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NoiseVariance is the variance of this noise component. Typically, a model estimation function such as polyest determines this variance. Use this input to specify an initial value for the noise variance when you create an idpoly model. Default: N y -by- N y identity matrix. When sys0 is an identified model, its estimated parameter covariance is lost during conversion. If you want to translate the estimated parameter covariance during the conversion, use translatecov.

Specify optional comma-separated pairs of Name,Value arguments. Name is the argument name and Value is the corresponding value. Name must appear inside single quotes ' '. You can specify several name and value pair arguments in any order as Name1,Value1, Use Name,Value arguments to specify additional properties of idpoly models during model creation. If you create an idpoly model sys using the idpoly command, sys. A , sys. B , sys. C , sys. D , and sys. F contain the initial coefficient values that you specify with the A , B , C , D , and F input arguments, respectively.

If you obtain an idpoly model by identification, then sys. F contain the estimated values of the coefficients. For an idpoly model sys , each property sys. F is an alias to the corresponding Value entry in the Structure property of sys. For example, sys. A is an alias to the value of the property sys. For SISO polynomial models, the values of the numerator coefficients are stored as a row vector in order of:.

Ascending powers of z —1 or q —1 for discrete-time transfer functions. The leading coefficients of A , C , and D are fixed to 1. Any coefficient whose initial value is not known is stored as NaN. The leading coefficients of the off-diagonal entries of A are fixed to zero.

The leading coefficients of all entries of C , D , and F , are fixed to 1. The value of Variable is reflected in the display, and also affects the interpretation of the A , B , C , D , and F coefficient vectors for discrete-time models. Transport delays. IODelay contains the initial values of the transport delay that you specify with a Name,Value argument pair.

For an idpoly model sys , the property sys. IODelay is an alias to the value of the property sys. For continuous-time systems, transport delays are expressed in the time unit stored in the TimeUnit property. For discrete-time systems, transport delays are expressed as integers denoting delay of a multiple of the sample time Ts. Specify IntegrateNoise as a logical vector of length equal to the number of outputs. In this case, the corresponding D polynomial contains an additional term which is not represented in the property sys.

This integrator term is equal to [1 0] for continuous-time systems, and equal to [1 -1] for discrete-time systems. Information about the estimable parameters of the idpoly model. F contain information about the polynomial coefficients. IODelay contains information about the transport delay. IntegrateNoise contain information about the integration terms on the noise.

Each contains the following fields:. Value — Parameter values. Value contains the initial or estimated values of the A coefficients. For SISO models, each property sys. D , sys. F , and sys. IODelay is an alias to the corresponding Value entry in the Structure property of sys. For MIMO models, sys. A i,j.

Value , and similarly for the other identifiable coefficient values. Minimum — Minimum value that the parameter can assume during estimation. Free — Logical value specifying whether the parameter is a free estimation variable. For example, if B is a 3-by-3 matrix, sys.

In this case, only the diagonal entries in B are estimable. For fixed values, such as the leading coefficients in sys. Value , the corresponding value of Free is always false. Scale — Scale of the parameter's value. Scale is not used in estimation. Info — Structure array for storing parameter units and labels. The structure has Label and Unit fields. An inactive polynomial, such as the B polynomial in a time-series model, is not available as a parameter in the Structure property.

Structure contains the fields sys. IODelay , and sys. However, there is no field in sys. Structure corresponding to B , C , D , or F. An identified model includes a white Gaussian noise component e t. Typically, the model estimation function such as arx determines this variance.

Summary report that contains information about the estimation options and results when the polynomial model is obtained using estimation commands, such as polyest , armax , oe , and bj. Use Report to query a model for how it was estimated, including its:. If you obtain the polynomial model using estimation commands, the fields of Report contain information on the estimation data, options, and results.

For more information on this property and how to use it, see the Output Arguments section of the corresponding estimation command reference page and Estimation Report. Input delay for each input channel, specified as a scalar value or numeric vector. For continuous-time systems, specify input delays in the time unit stored in the TimeUnit property.

For discrete-time systems, specify input delays in integer multiples of the sample time Ts. For a system with Nu inputs, set InputDelay to an Nu -by-1 vector. Each entry of this vector is a numerical value that represents the input delay for the corresponding input channel. You can also set InputDelay to a scalar value to apply the same delay to all channels. Changing this property does not discretize or resample the model.

