Characterization Open-Loop Dynamic Process (Experimental Modeling)

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Characterization Open-Loop Dynamic Process
(Experimental Modeling)

Abstract—This paper deals with a case study from the class of Control Engineering. This case study is about the investigation and the use of three graphic methods to obtain the parameters of transfer function of a plant given this structure.

Index Terms—control engineering, graphic methods

1. INTRODUCTION

T

his project consist on learn graphic methods in order to obtain a good approximation to the transfer function of a plant. The propose of the transfer function of the plant given by the instructions of the project is:

[pic 1]

In order to complete this task we research for three methods in the book  "Tuning of  industrial Control Systems" by Armando Corripio. We selected the following methods:

• Tangent
• Two points
• Tangent-and-point

1. Theoretical fundaments

1. Process Gain

In the methods we need approximate the values of  k, τ and t0. Let's see how obtain the steady-state gain k first. The gain is defined as the steady-state change in output over the change in the input:

[pic 2]

To measure the change in the output, we need to measure after the process reaches a new steady state after the input enter to the system, and we need to measure also the steady state before the input enter  to the system. The change of the input is measured in the same way but focusing in the input.

1. Tangent Method

In this method we need to draw the tangent to the response line at the inflexion point, this point when the maximum rate occurs. The time constant(τ) is defined as the distance in the time axis between the point where the tangent crosses the initial steady-state value and the point where the tangent crosses the new steady state value. The dead time(t0) is the distance in the time axis between the occurrence of the input step change and the point where the tangent line crosses the initial steady state.

1. Tangent-and-point

This method is similar to the tangent method but it has some differences. The dead time(t0) is estimate in the same way. In order to obtain the time constant(τ) we need to determine the point in which the step response reaches 63.2 percent of its total steady-state change then the time constant is the distance in the time axis between the tangent crosses the initial steady state and the point where the response reaches 63.2 percent of the total change. In the following expression its seen how we will obtain the time constant(τ):

[pic 3]

 Where τ is the time constant, t1 is the time where the response reaches 63.2 percent of the total change and t0 is the dead time.

1. Two point method

In this method we will use the 63.2 percent point defined in the tangent-and-point method and another point: where the step response reaches 28.3 of its total steady-state change. The time constant and the dead time are calculated with the following formulas:

[pic 4][pic 5]

Where t2 is when the step response reaches 28.3 of its total steady-state change, t1 is when the response reaches 63.2 percent of the total change, t0 is the dead time, and τ is the time constant.

1. Case study results

1. Conclusion

In this project we have the opportunity to learn different methods to the methods view in class. This methods have some gate of imprecision, but they are easier to apply and also they can be used only with the graph of the response of the system, we do not need to analyze the system, which in many cases is the hardest part of the problems.      

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