伝達関数モデル

伝達関数モデルは、多項式の比を使用してシステムの入力と出力間の関係を記述します。"モデル次数" は、分母多項式の次数と等しくなります。分母多項式の根はモデルの "極" と呼ばれます。分子多項式の根はモデルの "零点" と呼ばれます。

伝達関数モデルのパラメーターはその極、零点、および伝達遅延です。

連続時間では、伝達関数モデルは次の形式になります。

$Y (s) = \frac{n u m (s)}{d e n (s)} U (s) + E (s)$

ここで、Y(s)、U(s)、および E(s) はそれぞれ出力、入力、およびノイズのラプラス変換を表します。num(s) および den(s) は、入力と出力間の関係を定義する分子多項式と分母多項式を表します。

詳細については、What are Transfer Function Models?を参照してください。

アプリ

Identify models of dynamic systems from measured data

`idtf`	Transfer function model with identifiable parameters
`tfest`	Estimate transfer function
`pem`	Prediction error minimization for refining linear and nonlinear models

`delayest`	Estimate time delay (dead time) from data
`init`	Set or randomize initial parameter values

`tfdata`	伝達関数データにアクセスする
`getpvec`	Obtain model parameters and associated uncertainty data
`setpvec`	Modify values of model parameters
`getpar`	Obtain attributes such as values and bounds of linear model parameters
`setpar`	Set attributes such as values and bounds of linear model parameters

tfestOptions Option set for tfest

What are Transfer Function Models?
Transfer function models describe the relationship between the inputs and outputs of a system using a ratio of polynomials. The model order is equal to the order of the denominator polynomial. The roots of the denominator polynomial are referred to as the model poles. The roots of the numerator polynomial are referred to as the model zeros.
Estimate Transfer Function Models in the System Identification App
Use the app to set model configuration and estimation options for estimating a transfer function model.
Estimate Transfer Function Models at the Command Line
General workflow for estimating transfer function models at the command line.
Data Supported by Transfer Function Models
Characteristics of estimation data for transfer function identification.

Estimate Transfer Function Models by Specifying Number of Poles
This example shows how to identify a transfer function containing a specified number of poles for given data.
Estimate Transfer Function Models with Transport Delay to Fit Given Frequency-Response Data
This example shows how to identify a transfer function to fit a given frequency response data (FRD) containing additional phase roll off induced by input delay.
Estimate Transfer Function Models With Prior Knowledge of Model Structure and Constraints
This example shows how to estimate a transfer function model when the structure of the expected model is known and apply constraints to the numerator and denominator coefficients.
Estimate Transfer Functions with Delays
This example shows how to estimate transfer function models with I/O delays.
Estimate Transfer Function Models with Unknown Transport Delays
This example shows how to estimate a transfer function model with unknown transport delays and apply an upper bound on the unknown transport delays.

Troubleshoot Frequency-Domain Identification of Transfer Function Models
Improve frequency-domain model estimation by preprocessing data and applying frequency-dependent weighting filters.

Transfer Function Structure Specification
Specify the values and constraints for the numerator, denominator and transport delays.
Specifying Initial Conditions for Iterative Estimation of Transfer Functions
Specify how initial conditions are handled during model estimation in the app and at the command line.