Use c2d and d2c to convert between continuous- and discrete-time representations. Use d2d to change the sample time of a discrete-time system. Units for the time variable, the sample time Ts , and any time delays in the model, specified as one of the following values:. Changing this property has no effect on other properties, and therefore changes the overall system behavior.

Use chgTimeUnit to convert between time units without modifying system behavior. Alternatively, use automatic vector expansion to assign input names for multi-input models. For example, if sys is a two-input model, enter:. When you estimate a model using an iddata object, data , the software automatically sets InputName to data. You can use the shorthand notation u to refer to the InputName property. Use InputUnit to keep track of input signal units. InputUnit has no effect on system behavior.

Input channel groups. The InputGroup property lets you assign the input channels of MIMO systems into groups and refer to each group by name. Specify input groups as a structure. In this structure, field names are the group names, and field values are the input channels belonging to each group. For example:. You can then extract the subsystem from the controls inputs to all outputs using:.

Alternatively, use automatic vector expansion to assign output names for multi-output models. For example, if sys is a two-output model, enter:. When you estimate a model using an iddata object, data , the software automatically sets OutputName to data. You can use the shorthand notation y to refer to the OutputName property.

Use OutputUnit to keep track of output signal units. OutputUnit has no effect on system behavior. Output channel groups. The OutputGroup property lets you assign the output channels of MIMO systems into groups and refer to each group by name. Specify output groups as a structure. In this structure, field names are the group names, and field values are the output channels belonging to each group. You can then extract the subsystem from all inputs to the measurement outputs using:.

Any text that you want to associate with the system, specified as a character vector or cell array of character vectors. For arrays of identified linear IDLTI models that are derived by sampling one or more independent variables, this property tracks the variable values associated with each model. This information appears when you display or plot the model array. Use this information to trace results back to the independent variables.

Set the field names of the data structure to the names of the sampling variables. Set the field values to the sampled variable values associated with each model in the array. All sampling variables should be numeric and scalar valued, and all arrays of sampled values should match the dimensions of the model array.

For example, if you collect data at various operating points of a system, you can identify a model for each operating point separately and then stack the results together into a single system array. An inactive polynomial, such as the B polynomial in a time series model, is not available as a parameter in the Structure property. Structure contains the fields sys. A and sys.

Variance covariance matrix of the model innovations e , specified as a scalar or a positive semidefinite matrix. An identified model includes a white Gaussian noise component e t. NoiseVariance is the variance of this noise component. Typically, the model estimation function such as polyest determines this variance. Summary report that contains information about the estimation options and results for a state-space model obtained using estimation commands, such as polyest , armax , oe , and bj.

Use Report to find estimation information for the identified model, including:. If you create the model by construction, the contents of Report are irrelevant. If you obtain the model using estimation commands, the fields of Report contain information on the estimation data, options, and results. For more information on this property and how to use it, see the Output Arguments section of the corresponding estimation command reference page and Estimation Report.

Input delay for each input channel, specified as a scalar value or numeric vector. For continuous-time systems, specify input delays in the time unit stored in the TimeUnit property. For discrete-time systems, specify input delays in integer multiples of the sample time Ts. For example, setting InputDelay to 3 specifies a delay of three sample times. For a system with N u inputs, set InputDelay to an N u -by-1 vector. Each entry of this vector is a numerical value that represents the input delay for the corresponding input channel.

You can also set InputDelay to a scalar value to apply the same delay to all channels. In estimation, InputDelay is a fixed constant of the model. The software uses the IODelay property for estimating time delays. To specify initial values and constraints for estimation of time delays, use sys. Output delay for each output channel, specified as 0.

This value is fixed for identified systems such as idpoly. Discrete-time model with an unspecified sample time — Discrete-time model with a specified sampling time — Positive scalar representing the sampling period expressed in the unit specified by the TimeUnit property of the model. Changing this property does not discretize or resample the model. Use c2d and d2c to convert between continuous- and discrete-time representations.

Use d2d to change the sample time of a discrete-time system. Units for the time variable, the sample time Ts , and any time delays in the model, specified as a scalar. Changing this property does not resample or convert the data. Modifying the property changes only the interpretation of the existing data. Use chgTimeUnit to convert data to different time units.

Single-input model — Character vector, for example, 'controls'. Alternatively, use automatic vector expansion to assign input names for multi-input models. For example, if sys is a two-input model, enter the following:.

When you estimate a model using an iddata object data , the software automatically sets InputName to data. You can use the shorthand notation u to refer to the InputName property. Use InputUnit to keep track of input signal units.

