Fuzzy control problem:(1)input 2 expects a value in range [-1.5 1.5], but has a value of 4.36559e+24;

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Ke 2024-5-14

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评论： Ke 2024-6-28

采纳的回答： Sam Chak

In 'EV_Thermal_Management_wendukongzhi_zhileng/Controls/Compressor Control/ÿÿÿÿ/Fuzzy Logic

Controller', input 2 expects a value in range [-1.5 1.5], but has a value of 4.36559e+24.

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组件:Simulink | 类别:Model 警告

In 'EV_Thermal_Management_wendukongzhi_zhileng/Controls/Compressor Control/ÿÿÿÿ/Fuzzy Logic

Controller', no rules fired for Output 1. Defuzzified output value set to its mean range value 0.

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Ke 2024-5-15

编辑：Walter Roberson 2024-5-17

在 MATLAB Online 中打开

mhkz.slx

I've committed the code content of the simulink file and the fis file. Can you help me see what the problem is?

fis file :

[System]
Name='mhPID'
Type='mamdani'
Version=2.0
NumInputs=2
NumOutputs=3
NumRules=49
AndMethod='min'
OrMethod='max'
ImpMethod='min'
AggMethod='max'
DefuzzMethod='centroid'
[Input1]
Name='e'
Range=[-3 3]
NumMFs=7
MF1='NB':'trimf',[-4.275 -3 -2]
MF2='NM':'trimf',[-3 -2 -1]
MF3='NS':'trimf',[-2 -1 0]
MF4='ZO':'trimf',[-1 0 1]
MF5='PS':'trimf',[0 1 2]
MF6='PM':'trimf',[1 2 3]
MF7='PB':'trimf',[2 3 4.055]
[Input2]
Name='ec'
Range=[-1.5 1.5]
NumMFs=7
MF1='NB':'trimf',[-2 -1.5 -0.9999]
MF2='NM':'trimf',[-1.5 -0.9999 -0.5001]
MF3='NS':'trimf',[-0.9999 -0.5001 0]
MF4='ZO':'trimf',[-0.5001 0 0.5001]
MF5='PS':'trimf',[0 0.5001 0.9999]
MF6='PM':'trimf',[0.5001 0.9999 1.5]
MF7='PB':'trimf',[0.9999 1.5 2.001]
[Output1]
Name='kp'
Range=[-5 5]
NumMFs=7
MF1='NB':'trimf',[-6.667 -5 -3.333]
MF2='NM':'trimf',[-5 -3.333 -1.667]
MF3='NS':'trimf',[-3.333 -1.667 2.22e-16]
MF4='ZO':'trimf',[-1.667 -5.551e-17 1.667]
MF5='PS':'trimf',[2.22e-16 1.667 3.333]
MF6='PM':'trimf',[1.667 3.333 5]
MF7='PB':'trimf',[3.333 5 6.667]
[Output2]
Name='ki'
Range=[-2 2]
NumMFs=7
MF1='NB':'trimf',[-2.667 -2 -1.333]
MF2='NM':'trimf',[-2 -1.333 -0.6667]
MF3='NS':'trimf',[-1.333 -0.6667 -1.11e-16]
MF4='ZO':'trimf',[-0.6667 0 0.6667]
MF5='PS':'trimf',[-1.11e-16 0.6667 1.333]
MF6='PM':'trimf',[0.6667 1.333 2]
MF7='PB':'trimf',[1.333 2 2.667]
[Output3]
Name='kd'
Range=[-1 1]
NumMFs=7
MF1='NB':'trimf',[-1.333 -1 -0.6667]
MF2='NM':'trimf',[-1 -0.6667 -0.3333]
MF3='NS':'trimf',[-0.6667 -0.3333 -5.551e-17]
MF4='ZO':'trimf',[-0.3333 0 0.3333]
MF5='PS':'trimf',[-5.551e-17 0.3333 0.6667]
MF6='PM':'trimf',[0.3333 0.6667 1]
MF7='PB':'trimf',[0.6667 1 1.333]
[Rules]
1 1, 7 1 5 (1) : 1
1 2, 7 1 3 (1) : 1
1 3, 6 2 1 (1) : 1
1 4, 6 2 1 (1) : 1
1 5, 5 3 1 (1) : 1
1 6, 4 4 2 (1) : 1
1 7, 4 4 5 (1) : 1
2 1, 7 1 5 (1) : 1
2 2, 7 1 3 (1) : 1
2 3, 6 2 1 (1) : 1
2 4, 5 3 2 (1) : 1
2 5, 5 3 3 (1) : 1
2 6, 4 4 3 (1) : 1
2 7, 3 4 4 (1) : 1
3 1, 6 1 4 (1) : 1
3 2, 6 3 2 (1) : 1
3 3, 6 3 2 (1) : 1
3 4, 5 3 2 (1) : 1
3 5, 4 4 3 (1) : 1
3 6, 3 5 3 (1) : 1
3 7, 3 5 4 (1) : 1
4 1, 6 1 4 (1) : 1
4 2, 6 2 3 (1) : 1
4 3, 5 3 3 (1) : 1
4 4, 4 4 3 (1) : 1
4 5, 3 5 3 (1) : 1
4 6, 2 6 3 (1) : 1
4 7, 2 6 4 (1) : 1
5 1, 5 2 4 (1) : 1
5 2, 5 3 4 (1) : 1
5 3, 4 4 4 (1) : 1
5 4, 3 5 4 (1) : 1
5 5, 3 5 4 (1) : 1
5 6, 2 6 4 (1) : 1
5 7, 2 7 4 (1) : 1
6 1, 5 4 7 (1) : 1
6 2, 4 4 3 (1) : 1
6 3, 3 5 5 (1) : 1
6 4, 2 5 5 (1) : 1
6 5, 2 6 5 (1) : 1
6 6, 2 7 5 (1) : 1
6 7, 1 7 7 (1) : 1
7 1, 4 4 7 (1) : 1
7 2, 4 4 6 (1) : 1
7 3, 3 5 5 (1) : 1
7 4, 2 5 6 (1) : 1
7 5, 2 6 5 (1) : 1
7 6, 1 7 5 (1) : 1
7 7, 1 7 7 (1) : 1

