Fuzzy logic against PID. We cross a hedgehog and a snake. Aircraft engine and control algorithms for nuclear power plants

3r3-31. 3r38080. Probably, everyone who studied the theory of automatic control often had doubts about how these two, three or even ten squares of transfer functions in a model represent the dynamics of a complex unit, such as a nuclear reactor or an aircraft engine. Is there no cheating here? It is possible that working with simple models will cease to work with complex models in "real" life.

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3r38080. In this article, we will experiment with the “real” model of an aircraft engine. Having weighed it with “real” models of equipment and control algorithms from a nuclear power plant.

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3r38080. Initially, the model was written in FORTRAN and intended for some highly scientific purposes related to engine control systems. This model was given to us as an example and our task was to repeat the model in a structural form and prove that it coincides with the original one. What was done.

3r3678.

As soon as the model turned from listing Fortran into a structural scheme, it became easy and convenient to work with it, conducting any of the most “sophisticated” experiments. It was not by chance that I had real NPP control algorithms. That allowed us to quickly assemble a model for experiments, without using any formulas, yes, yes, only pictures. 3r3678.

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first article 3r3696. . (see figure 18). The input is the mismatch, the first and second derivatives of the mismatch are determined numerically and a simple base of three rules is used: 3r3678.

3r33450.

3r37474. If ** less than 3r3658. and 3r3657. decreases ** and 3r3657. slows down [/b] =>** reduce. 3r3658. 3r33775. 3r37474. If norm and 3r3657. constant ** and not

**changes**=>

**Do not change**. 3r33775.

3r37474. If

**more**and 3r3657. increases [/b] and 3r3657. speeding up [/b] =>

**increase**. 3r33775.

3r3r7777. 3r3678.

3r38080. 3r3678.

**Figure 18. Diagram of a fuzzy regulator. 3r3658.**

3r3678.

3r38080. To configure, we use the same variables that we used in 3r3498. first article 3r3696. , Are the deviation ranges of the first and second derivatives of the deviation.

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3r38080. After optimization, we start the same transition process.

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3r38080. 3r3678.

[b] Figure 19. Revolutions and controls for fuzzy logic 3r3658.

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3r38080. Judging by the schedule 1? the fuzzy logic coped much better with the increase in speed of the aircraft engine!

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3r38080. Now we will change the conditions of the task, which are set to a positive step of 300 rpm, and experience a negative step of -1500 rpm. (If we take more, the valve may close, but I don’t know how the model behaves at zero fuel consumption, although the real engine allows a short-term cessation of fuel supply.) 3r3678.

At the 20th second of the calculation, we will set the frequency equal to 2100 rpm. And let's see how our regulators will work. The first in the ring - Fuzzy Logic.

3r3678.

3r38080. 3r33535. 3r3678.

[b] Figure 20. Testing the reduction in speed. Fuzzy logic

3r3678.

3r38080. To configure, we use the same variables that we used in 3r3498. first article 3r3696. , Are the deviation ranges of the first and second derivatives of the deviation.

3r3678.

3r38080. After optimization, we start the same transition process.

3r3678.

3r38080. 3r3678.

[b] Figure 19. Revolutions and controls for fuzzy logic 3r3658.

3r3678.

3r38080. Judging by the schedule 1? the fuzzy logic coped much better with the increase in speed of the aircraft engine!

3r3678.

3r38080. Now we will change the conditions of the task, which are set to a positive step of 300 rpm, and experience a negative step of -1500 rpm. (If we take more, the valve may close, but I don’t know how the model behaves at zero fuel consumption, although the real engine allows a short-term cessation of fuel supply.) 3r3678.

At the 20th second of the calculation, we will set the frequency equal to 2100 rpm. And let's see how our regulators will work. The first in the ring - Fuzzy Logic.

3r3678.

3r38080. 3r33535. 3r3678.

[b] Figure 20. Testing the reduction in speed. Fuzzy logic

3r3678.

3r38080. The second experiment is with the PID controller. And what do we see? This is a complete failure, the PID regulator, tuned to increase the frequency of revolutions, did not cope with a decrease in frequency. (see 21) Something anxiously became for me now for our nuclear power plants.

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3r38080. The engine model at low revs was absolutely uncontrollable with the help of a PID regulator tuned to control at high revs.

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3r38080. By the way, it can be seen that a brief shutoff of the fuel supply (the valve closes completely) does not lead to the collapse of the model of a turbojet engine.

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3r38080. 3r33548. 3r3678.

**Figure 21. Testing the reduction in speed. PID regulator. 3r3658.**

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3r38080. A test with a traffic controller is suggested, which uses the second derivative. Since such a model has already been made to

previous article 3r3696. (see Fig. 22), then turning the fuzzy logic into a traffic violation is a matter of two seconds. (see fig. 23).