InputUnit has no effect on system behavior. Input channel groups, specified as a structure. The InputGroup property lets you divide the input channels of MIMO systems into groups so that you can refer to each group by name. In the InputGroup structure, set field names to the group names, and field values to the input channels belonging to each group.

For example, create input groups named controls and noise that include input channels 1, 2 and 3, 5, respectively. You can then extract the subsystem from the controls inputs to all outputs using the following syntax:. Single-input model — Character vector, for example, 'measurements'. Alternatively, use automatic vector expansion to assign output names for multi-output models. For example, if sys is a two-output model, enter the following:.

When you estimate a model using an iddata object data , the software automatically sets OutputName to data. You can use the shorthand notation y to refer to the OutputName property. Single-input model — Character vector, for example, 'seconds'. Use OutputUnit to keep track of output signal units. OutputUnit has no effect on system behavior. Output channel groups, specified as a structure.

The OutputGroup property lets you divide the output channels of MIMO systems into groups and refer to each group by name. In the OutputGroup structure, set field names to the group names, and field values to the output channels belonging to each group. For example, create output groups named temperature and measurement that include output channels 1, and 3, 5, respectively.

You can then extract the subsystem from all inputs to the measurement outputs using the following syntax:. For a single note, specify Notes as a string or a character vector. For multiple notes, specify Notes as a string array. The property preserves the string or character data type that you specify. When you specify a character vector, the software packages the character vector in a 1-by-1 cell array. For example, if sys1 , sys2 , and sys3 are dynamic system models, you can set their Notes properties as follows.

For arrays of identified linear IDLTI models that you derive by sampling one or more independent variables, this property tracks the variable values associated with each model. This information appears when you display or plot the model array. Use this information to trace results back to the independent variables. Set the field names of the data structure to the names of the sampling variables. Set the field values to the sampled variable values associated with each model in the array. All sampling variables must be numeric and scalar valued, and all arrays of sampled values must match the dimensions of the model array.

For example, suppose that you collect data at various operating points of a system. You can identify a model for each operating point separately and then stack the results together into a single system array. You can tag the individual models in the array with information regarding the operating point.

Here, sys is an array containing three identified models obtained at , , and rpm, respectively. In general, any function applicable to Dynamic System Models is applicable to an idpoly model object. These functions are of four general types. Functions that operate and return idpoly model objects enable you to transform and manipulate idpoly models. For instance:. Use merge to merge estimated idpoly models. Use c2d to convert an idpoly model from continuous to discrete time.

Use d2c to convert an idpoly model from discrete to continuous time. Functions that perform analytical and simulation functions on idpoly models, such as bode and sim. Functions that retrieve or interpret model information, such as advice and getpar. Functions that convert idpoly models into a different model type, such as idtf for time domain or idfrd for frequency domain. The following lists contain a representative subset of the functions that you can use with idpoly models.

Create an idpoly model representing the single-input, single-output ARMAX model described by the following equation:. To create the idpoly model, define the A , B , and C polynomials that describe the relationships between the output, input, and noise values, respectively. Because there are no denominator terms in the system equation, D and F are 1.

The display shows all the polynomials and allows you to verify them. The display also states that there are five free coefficients. Create an idpoly model with specified noise variance nv and sample time Ts.

To do so, you must also include values of 1 for D and F. Specify an input-output delay iod of one sample when you create an idpoly model. You can use sys to specify an initial parameterization for estimation with commands such as polyest or armax. Create an idpoly model representing the single-output ARMA model described by the following equation:.

Because a time series has no measured inputs, this model contains only A and C polynomials. Create a continuous-time time-series by specifying a sample time of 0 for the name-value pair argument 'Ts'. You can also set the sample time using the Ts input argument rather than the name-value pair argument, but the syntax is more complex. You must specify the D value as 1 or empty, and set both the F position and the noise variance position if you are not specifying noise variance to empty.

Create an idpoly model representing the one-input, two-output ARMAX model described by the following equations:. To create the idpoly model, define the A , B , and C polynomials that describe the relationships between the outputs, inputs, and noise values. Because there are no denominator terms in the system equations, D and F are 1. Define the cell array containing the coefficients of the A polynomials. You can read the values of each entry in the A cell array from the left side of the equations describing the system.

Define the cell array containing the coefficients of the B polynomials. B describes the polynomials that give the dependence of the outputs y 1 and y 2 on the input u. Define the cell array containing the coefficients of the C polynomials. C describes the polynomials that give the dependence of the outputs y 1 and y 2 on the noise terms e 1 and e 2. The entries of C can be read from the equations similarly to those of A and B.

