Process Models

The Process Models dialog is opened by chosing the corresponding item in the pop-up menu Estimate in the ident window.

The dialog box gives access to so called Process Models, and operates on the Working Data set in the main ident window.

Process Models are simple continuous time models that are described in terms of the main time constants, the static gain, a possible dead-time, and a possible process zero (Non-constant numerator). Multi-input models can be handled, and noise descriptions of certain structures can be added.

A typical such model is the transfer function

G(s) = K exp(-Td s)/(1+ s Tp1)

How to define the model structure

Parameter values and constraints

More... about the Procss Models dialog (Disturbance Model, Focus, 'Initial State and Covariance).

Iteration Information.

Help topics.


Defining a Process Model

Defining a Process Model

Poles
Select the number of poles (time constants) using the popup-menu.
Choose if they should all be real or if possibly complex (underdamped) modes should be allowed at the popup-menu beside.
Delay
Indicate by checking the 'Delay' box if a dead-time (time delay) should be included.
Integration (self-regulating process)
Check the 'Integrator' box to enforce an integration in the process model.
Zero
Indicate by checking the 'Zero' box if a process zero (extra numerator coefficient) should be included.
Model Name
A default model name is generated online. It is built up as an acronym from the number of poles, and whether a D(elay) an I(ntegrator) a Z(ero) are included and whether U(nderdamped) modes are allowed. The model name can be changed by simply typing the desired name in the corresponding box.
Multi-input Models
Use the 'Input Number' popup-menu to select input channel. Check 'Same structure for all channels' if the chosen structure should be the same for all inputs. Otherwise, go through all the inputs and determine the structure for each channel.
Parameter Values and Constraints

Parameter Values and Constraints

If you know certain parameters, enter their values and check them as 'known' in the right side of the dialog window. If you have initial guesses of the parameters enter them in the 'Value' box, but do not check the 'Known' box. If you know bounds on the parameters enter them as min and max values. If you do not know initial values just enter 'Auto' or leave the corresponding box empty. A special start-up process will then be invoked. Generally speaking it is better to rely upon this process than entering a bad guess.

Finally press the Estimate button to perform the estimation and enter the resulting model into the Model board. The estimated values of the parameters are automatically entered in the 'Value' boxes.

Manipulating Initial Guesses

By pressing the button 'Value --> Initial', the current model values are tranferred to the initial guesses. This may be valuable when you want to continue the search for a good model from the current one, either by trying more iterations (press 'Estimate' again) or by first modifying the structure, like adding another pole or zero.

The button 'Clear Initial' clears all the initial guesses, to invoke the special initialization routine.

Note that both these buttons apply to all inputs in the multi-input case.


More on the Process Models Dialog

More on the Process Models Dialog

Disturbance Model
Offers the choices None, Order 1 and Order 2.
'None'
does not provide any model of the disturbances.
'Order 1'
Estimates an additional, continuous time first order ARMA model for the additive noise:

y = G u + H e

where H is a first order rational filter C/D and e is white noise.

'Order 2'
Same as above, but a second order ARMA model.
Focus
Offers the choices Prediction, Estimation, Filter, and Stability.
'Prediction'
gives a standard prediction error estimation method. This has optimal statistical properties but from an approximation point,it typically favors a model fit at high frequencies.
'Simulation'
approximates the dynamics of the model (the transfer function from measured inputs to outputs) in a norm that is given by the input spectrum. For the noise model, a prediction error method is used, while the dynamics model is kept constant.
'Filter'
gives an additional weighting for the dynamics model fit, by the frequency contents of a user defined filter. When this option is chosen, a filter dialog window opens and you can design standard Butterworth filters that are used for the model fit.
'Stability'
forces the identified model to be stable.
Initial State
The models require certain initial signal values to compute model outputs, the initial state. For systems with slowly decaying responses, it may be very important to handle these initial states in a good way. The popupmenu gives you the following options:
Auto
This is the default. An automatic choice between the alternatives below is made, guided by the data properties.
Zero
All necessary initial values are taken as zero.
Estimate
The unknown intial values are treated as parameters, which are estimated.
Backcast
The initial values are estimated directly with a backwards filtering method.
Covariance
Covariance = 'Estimate' is the default and normal choice. The the uncertainty of the estimated model will also be computed, and the confidence region of any Model View will also be diplayed whan asked for in the Options menu. For large models, the handling of uncertainty meausures may dominate the computation time.
Covariance = 'None' suppresses the estimation and handling of uncertainty measures.

Help topics.

(file idprocest.htm)