simOptions

Option set for sim

Syntax

opt = simOptions

opt = simOptions(Name,Value)

Description

opt = simOptions creates the default option set for sim.

opt = simOptions(Name,Value) creates an option set with the options specified by one or more Name,Value pair arguments.

Examples

Create Default Option Set for Model Simulation

opt = simOptions;

Specify Options for Model Simulation

Create an option set for sim specifying the following options.

• Zero initial conditions

• Input offset of 5 for the second input of a two-input model

opt = simOptions('InitialCondition','z','InputOffset',[0; 5]);

Add Noise to Simulation Output

Create noise data for a simulation with 500 input data samples and two outputs.

noiseData = randn(500,2);

Create a default option set.

opt = simOptions;

Modify the option set to add the noise data.

opt.AddNoise = true;
opt.NoiseData = noiseData;

Use Historical Data to Specify Initial Conditions for Model Simulation

Use historical input-output data as a proxy for initial conditions when simulating your model.

Load a two-input, one-output data set.

load iddata7 z7

Identify a fifth-order state-space model using the data.

sys = n4sid(z7, 5);

Split the data set into two parts.

zA = z7(1:15);
zB = z7(16:end);

Simulate the model using the input signal in zB.

uSim = zB;

Simulation requires initial conditions. The signal values in zA are the historical data, that is, they are the input and output values for the time immediately preceding data in zB. Use zA as a proxy for the required initial conditions.

IO = struct('Input',zA.InputData,'Output',zA.OutputData);
opt = simOptions('InitialCondition',IO);

Simulate the model.

ysim = sim(sys,uSim,opt);

To understand how the past data is mapped to the initial states of the model, see Understand Use of Historical Data for Model Simulation.

Obtain and Apply Estimated Initial Conditions

Load and plot the data.

load iddata1ic z1i
plot(z1i)

Examine the initial value of the output data y(1).

ystart = z1i.y(1)

ystart = 
-3.0491

The measured output does not start at 0.

Estimate a second-order transfer function sys and return the estimated initial condition ic.

[sys,ic] = tfest(z1i,2,1);
ic

ic = 
  initialCondition with properties:

     A: [2x2 double]
    X0: [2x1 double]
     C: [0.2957 5.2441]
    Ts: 0

ic is an initialCondition object that encapsulates the free response of sys, in state-space form, to the initial state vector in X0.

Simulate sys using the estimation data but without incorporating the initial conditions. Plot the simulated output with the measured output.

y_no_ic = sim(sys,z1i);
plot(y_no_ic,z1i)
legend('Model Response','Output Data')

The measured and simulated outputs do not agree at the beginning of the simulation.

Incorporate the initial condition into the simOptions option set.

opt = simOptions('InitialCondition',ic);
y_ic = sim(sys,z1i,opt);
plot(y_ic,z1i)
legend('Model Response','Output Data')

The simulation combines the model response to the input signal with the free response to the initial condition. The measured and simulated outputs now have better agreement at the beginning of the simulation. This initial condition is valid only for the estimation data z1i.

Input Arguments

Name-Value Arguments

Specify optional pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Before R2021a, use commas to separate each name and value, and enclose Name in quotes.

Example: 'AddNoise',true','InputOffset',[5;0] adds default Gaussian white noise to the response model and specifies an input offset of 5 for the first of two model inputs.

InitialCondition — Simulation initial conditions

[] (default) | column vector | matrix | initialCondition object | object array | structure | structure array | 'model'

Simulation initial conditions, specified as one of the following:

• 'z' — Zero initial conditions.

• Numerical column vector of initial states with length equal to the model order.

  For multiexperiment data, specify a matrix with Ne columns, where Ne is the number of experiments, to configure the initial conditions separately for each experiment. Otherwise, use a column vector to specify the same initial conditions for all experiments.

  Use this option for state-space models (idss and idgrey) only.

• initialCondition object — initialCondition object that represents a model of the free response of the system to initial conditions. For multiexperiment data, specify a 1-by-N_e array of objects, where N_e is the number of experiments.

  Use this option for linear models only. For an example, see Obtain and Apply Estimated Initial Conditions.

• Structure with the following fields, which contain the historical input and output values for a time interval immediately before the start time of the data used in the simulation:

  Field	Description
  Input	Input history, specified as a matrix with Nu columns, where Nu is the number of input channels. For time-series models, use []. The number of rows must be greater than or equal to the model order.
  Output	Output history, specified as a matrix with Ny columns, where Ny is the number of output channels. The number of rows must be greater than or equal to the model order.

  For an example, see Use Historical Data to Specify Initial Conditions for Model Simulation.

  For multiexperiment data, configure the initial conditions separately for each experiment by specifying InitialCondition as a structure array with Ne elements. To specify the same initial conditions for all experiments, use a single structure.

  The software uses data2state to map the historical data to states. If your model is not idss, idgrey, idnlgrey, or idnlarx, the software first converts the model to its state-space representation and then maps the data to states. If conversion of your model to idss is not possible, the estimated states are returned empty.