Ke 2024-5-15

Thank you very much for your answer, I tried to experiment with the method you provided. Can you share your model with me?

Ke 2024-5-15

Hello, I tried it and found that it still doesn't seem to be ideal, I can't get the rate of change without using the Derivative block.

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采纳的回答

Sam Chak 2024-5-15

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2118566-fuzzy-control-problem-1-input-2-expects-a-value-in-range-1-5-1-5-but-has-a-value-of-4-36559e-24#answer_1458246

mhkz_Prefilter.slx

Hi @柯

If there is no other way to directly measure the time derivative signal from the system, the proposed configuration with a Pre-filter at the Setpoint and a Filtered Derivative transfer function can be used to replace the original Derivative block. This configuration should effectively address the issue of derivative kick caused by setpoint jumps.

In Scope 1, you can see that the maximum value of dedt (the derivative of the error) is less than 1.5, which falls within the range of the fuzzy input 'ec'. This indicates that the proposed configuration successfully manages the derivative kick issue.

Scope 2 demonstrates how the fuzzy PID gains vary over time, maintaining non-negative values throughout the simulation. To achieve this, a small trick using the 'Abs' block is employed. Please note that in your original system, you should remove any additional blocks related to gain adjustment. Only the Pre-filter and the Filtered Derivative are necessary.

Lastly, Scope 3 illustrates the stability achieved by the Double Integrator system. A Simulink model is also attached for your reference and the original FIS file is unchanged.