The display also states that there are 12 free coefficients. Leading terms of diagonal entries in A are always fixed to 1. Leading terms of all other entries in A are always fixed to 0. Model a dynamic system using a transfer function. Then use idpoly to convert the transfer-function model into polynomial form. Using idtf , construct the continuous-time, single-input, single-output SISO transfer function model described by the following equation:. Choose a web site to get translated content where available and see local events and offers.

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Search MathWorks. Open Mobile Search. Off-Canvas Navigation Menu Toggle. Main Content. Description An idpoly model represents a system as a continuous-time or discrete-time polynomial model with identifiable estimable coefficients. Creation You can obtain an idpoly model in one of three ways.

Input Arguments expand all sys0 — Dynamic system dynamic system model. For each polynomial, the coefficients are stored in the following order: Ascending powers of z —1 or q —1 for discrete-time polynomial models. B — Not constrained F — Fixed to 1. B — [] C — 1 for all outputs D — 1 for all outputs F — []. IODelay — Transport delays 0 default scalar numeric array. IntegrateNoise — Presence of integration on noise channels logical vector of zeros default logical vector.

Structure — Information about the estimable parameters structure property values. For a system with N y outputs and N u inputs, the dimensions of the Structure elements are as follows: sys. Field Description Examples Value Parameter values.

Each property is an alias of the corresponding Value entry in the Structure property of sys. NaN represents unknown parameter values. A is an alias of the value of this property. A i,j. Minimum Minimum value that the parameter can assume during estimation sys. Minimum must be greater than or equal to zero. Maximum Maximum value that the parameter can assume during estimation Free Boolean specifying whether the parameter is a free estimation variable.

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Asked 9 years, 1 month ago. Modified 9 years, 1 month ago. Viewed times. Improve this question. Add a comment. Sorted by: Reset to default. Highest score default Date modified newest first Date created oldest first. Improve this answer. Sign up or log in Sign up using Google.

Sign up using Facebook. Sign up using Email and Password. Post as a guest Name. Email Required, but never shown. The Overflow Blog. Privacy is a moving target. Featured on Meta. Estimate the idpoly model based on output or input-output measurements of a system, using commands such as polyest , arx , armax , oe , bj , iv4 , or ivar. These commands estimate the values of the free polynomial coefficients. The estimated values are stored in the A , B , C , D , and F properties of the resulting idpoly model.

The Report property of the resulting model stores information about the estimation, such as handling of initial conditions and options used in estimation. When you obtain an idpoly model by estimation, you can extract estimated coefficients and their uncertainties from the model using commands such as polydata , getpar , or getcov. Create an idpoly model using the idpoly command. You can create an idpoly model to configure an initial parameterization for estimation of a polynomial model to fit measured response data.

When you do so, you can specify constraints on the polynomial coefficients. For example, you can fix the values of some coefficients, or specify minimum or maximum values for the free coefficients. You can then use the configured model as an input argument to polyest to estimate parameter values with those constraints.

Convert an existing dynamic system model to an idpoly model using the idpoly command. Create an idpoly model representing the one-input, two-output ARMAX model described by the following equations:. To create the idpoly model, define the A , B , and C polynomials that describe the relationships between the outputs, inputs, and noise values.

Because there are no denominator terms in the system equations, B and F are 1. You can read the values of each entry in the A cell array from the left side of the equations describing the system. This polynomial is , because each factor of corresponds to a unit time decrement.

From the equations,. B describes the polynomials that give the dependence of the outputs and on the input. Similarly, from the equations,. C describes the polynomials that give the dependence of the outputs and on the noise terms and. The entries of C can be read from the equations similarly to those of A and B. The display shows all the polynomials and allows you to verify them. The display also states that there are 12 free coefficients. Leading terms of diagonal entries in A are always fixed to 1.

Leading terms of all other entries in A are always fixed to 0. You can use sys to specify an initial parametrization for estimation with such commands as polyest or armax. For SISO models, specify the initial values of the polynomial coefficients as row vectors. Specify the coefficients in order of:. Ascending powers of z —1 or q —1 for discrete-time polynomial models.

The leading coefficients of A , C , D , and F must be 1. Use NaN for any coefficient whose initial value is not known. Each entry in the cell array contains the coefficients of a particular polynomial that relates input, output, and noise values.

