pem - Prediction error estimate of linear or nonlinear model

Examples

Refine Estimated State-Space Model

Estimate a discrete-time state-space model using the subspace method and refine it by minimizing the prediction error.

Estimate a discrete-time state-space model using n4sid, which applies the subspace method.

load iddata7 z7;
z7a = z7(1:300);
opt = n4sidOptions('Focus','simulation');
init_sys = n4sid(z7a,4,opt);

init_sys, the estimated state-space model, provides a 73.85% fit to the estimation data (see init_sys.Report.Fit.FitPercent). Use pem to improve the closeness of the fit.

Obtain a refined estimated model by using pem.

sys = pem(z7a,init_sys);

Analyze the results.

compare(z7a,sys,init_sys);

sys refines the estimated model and provides a 74.54% fit to the estimation data (see init_sys.Report.Fit.FitPercent).

Configure Estimation Using Process Model

Create a process model structure and update its parameter values to minimize prediction error.

Create a process model and initialize its coefficients.

init_sys = idproc('P2UDZ');
init_sys.Kp = 10;
init_sys.Tw = 0.4;
init_sys.Zeta = 0.5;
init_sys.Td = 0.1;
init_sys.Tz = 0.01;

Use init_sys, a process model created by direct construction, to configure the estimation by pem. The Kp, Tw, Zeta, Td and Tz coefficients of init_sys are configured with their initial guesses.

Estimate a prediction error minimizing model using measured data.

load iddata1 z1;
opt = procestOptions('Display','on','SearchMethod','lm');
sys = pem(z1,init_sys,opt);

As init_sys is an idproc model, use the corresponding option set command, procestOptions to create an estimation configuring option set. The estimation is set to use the Levenberg-Marquardt search method ('SearchMethod','lm') and will display the iterative search results during estimation ('Display','on').

sys is an estimated process model, which provides a 70.63% fit to the measured data (see sys.Report.Fit.FitPercent).

Estimate Nonlinear Grey-Box Model

Estimate the parameters of a nonlinear grey box model to fit DC motor data.

Load the experimental data, and specify the signal attributes such as start time, and units.

load(fullfile(matlabroot, 'toolbox', 'ident', 'iddemos', 'data', 'dcmotordata'));
data = iddata(y, u, 0.1);
set(data,'Tstart',0,'TimeUnit','s');

Configure the nonlinear grey-box model (idnlgrey) model.

For this example, use the shipped file dcmotor_m.m. To view this file, enter edit dcmotor_m.m at the MATLAB command prompt.

file_name = 'dcmotor_m';
order = [2 1 2];
parameters = [1; 0.28];
initial_states = [0; 0];
Ts = 0;
init_sys = idnlgrey(file_name,order,parameters,initial_states,Ts);
set(init_sys,'TimeUnit','s');

setinit(init_sys,'Fixed',{false false});

init_sys is a nonlinear grey-box model with its structure described by dcmotor_m.m. The model has one input, two outputs and two states, as specified by order.

setinit(init_sys,'Fixed',{false false}) specifies that the initial states of init_sys are free estimation parameters.

Estimate the model parameters and initial states.

sys = pem(data,init_sys);

sys is an idnlgrey model, which encapsulates the estimated parameters and their covariance.

Analyze the estimation result.

compare(data,sys,init_sys);

sys provides a 98.34% fit to the estimated data.