Scope 1

Scope 2

Scope 3

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Sam Chak 2024-5-16

编辑：Sam Chak 2024-5-16

mhkz_Earlier_Version.slx

Sure @柯, here is the model saved in an earlier version. If you find the solution to the derivative kick helpful, please consider clicking 'Accept' ✔ on the answer and voting 👍 for it. Your support is greatly appreciated!

Please note that your fuzzy PID controller follows this form:

It is important to consider that all three nominal gains

are fixed at 1 and are less than or equal to the absolute value of the fuzzy gains

. At some point, the summed control gains

may become zero or negative, which can potentially destabilize your original system. This observation was made while attempting to stabilize the Double Integrator (see Scope 2).

The second issue pertains to the membership functions. While I'm not an expert in Mamdani fuzzy systems, I noticed that you designed 7 input membership functions for both 'e' and 'ec' inputs. Since you opted for all possible rules (

), ideally, the number of output membership functions should be 13. However, I see that you only have 7 output membership functions for each fuzzy control gain.

The third issue pertains to the Saturation block placed at the output of the PID controller. With the current configuration, you are limiting the output of the controller to a range of 0 to 1. As a result, the controller's output is unidirectional, regardless of whether the error signal is negative or positive.

If you're experiencing performance issues with the designed fuzzy controller, I suggest creating a question for further investigation. This way, we can delve deeper into the specific challenges you're facing and explore potential solutions for the fuzzy control system.

Ke 2024-5-17

移动：Sam Chak 2024-5-17

Hello, I found that the model you built does not seem to initialize the PID parameters, and directly input the output of the fuzzy rules into the PID controller as the values of KP, KI, KD, will this have an impact?

2. In addition, you mentioned that my membership function should be 13, I don't understand this too much, and the output membership function I set is also 7 triangle membership functions with the input.

3. Regarding the unlimited output, I want to control the speed of my compressor to ensure that his speed is within a reasonable range and cannot exceed the maximum range.

Sam Chak 2024-5-17

Hi @柯

Thanks for your feedback. The reason I modified the PID structure is because you didn't supply the Compressor model for me to test. So, I created the simplest unstable model, a Double Integrator system, to run the PID controller.

Next, I needed to rule out the possibility that the Simulink error was caused by the fuzzy system you originally designed. Since I cannot alter anything in your fuzzy system, I can only modify the mechanisms outside of it to produce PID gain values that stabilize the Double Integrator system.

With the Double Integrator now stable, the system output signal fed back to the fuzzy system won't blow up. This allowed me to focus on fixing the "Derivative Kick" issue, and I proposed using the Prefilter (pastel red block) and the Filtered Derivative (pastel blue block). After testing the Double Integrator system again, the "Derivative Kick" issue was resolved.

That's why I mentioned that only the Prefilter and the Filtered Derivative are necessary, and the rest should remain the same as in the original Simulink file "mhkz.slx". Please let me know if the implementation of the Prefilter and the Filtered Derivative has indeed fixed the "Derivative Kick" issue for your system.

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Sam Chak 2024-5-17

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2118566-fuzzy-control-problem-1-input-2-expects-a-value-in-range-1-5-1-5-but-has-a-value-of-4-36559e-24#answer_1459256

Hi @柯

This following issue does not affect the original "derivative kick" problem described in this thread. So, it should be treated separately.

On the reason why the number of output membership functions (MFs) should be ideally 13, first, you need to review the If–Then rulebase (see Fig. 1). Look at the yellow boxes - you'll see that many of the output MFs are reused throughout the 49 rules. This causes the Fuzzy Kp surface in Fig. 2 to look a little strange.

Going back to the rulebase, since there are 2 inputs (e and ec) and each input has 7 MFs, there are 7 rule sets of 7 rules (see the 1st rule set in the orange box). However, there were only 4 output MFs in your original Kp design (see Fig. 3). So, for each rule set, you only have 4 output MFs to fill up the 7 rules, and thus, reusing some MFs is inevitable, making the fuzzy rules inflexible and less unique.

