# compare

Compare model output and measured output

## Syntax

```compare(data,sys)compare(data,sys,prediction_horizon)compare(data,sys,style,prediction_horizon)compare(data,sys1,...,sysN,prediction_horizon)compare(data,sys1,style1,...,sysN,styleN,prediction_horizon)compare(___,opt)[y,fit,x0] = compare(___)```

## Description

`compare(data,sys)` plots the simulated response of a dynamic system model, `sys`, superimposed over validation data, `data`, for comparison. The plot also displays the normalized root mean square (NRMSE) measure of the goodness of the fit.

The matching of the input/output channels in `data` and `sys` is based on the channel names. Thus, it is possible to evaluate models that do not use all the input channels that are available in `data`.

`compare(data,sys,prediction_horizon)` compares the predicted response of `sys` to the measured response in `data`. Measured output values in data up to time `t-prediction_horizon` are used to predict the output of `sys` at time `t`.

`compare(data,sys,style,prediction_horizon)` uses `style` to specify the line type, marker symbol, and color.

`compare(data,sys1,...,sysN,prediction_horizon)` compares multiple dynamic systems responses on the same axes. `compare` automatically chooses colors and line styles in the order specified by the `ColorOrder` and `LineStyleOrder` properties of the current axes.

`compare(data,sys1,style1,...,sysN,styleN,prediction_horizon)` compares multiple systems responses on the same axes using the line type, marker symbol, and color specified for each system.

`compare(___,opt)` configures the comparison using an option set, `opt`.

```[y,fit,x0] = compare(___)``` returns the model response, `y`, goodness of fit value, `fit`, and the initial states, `x0`. No plot is generated.

## Input Arguments

 `data` Validation data. Specify data as either an `iddata` or `idfrd` object. If `sys` is an `iddata` object, then `data` must be an `iddata` object with matching domain, number of experiments and time or frequency vectors. If `sys` is a frequency response model (`idfrd` or `frd`), then `data` must be a frequency response model too. `data` can represent either time- or frequency-domain data when comparing with linear models. `data` must be time-domain data when comparing with a nonlinear model. For frequency domain data, the real and imaginary parts of the corresponding frequency functions are shown in separate axes. When `data` is an FRD model, the frequency responses of `data` and `sys` are plotted. `sys` `iddata` object or dynamic system model. When the time or frequency units of `data` do not match those of `sys`, `sys` is rescaled to match the units of `data`. `prediction_horizon` Prediction horizon. Specify `prediction_horizon` as `Inf` to obtain a pure simulation of the system. `prediction_horizon` is ignored when `sys` is an `iddata` object, an FRD model or a dynamic system with no noise component. `prediction_horizon` is also ignored when using frequency response validation data. For time-series models, use a finite value for `prediction_horizon`. Default: `Inf` `style` Line style, marker, and color of both the linear and marker, specified as a one-, two-, or three-part string enclosed in single quotes (`' '`). The elements of the string can appear in any order. The string can specify only the line style, the marker, or the color. For more information about configuring the `style` string, see Specify Line Style, Color, and Markers in the MATLAB® documentation. `opt` Comparison option set. `opt` is an option set created using `compareOptions`, which specifies options including: Handling of initial conditionsSample range for computing fit numbersData offsetsOutput weighting

## Output Arguments

 `y` Model response. Measured output values in `data` up to time ```t = t-prediction_horizon``` are used to predict the output of `sys` at time t. For multimodel comparisons, `y` is a cell array, with one entry for each input model. For multiexperiment data, `y` is a cell array, with one entry for each experiment. For multimodel comparisons using multiexperiment data, `y` is an Nsys-by-Nexp cell array. Nsys is the number of models, and Nexp is the number of experiments. If `sys` is a model array, then `y` is an array, with an entry corresponding to each model in `sys` and experiment in `data`. `fit` NRMSE fitness value. The fit is calculated (in percentage) using: $\text{fit}=100\left(1-\frac{||y-\stackrel{^}{y}||}{||y-\text{mean}\left(y\right)||}\right)$ where y is the validation data output and $\stackrel{^}{y}$ is the output of `sys`. For FRD models, `fit` is calculated by comparing the complex frequency response. The magnitude and phase curves shown in the plot are not compared separately. If `data` is an `iddata` object, `fit` is an Ny-by-1 vector, where Ny is the number of outputs. If `data` is an FRD model with Ny outputs and Nu inputs, `fit` is an Ny-by-Nu matrix. Each entry of `fit` corresponds to an input/output pair in `sys`. For multimodel comparisons, `fit` is a cell array, with one entry for each input model. For multiexperiment data, `fit` is a cell array, with one entry for each experiment. For multimodel comparisons using multiexperiment data, `fit` is an Nsys-by-Nexp cell array. Nsys is the number of models, and Nexp is the number of experiments. `x0` Initial conditions used to compute system response. When `sys` is an `frd` or `iddata` object, `x0` is `[]`. For multimodel comparisons, `x0` is a cell array, with one entry for each input model. For multiexperiment data, `x0` is a cell array, with one entry for each experiment. For multimodel comparisons using multiexperiment data, `x0` is an Nsys-by-Nexp cell array. Nsys is the number of models, and Nexp is the number of experiments.

## Examples

collapse all

### Compare Estimated Model to Measured Data

Estimate a state-space model for measured data.

```load iddata1 z1; sys = ssest(z1,3); ```

`sys`, an `idss` model, is a continuous-time state-space model.

Compare the predicted output for 10 steps ahead to the measured output.

```prediction_horizon = 10; compare(z1,sys,prediction_horizon); ```

### Compare Multiple Estimated Models to Measured Data

Compare the outputs of multiple estimated models, of differing types, to measured data.

This example compares the outputs of an estimated process model and an estimated Output-Error polynomial model to measured data.

Estimate a process model and an Output-Error polynomial for frequency response data.

```load demofr % frequency response data zfr = AMP.*exp(1i*PHA*pi/180); Ts = 0.1; data = idfrd(zfr,W,Ts); sys1 = procest(data,'P2UDZ'); sys2 = oe(data,[2 2 1]); ```

`sys1`, an `idproc` model, is a continuous-time process model. `sys2`, an `idpoly` model, is a discrete-time Output-Error model.

Compare the frequency response of the estimated models to data.

```compare(data,sys1,'g',sys2,'r'); ```

### Compare Estimated Model to Data and Specify Comparison Options

Compare an estimated model to measured data. Specify that the initial conditions be estimated such that the prediction error of the observed output is minimized.

Estimate a transfer function for measured data.

```load iddata1 z1; sys = tfest(z1,3); ```

`sys`, an `idtf` model, is a continuous-time transfer function model.

Create an option set to specify the initial condition handling.

```opt = compareOptions('InitialCondition','e'); ```

Compare the estimated transfer function model's output to the measured data using the comparison option set.

```compare(z1,sys,opt); ```