Discrete or continuous time low pass filter (2023)

Table of Contents
Description equations initial conditions Limitation of the integral Bypass filter dynamics examples ports Entry Tu—filter inputVector Production j—filter outputVector Parameter Win—filter gain 1(Default) | positive number constant time—filter time constant 1(Default) | positive number Upper limit of saturation—state cap inf(Default) | Real number Lower limit of saturation—lower state border -inf(Default) | Real number initialization—Specification of the initial state Inherited from block input(Standard) |Specify as a parameter initial state—initial state 0(Default) | Real number Sample Time (-1 for Legacy)—block sampling time -1(Standard) |0| positive Skala references advanced skills C/C++ code generation Generate C and C++ code with Simulink® CoderTM. history See also blocks ComandoMATLAB America Europa Pacific Asia Videos

Discrete or continuous-time low-pass filter

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  • Discrete or continuous time low pass filter (1)

Libraries:
Simscape / Electrical / Controls / General Controls

Description

IsLow-pass filter (discrete or continuous)block implements a low-pass filter according to IEEE 421.5-2016[1]. In the standard, the filter is referred to as a simple time constant.

You can switch between continuous and discrete implementation of the integrator using thesample timeParameter.

equations

Continually

To set the continuous time filter, set thesample timeproperty to0. This representation corresponds to the continuous transfer function:

GRAMM(S)=kTS+1,

Wo:

  • kis the gain of the filter.

  • Tis the time constant of the filter.

From the previous transfer function, the equations that define the filter are:

{X˙(T)=1T(kTu(T)−X(T))j(T)=X(T)   j(0)=X(0)=kTu0,

Wo:

  • Tuis filter input.

  • Xis the condition of the filter.

  • jis the output of the filter.

  • Tis the simulation time.

  • Tu0is the initial input for the block.

Discreet

(Video) DSP Lecture 14: Continuous-time filtering with digital systems; upsampling and downsampling

To configure the discrete time filter, configure thesample time-Property to a positive non-zero value or on-1to inherit the sample time from a previous block. The discrete representation corresponds to the transfer function:

GRAMM(z)=k(TS/T)z−11+(TS/T−1)z−1,

Wo:

  • kis the gain of the filter.

  • Tis the time constant of the filter.

  • TSis the filter sampling time.

Starting from the discrete transfer function, the filter equations are defined by the direct Euler method:

Wo:

  • Tuis the input of the filter.

  • Xis the condition of the filter.

  • jis the output of the filter.

  • Norteis the simulation time step.

  • Tu0is the initial input for the block.

initial conditions

To specify the initial conditions for this block, setinitializationA:

  • Inherited from block input— The block sets the initial output state and conditions to the initial input.

  • Specify as a parameter— The block sets the initial condition of the state to the value ofinitial state.

Limitation of the integral

ChooseUpper limit of saturationjLower limit of saturationParameter to use anti-windup saturation method.

The anti-windup technique limits the state of the integrator between the lower saturation limitAand upper saturation limitB:

A<=X<=B .

Because the state is clipped, the output can respond immediately to an input sign reversal when the integral saturates. This block diagram shows the implementation of the anti-windup saturation method in the filter.

Discrete or continuous time low pass filter (2)

This block does not provide a saturation accounting method. To use the windup saturation method, set theUpper limit of saturationParameter ainf, IsLower limit of saturationParameter a-infand append asaturationblock at the exit.

Bypass filter dynamics

Set the time constant to a value less than or equal to the sample time to ignore filter dynamics. If omitted, the block feeds the gain-scaled input directly to the output:

T≤TS→j=kTu

In the continuous case, the sampling time and the time constant must be zero.

examples

Electric motor DynoModel an electric vehicle dynamometer test. The test environment contains an asynchronous machine (ASM) and an indoor permanent magnet synchronous machine (IPMSM) connected back-to-back via a mechanical axis. Both machines are powered by high-voltage batteries via regulated three-phase converters. The 164 kW ASM generates the loading torque. The 35 kW IPMSM is the electric machine tested. The Control Machine Under Test (IPMSM) subsystem controls the torque of the IPMSM. The controller includes a multi-rate PI-based control structure. The open loop torque control speed is slower than the closed loop current control speed. Task scheduling for the controller is implemented as a Stateflow® state machine. The Control Load Machine (ASM) subsystem uses a single rate to control the speed of the ASM. The visualization subsystem contains panes that you can use to view the simulation results.

open model

3-phase asynchronous drive with sensor control Monitor and analyze the operation of an asynchronous machine (ASM) by field-oriented control of the rotor with a sensor. The model shows the main circuit with three additional subsystems containing the controls, measurements and oscilloscopes. The control subsystem contains two controllers: one for the line-side (AC/DC) converter and one for the machine-side (DC/AC) converter. The Scopes subsystem contains two time ranges: one for grid-side converters and one for ASM. When the model runs, a spectrum analyzer opens and displays the frequency data for the phase A supply current.

open model

3-phase asynchronous drive with sensorless control Monitor and analyze the operation of an asynchronous machine (ASM) using field-oriented control of the sensorless rotor. The model shows the main circuit with three additional subsystems containing the controls, measurements and oscilloscopes. The control subsystem contains two controllers: one for the line-side (AC/DC) converter and one for the machine-side (DC/AC) converter. The Scopes subsystem contains two time ranges: one for grid-side converters and one for ASM. When the model runs, a spectrum analyzer opens and displays the frequency data for the phase A supply current.

open model

(Video) Discrete-time Processing of Continuous-time Signals: Equivalent Filter

ports

Entry

expand all

Low-pass filter input signal. The block uses the initial input value to determine the initial value of the state.

Type of data:einzel|double

Production

expand all

low pass filter output.

Type of data:einzel|double

(Video) Applied DSP No. 6: Digital Low-Pass Filters

Parameter

expand all

Gain of the low-pass filter.

Time constant of the low-pass filter. Set this value to less than in the discrete implementationsample timeto bypass the dynamics of the filter.

Upper state limit of the low-pass filter. Set thisinffor an unsaturated upper limit or to a finite value to avoid upper unwinding of the filter's integrator.

Lower state limit of the low-pass filter. Set this-inffor an unsaturated lower bound, or to a finite value to avoid a slight reduction in the filter integrator.

Give the initial state condition for this block. For more information, seeinitial conditions.

initial state of the block.

(Video) [ ECE 6435 ] Continuous Time Filters

dependencies

To enable this parameter, setinitializationASpecify as a parameter.

Time between consecutive executions of blocks. During execution, the block generates output and updates its internal state as necessary. For more information, seeWhat is trial period?jSpecify probationary period.

For legacy discrete-time operation, set this parameter to-1. Set this parameter to a positive integer for discrete-time operation. Set this parameter to for continuous timed operation0.

If this block is in a masked subsystem or subsystem variant that supports switching between continuous and discrete operation, promote this parameter to ensure correct switching between continuous and discrete implementation of the block. For more information, seeFoster block parameters in a skin.

references

[1]IEEE Recommended Practice for Excitation System Models for Power System Stability Studies.IEEE-Standard 421.5-2016. Piscataway, NJ: IEEE-SA, 2016.

advanced skills

C/C++ code generation
Generate C and C++ code with Simulink® CoderTM.

history

Introduced in R2017b

See also

blocks

  • Filtered derivative (discrete or continuous)|Lead lag (discrete or continuous)|Washed (discreetly or continuously)|Integrator (discrete or continuous)|Wrapped-state integrator (discrete or continuous)

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Videos

                                                                                                                                                                                                                                                                                                                        
1. Discrete-time low-pass filtering.wmv



    


    
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