PII PII -- Programs of Interactive Programs of Interactive IdentificationIdentification

( ( brief description ).brief description ).

© Central Aerohydrodynamics Institute (TsAGI), Flight Dynamics and Control Department.

Zhukovsky, Moscow region, 140160, Russia. e-mail: krit@tsagi.rssi.ru

PII is designed for:PII is designed for:

u determination of the relationships between the dependent variable and some independent ones

u identification of dynamic system parameters

PII consists of two parts:PII consists of two parts:• PIIREGRPIIREGR - linear regression

• PIIMTMPIIMTM - nonlinear dynamic system identification

System requirementsSystem requirements

The program uses reliable mathematical techniques and has user-friendly interface based on menu, hot-keys, dialogue, graphic and hint windows. It works properly on any IBM PC computers with the processor from 286 up to modern ones. To increase speed it works directly with video-memory. That is why we recommend to use it in DOS mode.

Program for linear Program for linear regression PIIREGRregression PIIREGR

PIIREGR uses method of linear regression to:u estimate parameters of the given model -

parameters identificationu exclude statistically insignificant regressors from

the model - structure identification

This program is used in TsAGI during 5 years mainly for creating the mathematical models of the aerodynamic forces and moments coefficients based on wind-tunnel or flight test data. It is necessary to create the data base for simulation of aircraft flight dynamics.

Stages of working with Stages of working with PIIREGRPIIREGR

u reading or creating (by built-in or external editor) the file with the mathematical model description

u reading file or group of files containing experimental data on processes realizations

u performing regression in interactive manneru keeping the results of regression

Reading or creating the Reading or creating the mathematical model and datamathematical model and data

u If the model already exists, read it using menu model|read. In order to create model choose model|edit or press <F4> to call built-in editor and then create it following the rules of the special language. You should use cursor keys to move selected bar along line and pop-up menus and <Enter> to execute the marked menu command.

u To read file with the experimental data choose the menu data|read data file or press <F3>.

Performing the regressionPerforming the regression

u Select menu window to choose windows to be shown or window|all to see all the windows

u To start regression procedure choose run|regressionor press <F5>

u To make one step of regression choose run|step of regression or press <F6>

u To identify the model choose run|identification or press <F7>

Starting the regressionStarting the regression(screen view)(screen view)Regressors

Coefficients of the regression

Menu

Process

After the first step of the After the first step of the regressionregression

model

The regression is completedThe regression is completed

Process(white)

Model(yellow)

Statistical criteriaStatistical criteria Fisher’scriterion

R2 criterion

Saving the resultsSaving the results

u To save resulting coefficients choose data|wrightcoefficients and then input the file name where coefficients to be saved

u To create the full protocol ( file name.log ) choose options|auto log record before the start of the regression procedure. You can see this file with any text editor or viewer

PIIREGR demo versionPIIREGR demo version

The simplest example is supplied to evaluatePIIREGR:

u process with the noise is expanded into Fourier series ( model is in the file ..regr\model1.mod, process is in the file ..regr\process1.dat )

y x x x x x r( ) sin . sin . cos . sin .= - + - +0 5 2 0 3 5 0 1 7 0 5

r £ 1

Program for identification of Program for identification of dynamic systems dynamic systems -- PIIMTMPIIMTM

PIIMTM is used to estimate parameters of the givenmodel presented in the general nonlinear form

p is the vector of system parameters identified with theobjective function minimization

ddt

a p b i k

n k

i i i

x F x,p x R p R

G G x,p

= Î Î

=£ £ Î

ì

í

ïï

î

ïï

( ), ,

( ),, [ , ]

mod

1

F( ) { ( ) ( )} minmod expp G x,p G x,pp

= - ®2

Application fieldApplication fieldThis program is used in TsAGI during 5 years for creating the mathematical models of the unsteady aerodynamic forces and moments coefficients based on wind-tunnel or flight test data in a wide range of motion parameters. It is necessary to create the data base for simulation of aircraft flight dynamics at high incidences. A great number of interesting results was obtained with the aid of this program. Some of them were reported on 10th and 11th IFAC Symposium:

