Estimate process model using time or frequency data

`[`

returns
the estimated value of the offset in input signal. Input offset is
automatically estimated when the model contains an integrator, or
when you set the `sys`

,`offset`

] = procest(___)`InputOffset`

estimation option
to `'estimate'`

using `procestOptions`

.
Use `offset`

with any of the previous syntaxes.

`data`

— Estimation data`iddata`

| `idfrd`

| `frd`

Estimation data, specified as an `iddata`

object
containing the input and output signal values, for time-domain estimation.
For frequency-domain estimation, `data`

can be
one of the following:

`iddata`

object with its properties specified as follows:`InputData`

— Fourier transform of the input signal`OutputData`

— Fourier transform of the output signal`Domain`

—`'Frequency'`

`data`

must have at least one input and one
output.

Time-series models, which are models that contain no measured
inputs, cannot be estimated using `procest`

. Use `ar`

, `arx`

,
or `armax`

for time-series models instead.

`type`

— Process model structurestringProcess model structure, specified as a string representing
an acronym for the model structure, such as `'P1D'`

or `'P2DZ'`

.
The acronym string is made up of:

`P`

— All`'Type'`

acronyms start with this letter.`0`

,`1`

,`2`

, or`3`

— Number of time constants (poles) to be modeled. Possible integrations (poles in the origin) are not included in this number.`I`

— Integration is enforced (self-regulating process).`D`

— Time delay (dead time).`Z`

— Extra numerator term, a zero.`U`

— Underdamped modes (complex-valued poles) permitted. If`U`

is not included in`type`

, all poles must be real. The number of poles must be 2 or 3.

For information regarding how `type`

affects
the structure of a process model, see `idproc`

.

For multiple input/output pairs use a cell array of acronyms, with one entry for each input/output pair.

`InputDelay`

— Input delays`0`

for all input channels (default) | numeric vectorInput delays, specified as a numeric vector specifying a time
delay for each input channel. Specify input delays in the time unit
stored in the `TimeUnit`

property.

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.

`init_sys`

— System for configuring initial parametrization`idproc`

objectSystem for configuring initial parametrization of `sys`

,
specified as an `idproc`

object. You obtain `init_sys`

by
either performing an estimation using measured data or by direct construction
using `idproc`

. The software uses
the parameters and constraints defined in `init_sys`

as
the initial guess for estimating `sys`

.

Use the `Structure`

property of `init_sys`

to
configure initial guesses and constraints for *Kp*, *T _{p1}*,

To specify an initial guess for the

*T*parameter of_{p1}`init_sys`

, set`init_sys.Structure.Tp1.Value`

as the initial guess.To specify constraints for the

*T*parameter of_{p2}`init_sys`

:Set

`init_sys.Structure.Tp2.Minimum`

to the minimum*T*value._{p2}Set

`init_sys.Structure.Tp2.Maximum`

to the maximum*T*value._{p2}Set

`init_sys.Structure.Tp2.Free`

to indicate if*T*is a free parameter for estimation._{p2}

If `opt`

is not specified, and `init_sys`

was
obtained by estimation, then the estimation options from `init_sys.Report.OptionsUsed`

are
used.

`opt`

— Estimation options`procestOptions`

option setEstimation options, specified as an `procestOptions`

option
set. The estimation options include:

Estimation objective

Handling on initial conditions and disturbance component

Numerical search method to be used in estimation

`sys`

— Identified process model`idproc`

modelIdentified process model, returned as an `idproc`

model
of a structure defined by `type`

.

Information about the estimation results and options used is
stored in the model's `Report`

property. `Report`

has
the following fields:

Report Field | Description | ||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

`Status` | Summary of the model status, which indicates whether the model was created by construction or obtained by estimation. | ||||||||||||||||||

`Method` | Estimation command used. | ||||||||||||||||||

`InitialCondition` | Handling of initial conditions during model estimation, returned as a string with one of the following values: `'zero'` — The initial conditions were set to zero.`'estimate'` — The initial conditions were treated as independent estimation parameters.`'backcast'` — The initial conditions were estimated using the best least squares fit.
This field is especially useful to view
how the initial conditions were handled when the | ||||||||||||||||||

`Fit` | Quantitative assessment of the estimation, returned as a structure. See Loss Function and Model Quality Metrics for more information on these quality metrics. The structure has the following fields:
| ||||||||||||||||||

`Parameters` | Estimated values of model parameters. | ||||||||||||||||||

`OptionsUsed` | Option set used for estimation. If no custom options
were configured, this is a set of default options. See | ||||||||||||||||||

`RandState` | State of the random number stream at the start of estimation.
Empty, | ||||||||||||||||||

`DataUsed` | Attributes of the data used for estimation. Structure with the following fields:
| ||||||||||||||||||

`Termination` | Termination conditions for the iterative search used for prediction error minimization. Structure with the following fields:
For
estimation methods that do not require numerical search optimization,
the |

For more information on using `Report`

, see Estimation Report.