The leading coefficients of the off-diagonal entries of A must be zero, for causality. The leading coefficients of all entries of C , D , and F , must be 1. Use [] for any polynomial that is not present in the wanted model structure. Sample time. For discrete-time models, Ts is a positive scalar representing the sample time expressed in the unit specified by the TimeUnit property of the model.

Default: —1 discrete-time model with unspecified sample time. An identified model includes a white, Gaussian noise component e t. NoiseVariance is the variance of this noise component. Typically, a model estimation function such as polyest determines this variance.

Use this input to specify an initial value for the noise variance when you create an idpoly model. Default: N y -by- N y identity matrix. When sys0 is an identified model, its estimated parameter covariance is lost during conversion. If you want to translate the estimated parameter covariance during the conversion, use translatecov.

Specify optional comma-separated pairs of Name,Value arguments. Name is the argument name and Value is the corresponding value. Name must appear inside single quotes ' '. You can specify several name and value pair arguments in any order as Name1,Value1, Use Name,Value arguments to specify additional properties of idpoly models during model creation.

If you create an idpoly model sys using the idpoly command, sys. A , sys. B , sys. C , sys. D , and sys. F contain the initial coefficient values that you specify with the A , B , C , D , and F input arguments, respectively. If you obtain an idpoly model by identification, then sys. F contain the estimated values of the coefficients. For an idpoly model sys , each property sys. F is an alias to the corresponding Value entry in the Structure property of sys.

For example, sys. A is an alias to the value of the property sys. For SISO polynomial models, the values of the numerator coefficients are stored as a row vector in order of:. Ascending powers of z —1 or q —1 for discrete-time transfer functions. The leading coefficients of A , C , and D are fixed to 1. Any coefficient whose initial value is not known is stored as NaN.

The leading coefficients of the off-diagonal entries of A are fixed to zero. The leading coefficients of all entries of C , D , and F , are fixed to 1. The value of Variable is reflected in the display, and also affects the interpretation of the A , B , C , D , and F coefficient vectors for discrete-time models. Transport delays. IODelay contains the initial values of the transport delay that you specify with a Name,Value argument pair. For an idpoly model sys , the property sys.

IODelay is an alias to the value of the property sys. For continuous-time systems, transport delays are expressed in the time unit stored in the TimeUnit property. For discrete-time systems, transport delays are expressed as integers denoting delay of a multiple of the sample time Ts. Specify IntegrateNoise as a logical vector of length equal to the number of outputs. In this case, the corresponding D polynomial contains an additional term which is not represented in the property sys.

This integrator term is equal to [1 0] for continuous-time systems, and equal to [1 -1] for discrete-time systems. Information about the estimable parameters of the idpoly model. F contain information about the polynomial coefficients. IODelay contains information about the transport delay. IntegrateNoise contain information about the integration terms on the noise. Each contains the following fields:.

Value — Parameter values. Value contains the initial or estimated values of the A coefficients. For SISO models, each property sys. D , sys. F , and sys. IODelay is an alias to the corresponding Value entry in the Structure property of sys. For MIMO models, sys. A i,j. Value , and similarly for the other identifiable coefficient values.

Minimum — Minimum value that the parameter can assume during estimation. Free — Logical value specifying whether the parameter is a free estimation variable. For example, if B is a 3-by-3 matrix, sys. In this case, only the diagonal entries in B are estimable. For fixed values, such as the leading coefficients in sys. Value , the corresponding value of Free is always false. Scale — Scale of the parameter's value. Scale is not used in estimation.

Info — Structure array for storing parameter units and labels. The structure has Label and Unit fields. An inactive polynomial, such as the B polynomial in a time-series model, is not available as a parameter in the Structure property. Structure contains the fields sys. IODelay , and sys. However, there is no field in sys. Structure corresponding to B , C , D , or F. An identified model includes a white Gaussian noise component e t.

Typically, the model estimation function such as arx determines this variance. Summary report that contains information about the estimation options and results when the polynomial model is obtained using estimation commands, such as polyest , armax , oe , and bj. Use Report to query a model for how it was estimated, including its:. If you obtain the polynomial model using estimation commands, the fields of Report contain information on the estimation data, options, and results.

For more information on this property and how to use it, see the Output Arguments section of the corresponding estimation command reference page and Estimation Report. Input delay for each input channel, specified as a scalar value or numeric vector. For continuous-time systems, specify input delays in the time unit stored in the TimeUnit property.

For discrete-time systems, specify input delays in integer multiples of the sample time Ts. For a system with Nu inputs, set InputDelay to an Nu -by-1 vector.

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