• 'model' — Use this option for idnlgrey models only. The software sets the initial states to the values specified in the sys.InitialStates property of the model sys.

• [] — Corresponds to zero initial conditions for all models except idnlgrey. For idnlgrey models, the software treats [] as 'model' and specifies the initial states as sys.InitialStates.

X0Covariance — Covariance of initial states vector

[] (default) | matrix

Covariance of initial states vector, specified as one of the following:

• Positive definite matrix of size Nx-by-Nx, where Nx is the model order.

  For multiexperiment data, specify as an Nx-by-Nx-by-Ne matrix, where Ne is the number of experiments.

• [] — No uncertainty in the initial states.

Use this option only for state-space models (idss and idgrey) when 'InitialCondition' is specified as a column vector. Use this option to account for initial condition uncertainty when computing the standard deviation of the simulated response of a model.

InputInterSample — Input-channel intersample behavior

'auto' | 'zoh' | 'foh' | 'bl'

Input-channel intersample behavior for transformations between discrete time and continuous time, specified as 'auto', 'zoh','foh', or 'bl'.

The definitions of the three behavior values are as follows:

• 'zoh' — Zero-order hold maintains a piecewise-constant input signal between samples.

• 'foh' — First-order hold maintains a piecewise-linear input signal between samples.

• 'bl' — Band-limited behavior specifies that the continuous-time input signal has zero power above the Nyquist frequency.

iddata objects have a similar property, data.InterSample, that contains the same behavior value options. When the InputInterSample value is 'auto' and the estimation data is in an iddata object data, the software uses the data.InterSample value. When the estimation data is instead contained in a timetable or a matrix pair, with the 'auto' option, the software uses 'zoh'.

The software applies the same option value to all channels and all experiments.

InputOffset — Input signal offset

[] (default) | column vector | matrix

Input signal offset, specified as a column vector of length Nu. Use [] if there are no input offsets. Each element of InputOffset is subtracted from the corresponding input data before the input is used to simulate the model.

For multiexperiment data, specify InputOffset as:

• An Nu-by-Ne matrix to set offsets separately for each experiment.

• A column vector of length Nu to apply the same offset for all experiments.

OutputOffset — Output signal offset

[] (default) | column vector | matrix

Output signal offset, specified as a column vector of length Ny. Use [] if there are no output offsets. Each element of OutputOffset is added to the corresponding simulated output response of the model.

For multiexperiment data, specify OutputOffset as:

• An Ny-by-Ne matrix to set offsets separately for each experiment.

• A column vector of length Ny to apply the same offset for all experiments.

AddNoise — Noise addition toggle

false (default) | true

Noise addition toggle, specified as a logical value indicating whether to add noise to the response model.

NoiseData — Noise signal data

[] (default) | matrix | cell array of matrices

Noise signal data specified as one of the following:

• [] — Default Gaussian white noise.

• Matrix with N_s rows and N_y columns, where N_s is the number of input data samples, and N_y is the number of outputs. Each matrix entry is scaled according to NoiseVariance property of the simulated model and added to the corresponding output data point. To set NoiseData at a level that is consistent with the model, use white noise with zero mean and a unit covariance matrix.

• Cell array of N_e matrices, where N_e is the number of experiments for multiexperiment data. Use a cell array to set the NoiseData separately for each experiment, otherwise set the same noise signal for all experiments using a matrix.

NoiseData is the noise signal, e(t), for the model

$$y(t)=Gu(t)+He(t).$$

Here,G is the transfer function from the input, u(t), to the output, y(t), and H is the noise transfer function.

NoiseData is used for simulation only when AddNoise is true.

OutputTimes — Times at which the output is calculated

[] (default) | vector | cell array

Times at which the output is calculated, specified as one of the following:

• Empty matrix, []. This is the default option, in which output times are not specified. For systems with inputs, the output sample times are chosen to be the same as those of the input signals. For autonomous systems (that is, systems with no inputs) a non-empty value for OutputTimes must be specified, otherwise, an error is generated during simulation.

• Time span [t_Min, t_Max], where t_Min and t_Max are expressed in the time units of the model.

• Time vector. A column vector of doubles. For models with inputs, the time vector must be contained within the time span of the simulation inputs (that is entries cannot be outside the time range of the input signals). For discrete-time models, the time interval must match the model sample time.

• Cell array. This option is used for multi-experiment simulations. Each element of the cell contains an array of time spans or time vectors, one array for each data experiment.

Output Arguments

opt — Option set for sim command

simOptions option set

Option set for sim command, returned as a simOptions option set.

Version History

Introduced in R2012a

R2022b: InputInterSample option allows intersample behavior specification for continuous models estimated from timetables or matrices.

iddata objects contain an InterSample property that describes the behavior of the signal between sample points. The InputInterSample option implements a version of that property in simOptions so that intersample behavior can be specified also when estimation data is stored in timetables or matrices.