`offset`

— Estimated value of input offsetvectorEstimated value of input offset, returned as a vector. When `data`

has
multiple experiments, `offset`

is a matrix where
each column corresponds to an experiment.

Obtain the measured input-output data.

load iddemo_heatexchanger_data; data = iddata(pt,ct,Ts); data.InputName = '\Delta CTemp'; data.InputUnit = 'C'; data.OutputName = '\Delta PTemp'; data.OutputUnit = 'C'; data.TimeUnit = 'minutes';

Estimate a first-order plus dead time process model.

```
type = 'P1D';
sysP1D = procest(data,type);
```

Compare the model with the data.

compare(data,sysP1D)

Plot the model residuals.

figure resid(data,sysP1D);

The figure shows that the residuals are correlated. To account for that, add a first order ARMA disturbance component to the process model.

opt = procestOptions('DisturbanceModel','ARMA1'); sysP1D_noise = procest(data,'p1d',opt);

Compare the models.

compare(data,sysP1D,sysP1D_noise)

Plot the model residuals.

figure resid(data,sysP1D_noise);

The residues of `sysP1D_noise`

are uncorrelated.

Use regularization to estimate parameters of an over-parameterized process model.

Assume that gain is known with a higher degree of confidence than other model parameters.

Load data.

load iddata1 z1;

Estimate an unregularized process model.

m = idproc('P3UZ','K',7.5,'Tw',0.25,'Zeta',0.3,'Tp3',20,'Tz',0.02); m1 = procest(z1,m);

Estimate a regularized process model.

```
opt = procestOptions;
opt.Regularization.Nominal = 'model';
opt.Regularization.R = [100;1;1;1;1];
opt.Regularization.Lambda = 0.1;
m2 = procest(z1,m,opt);
```

Compare the model outputs with data.

compare(z1,m1,m2);

Regularization helps steer the estimation process towards the correct parameter values.

Estimate a process model after specifying initial guesses for parameter values and bounding them.

Obtain input/output data.

```
data = idfrd(idtf([10 2],[1 1.3 1.2],'iod',0.45),logspace(-2,2,256));
```

Specify the parameters of the estimation initialization model.

```
type = 'P2UZD';
init_sys = idproc(type);
init_sys.Structure.Kp.Value = 1;
init_sys.Structure.Tw.Value = 2;
init_sys.Structure.Zeta.Value = 0.1;
init_sys.Structure.Td.Value = 0;
init_sys.Structure.Tz.Value = 1;
init_sys.Structure.Kp.Minimum = 0.1;
init_sys.Structure.Kp.Maximum = 10;
init_sys.Structure.Td.Maximum = 1;
init_sys.Structure.Tz.Maximum = 10;
```

Specify the estimation options.

opt = procestOptions('Display','full','InitialCondition','Zero'); opt.SearchMethod = 'lm'; opt.SearchOption.MaxIter = 100;

Estimate the process model.

sys = procest(data,init_sys,opt);

Since the `'Display'`

option is specified as `'full'`

, the estimation progress is displayed in a separate **Plant Identification Progress** window.

Compare the data to the estimated model.

compare(data,sys,init_sys);

Obtain input/output data.

load iddata1 z1 load iddata2 z2 data = [z1 z2(1:300)];

`data`

is a data set with 2 inputs and 2 outputs. The first input affects only the first output. Similarly, the second input affects only the second output.

In the estimated process model, the cross terms, modeling the effect of the first input on the second output and vice versa, should be negligible. If higher orders are assigned to those dynamics, their estimations show a high level of uncertainty.

Estimate the process model.

```
type = 'P2UZ';
sys = procest(data,type);
```

The `type`

variable denotes a model with complex-conugate pair of poles, a zero, and a delay.

To evaluate the uncertainties, plot the frequency response.

w = linspace(0,20*pi,100); h = bodeplot(sys,w); showConfidence(h);

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