear.FixedDelay

Delay block with fixed DelayTime

Information

The Input signal is delayed by a given time instant, or more precisely:

   y = u(time - delayTime) for time > time.start + delayTime
     = u(time.start)       for time ≤ time.start + delayTime

Extends from Modelica.Blocks.Interfaces.SISO (Single Input Single Output continuous control block).

Parameters

Name Description

delayTime Delay time of output with respect to input signal [s]

Name	Description
delayTime	Delay time of output with respect to input signal [s]

Connectors

Name Description

u Connector of Real input signal

y Connector of Real output signal

Name	Description
u	Connector of Real input signal
y	Connector of Real output signal

Modelica.Blocks.Nonlinear.PadeDelay

Pade approximation of delay block with fixed DelayTime

Information

The Input signal is delayed by a given time instant, or more precisely:

   y = u(time - delayTime) for time > time.start + delayTime
     = u(time.start)       for time ≤ time.start + delayTime

The delay is approximated by a Pade approximation, i.e., by a transfer function

           b[1]*s^m + b[2]*s^[m-1] + ... + b[m+1]
   y(s) = --------------------------------------------- * u(s)
           a[1]*s^n + a[2]*s^[n-1] + ... + a[n+1]

where the coefficients b[:] and a[:] are calculated such that the coefficients of the Taylor expansion of the delay exp(-T*s) around s=0 are identical upto order n+m.

The main advantage of this approach is that the delay is approximated by a linear differential equation system, which is continuous and continuously differentiable. For example, it is uncritical to linearize a system containing a Pade-approximated delay.

The standard text book version uses order "m=n", which is also the default setting of this block. The setting "m=n-1" may yield a better approximation in certain cases.

Literature:

Otto Foellinger: Regelungstechnik, 8. Auflage, chapter 11.9, page 412-414, Huethig Verlag Heidelberg, 1994

Extends from Modelica.Blocks.Interfaces.SISO (Single Input Single Output continuous control block).

Parameters

Name Description

delayTime Delay time of output with respect to input signal [s]

n Order of Pade approximation

m Order of numerator

Name	Description
delayTime	Delay time of output with respect to input signal [s]
n	Order of Pade approximation
m	Order of numerator

Connectors

Name Description

u Connector of Real input signal

y Connector of Real output signal

Name	Description
u	Connector of Real input signal
y	Connector of Real output signal

Modelica.Blocks.Nonlinear.VariableDelay

Delay block with variable DelayTime

Information

The Input signal is delayed by a given time instant, or more precisely:

   y = u(time - delayTime) for time > time.start + delayTime
     = u(time.start)       for time ≤ time.start + delayTime

where delayTime is an additional input signal which must follow the following relationship:

  0 ≤ delayTime ≤ delayMax

Extends from Modelica.Blocks.Interfaces.SISO (Single Input Single Output continuous control block).

Parameters

Name Description

delayMax maximum delay time

Name	Description
delayMax	maximum delay time

Connectors

Name Description

u Connector of Real input signal

y Connector of Real output signal

delayTime

Name	Description
u	Connector of Real input signal
y	Connector of Real output signal
delayTime

Automatically generated Mon Sep 23 17:20:25 2013.