Transf. Function

Transfer Function

In this example, the parameters of a first - order transfer function dynamic model are fitted to experimental values. Although this model is very simple an we will use only a few experimental data, this example is of use for illustrating the calculation procedure.

The start point is an experiment in which we measure the time evolution of a system's input and output variables, whit the aim of characterizing its dynamical behavior.

These experimental data can be fitted with a first - order transfer function:

In the following text box we can see the implementation in GOAL. You can copy the text to the clipboard and paste it in a text file:

PARAMETERS {{ REAL: a[-10;10] REAL: b[-1;1] }} MODEL {{ '*************************************************************** '***** DECLARATIONS ******************************************** '*************************************************************** Dim inExp(20), outExp(20), outCalc(20) '*************************************************************** '***** PREPROCESSING ******************************************* '*************************************************************** Sub PreProcessing() 'Inputs inExp(1) = 0: inExp(2) = 1: inExp(3) = 1: inExp(4) = 1: inExp(5) = 1: inExp(6) = 1: inExp(7) = 1: inExp(8) = 1: inExp(9) = 1: inExp(10) = 1: inExp(11) = 1: inExp(12) = 0: inExp(13) = 0: inExp(14) = 0: inExp(15) = 0: inExp(16) = 0: inExp(17) = 1: inExp(18) = 1: inExp(19) = 1: inExp(20) = 0 'Experimental outputs outExp(1) = 0: outExp(2) = 0: outExp(3) = 3: outExp(4) = 4.8: outExp(5) = 5.88: outExp(6) = 6.528: outExp(7) = 6.9168: outExp(8) = 7.1501: outExp(9) = 7.29: outExp(10) = 7.374: outExp(11) = 7.4244: outExp(12) = 7.4547: outExp(13) = 4.4728: outExp(14) = 2.6837: outExp(15) = 1.6102: outExp(16) = 0.9661: outExp(17) = 0.5797: outExp(18) = 3.3478: outExp(19) = 5.0087: outExp(20) = 6.0052 End Sub '*************************************************************** '***** OBJECTIVE FUNCTION ************************************** '*************************************************************** Function ObjectiveFunction() outCalc(1) = 0 dif = 0 'Transfer Function calculations for i = 2 to 20 outCalc(i) = a*inExp(i-1) - b*outCalc(i-1) dif = dif + (outCalc(i) - outExp(i))^2 next ObjectiveFunction = dif End Function '*************************************************************** '***** POSTPROCESSING ****************************************** '*************************************************************** Sub PostProcessing() 'TODO: Add the code of the postprocessing function here 'This code will be executed only once at the end of the execution End Sub }} CONSTRAINTS {{ }} ALGORITHM {{ POPULATION: 30 GENERATIONS: 100 REPRODUCTION_TYPE: 1 REPRODUCTION_PROBABILITY: 0,85 SELECTION_TYPE: 2 SELECTION_PROBABILITY: 0,85 MUTATION: 0,005 ELITISM: 1 REFRESH_PERIOD: 10 REFRESH_PERCENT: 10 }}

Send an e-mail to geneticoptimization@yahoo.es with questions or comments about this web page Last modification: 01/27/03

Send an e-mail to geneticoptimization@yahoo.es with questions or comments about this web page
Last modification: 01/27/03