We continue to study fuzzy logic together with the book by V. Gostev. "Fuzzy regulators in automatic control systems."
The next task, analyzed by the author, is the synthesis of digital fuzzy controllers with switching to two operating modes in the gas temperature control system of a two-rotor gas turbine engine (GTE).
Trying to deal with this problem, I decided to see how membership functions and their parameters affect the operation of regulators. And I could not pass by such a beautiful object from the world of fuzzy controllers as the response surface, - a 3D-graph of the dependence of the output of the fuzzy controller on two inputs to the controller.
As it turned out, this addictive activity (building a response surface) gives not just aesthetic pleasure, but proves in practice the well-known philosophical statement “beauty will save the world”.
Therefore, the analysis of the next task from the book of V. Gostev I have split into two parts:
- Analysis of the influence of the membership function parameters for phasing of input variables on the operation of the controller based on fuzzy logic.
- Immediate solution to the problem.
Next, under the cut, the first part.Attention! For those who first touch on the topic of fuzzy regulation, I recommend starting with this article: A simple controller based on fuzzy logic. Creation and customizationFuzzy controllers in the previous examples of the book used the phasification of input variables using triangular membership functions. The triangular function is good in that we explicitly set the break points in the form of parameters of the phase block, and thus control the coverage of the range of the input variable (see Fig. 1). Moreover, how a linear change in a triangular function works would seem to be fairly easy to imagine (actually not!).
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It can be seen that the control range is not completely covered, although 0 - 1 is specified in the properties. This is because even when the input value is 0, all the Gaussian functions after phaseization have a value other than 0. This can be seen when the animation of the circuit on the blocks in the form of blue columns reflecting the output values of the phaseization functions is turned on. On the dynamic image of the fuzzy inference block, the presence of two columns of diagrams does not allow the center of mass to shift to the right boundary — zero (see Fig. 7).
Figure 7. Scheme at the initial moment of calculation time, for c = dU
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In the next part we will analyze the engine