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3r38080. 3r33535. 3r3678.

[b] Figure 22. Block diagram of the PDA controller. 3r3658.

3r3678.

3r38080. 3r? 3572. 3r3678.

[b] Figure 23. Replacing the PID on the traffic rules in the control algorithm 3r3658.

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3r38080. We carry out the adjustment of the regulator by the method of optimization and repeat the reduction in speed.

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3r38080. 3r33585. 3r3678.

[b] Figure 24 Testing the reduction in RPM speed of the regulator 3r3658.

3r3678.

3r38080. The SDA worked with overshoot, but clearly better than PID, and almost as good as fuzzy logic. But there is an overshoot!

3r3678.

3r38080. [b] Complicate the problem - add noise to the sensor 3r33658.

3r3678.

3r38080. Now let's try to add white noise to the sensor measuring signals and see how the regulators behave with a real sensor. The dead zone at us 1% from the maximum turns is 40 rpm. Set the white noise to 50 rpm.

3r3678.

3r38080. Since the PID does not work at lower revs, we will test for increases.

3r3678.

3r38080. The traffic controller obviously does not cope with such noises, although it maintains the required speed, but the control valve shakes, as in the dance of St. Vitus, when the given speed stands. In Figure 2? a specially extended section 25-25 seconds of the

process. 3r3678.

3r38080. 3r31616. 3r3678.

[b] Figure 25 Speed increase with sensor noise. Traffic regulator regulator

3r3678.

3r38080. A test with a traffic controller is suggested, which uses the second derivative. Since such a model has already been made to

previous article 3r3696. (see Fig. 22), then turning the fuzzy logic into a traffic violation is a matter of two seconds. (see fig. 23).

3r3678.

3r38080. 3r33535. 3r3678.

[b] Figure 22. Block diagram of the PDA controller. 3r3658.

3r3678.

3r38080. 3r? 3572. 3r3678.

[b] Figure 23. Replacing the PID on the traffic rules in the control algorithm 3r3658.

3r3678.

3r38080. We carry out the adjustment of the regulator by the method of optimization and repeat the reduction in speed.

3r3678.

3r38080. 3r33585. 3r3678.

[b] Figure 24 Testing the reduction in RPM speed of the regulator 3r3658.

3r3678.

3r38080. The SDA worked with overshoot, but clearly better than PID, and almost as good as fuzzy logic. But there is an overshoot!

3r3678.

3r38080. [b] Complicate the problem - add noise to the sensor 3r33658.

3r3678.

3r38080. Now let's try to add white noise to the sensor measuring signals and see how the regulators behave with a real sensor. The dead zone at us 1% from the maximum turns is 40 rpm. Set the white noise to 50 rpm.

3r3678.

3r38080. Since the PID does not work at lower revs, we will test for increases.

3r3678.

3r38080. The traffic controller obviously does not cope with such noises, although it maintains the required speed, but the control valve shakes, as in the dance of St. Vitus, when the given speed stands. In Figure 2? a specially extended section 25-25 seconds of the

process. 3r3678.

3r38080. 3r31616. 3r3678.

[b] Figure 25 Speed increase with sensor noise. Traffic regulator regulator

3r3678.

3r38080. 3r33625. 3r3678.

**Figure 26 Speed increase with sensor noise. PID controller**

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3r38080. The transition process for the PID controller has not changed despite the noise in the speed sensor. Management comes with clear and long steps.

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3r38080. The alarm for the nuclear power plant receded.

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3r38080. 3r3678.

[b] Figure 27. Fuzzy controller with noise in the sensor. 3r3658.

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3r38080. The controller with fuzzy logic with noises also controls, but at the moments of application to the stationary state there are fluctuations in the position of the regulator. 3r3678.

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3r38080. [b] Findings. 3r3658.

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3r38080. The third series of tests of fuzzy logic against PID and traffic rules ended with the victory of fuzzy logic. Unlike the simple model

previous article 3r3696. .

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3r38080. It was impossible to control the PID controller at low revs.

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3r38080. The experimentally detected PID advantage is the absence of oscillations in the case of a noisy sensor.

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3r38080. By the way, the dynamics of the engine (overclocking schedule) turned out to be very similar to the dynamics of the simplified model.

3r3678.

3r38080. Archive with models for self-study, you can take

here

3r3r7787.

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3r3704. How to continue to research the model? 3r33770.

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3r3769. Check the engine acceleration on the regulator. 3r33770.

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3r3769. Replace the hydraulic drive. 3r33770.

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3r3769. Add an aircraft fuel system with tanks. 3r33770.

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3r3769. Do nothing and everything is clear. 3r33770.

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#### weber

Author**20-11-2018, 09:17**

Publication Date
#### Matlab / Algorithms / Analysis and design of systems / Mathematics

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