•Goman, M., A.Khrabrov and S.Usoltsev. Identification of Unsteady Aerodynamic Model of a Delta Wing at High Angles of Attack. 10th IFAC Symposium on System Identification, SYSID’94, p.p. 3.073-3.078

•Goman, M., A.Khrabrov and S.Usoltsev. Unsteady Aerodynamic Model for LargeAmplitude Maneuvers and its Parameter Identification, 11th IFAC Symposium on System Identification, SYSID’97.

Stages of working with Stages of working with PIIMTMPIIMTM

The following steps are necessary to identify a model:u describe model with the C++ language using some macrosu create an executable unit (with the aid of PIIMTM, C++

compiler and linker)u perform the identification (working with the executable unit)

Dynamic system identification consists of two steps:• search of the objective function F(p) minimum - external task• system modelling at fixed parameters p - internal taskTo solve these tasks for an acceptable time the program must have the high computation speed. That is why the model presentation as in the PIIREGR (run-time) is not acceptable here.

Working with executable unitWorking with executable unit

At first you should:u read process or group of processes (menu input|read data)u set sensors and fixed values (menus parameters|sensors and

fixed|set fixed).

u set parameters at which the model to be minimized (menu parameters|variables) and press F9 (run|evaluate) to see the results of modelling.

u choose the method of minimization (menu parameters|method)Now one can start identification.

Setting the guesses for the Setting the guesses for the unknown parametersunknown parameters

Unknownparametersand their values

Experimental process (z)

ConstraintsThese parameters are excluded fromidentification

Choosing the method of Choosing the method of minimizationminimization

Starting identificationStarting identification

Experimental process (z - deflection)

y = z’ - phase variable - speed(model)

Identification is being Identification is being performedperformed

Identification has been Identification has been performedperformed

Experimentalprocess (grey)

Model(white)

Objective function profileObjective function profile

Saving the resultsSaving the results

If the objective function minimum hasn’t been reached, repeat identification procedure one more ( if it is necessary choose new guesses for the unknown parameters). To see the obtained values of the unknown parameters press <F4>. If the results of identification are acceptable one can save them (menu results).

Demo versionDemo version

u The simplest dynamic system - the stone on the spring ( two unknown parameters) (..\mtm\example1\model1.exe )

You have the set of experimental data: . Task is to find a and b.

u More complicated model( 38 unknown parameters). Mathematical model of at high angles of attack (..\mtm\example2\model2.exe ) (for full description of the model look at Proceedings of the 10th and 11th IFAC Symposium on system identification)

To evaluate this program two examples in model description textand corresponding executable units are supplied:

C t q tL ( ( ), ( ))a

d xdt

a dxdt

b x2

222 0+ + =

t x t i Ni i, ( ), ...= 1

Information about developersInformation about developersPrograms of Interactive Identification Programs of Interactive Identification were developed in Flight Dynamics and Control Department of Central Aerohydrodynamics Institute (TsAGI), The leader of project is Dr. MikhailDr. Mikhail GomanGoman. . There is a possibility of development PII for Windows 95/NTThere is a possibility of development PII for Windows 95/NT

Our official address:Our official address:TsAGI, Zhukovsky, Moscow region, 140160, Russia.e-mail: krit@tsagi.rssi.ru (official)

sspchram@aha.ru (Dr. Andrew Khramtsovskiy)

Thank you for your attentionThank you for your attention

Now you have enough information to start demo versions of PIIREGR ( piiregr.exe ) and PIIMTM ( model1.exe, model2.exe )(which are in the directory piipres\regr\) in order to assure thatthese programs are excellent tools to perform linear regression and dynamic systems identification for any your purposes.

Warning! Demo version will works only with data sets and modelswhich are supplied.