To address this issue, you can add another 3 Positive MFs (mf8, mf9, mf10) on top of the existing 4 output MFs (see Fig. 4). Now there will be enough 7 distinct MFs for the 7 rules in the first rule set. If you add another 3 Negative MFs (mf11, mf12, mf13) on the Negative side for Kp, Ki and Kd, there are just enough MFs for the 7 rule sets (all 49 rules). That's why I mentioned ideally there should be "13 MFs for each output"!

Figure 1: Fuzzy If–Then rulebase.

Figure 2: Fuzzy Kp surface

Figure 3: Original Fuzzy Kp output membership functions

Figure 4: Modified Fuzzy Kp output MFs (positive side for demo only)

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Sam Chak 2024-5-26

Hi @柯

Thank you for the results. The reason I requested to test the tanh controller is because I wanted to confirm my suspicion that your designed PID Controller block with Internal Saturation [0, 1] may be the culprit that caused the performance bottleneck. The amplitude of a hyperbolic tangent function, tanh(x), is constrained between [-1, 1].

Observation 1:

With both sets of results, I can now compare the Cabin Temperature responses. Both Cabin Temperature responses appear to converge at nearly the same rate, though the response under the tanh controller converged slightly faster.

Observation 2:

In response to the disturbance, the Saturated PID Controller caused the Cabin Temperature to drop lower than the Setpoint (25°C). The occupants inside the Cabin may feel slightly uncomfortable with this offset. Under the tanh Controller, the Cabin Temperature is successfully regulated around the Setpoint (25°C) with very small deviations. The occupants inside the Cabin would likely not have noticed these minor changes in temperature.

Questions:

Before I provide any further recommendations, I would like to better understand the control design requirements.

Are you satisfied with the Cabin Temperature response converging at around 1,200 seconds?
If not, what is the desired settling time? For example, would you prefer it to converge around 600 seconds (equivalent to 10 minutes)?
What is the amplitude of the external disturbance?

Sam Chak 2024-5-27

Hi @柯

This topic is actually called disturbance rejection, and it remains an active area of research due to the various types of disturbances present in many complicated nonlinear systems. Consequently, cost-effective control strategies tailored to different applications are necessary.

Using the integral action in the PID controller to handle external disturbances is akin to treating the symptoms rather than the root cause (治标不治本). If the disturbance load is constant, such as a robot arm picking objects of different fixed weights (

), then the integral action tends to perform relatively well.

In contrast, the fast-switching action of the tanh controller

relies on its control magnitude (the larger

the better) and the switching frequency (how quickly it reacts to changes in the error caused by the disturbance) to overcome the external disturbance. While this approach is effective, as you noticed the fluctuation becomes smaller, it is similar to the Chinese proverb "Kill 1,000 enemy soldiers but lose 800 of your own" (杀敌一千，自损八百). Due to the fast-switching action, some mechanical parts in the control actuator may wear out more quickly and require costly frequent replacement.

Suggestion:

Ideally, if the external disturbance can be accurately measured, either directly or indirectly through observations of changes in the error, then it can be canceled out through the controller. This is treating the the root cause.

Since this is a controlled experiment, it should be possible, at least in simulations, to measure the rapid increase in the positive heat flow into the passenger compartment caused by the sudden closure of the adjacent battery circuit. Once this value is determined, the controller can be used to induce an opposite negative heat flow to counteract the positive heat flow and bring the cabin temperature back to the setpoint (25°C).

Sam Chak 2024-5-28

Hi @柯

I believe your idea of using fuzzy control is feasible, provided you understand the following:

The estimated mathematical model of the process system being controlled.
The nature of the disturbance (constant, state-dependent, or time-dependent).
The strategies employed by controllers to reject the corresponding disturbance.

Unless there are successful examples that you can directly follow, describing the fuzzy controller in the traditional way using Mamdani-type with many triangular membership functions and an abundance of ineffective "human" rules will make it very challenging to achieve the objective of rejecting the disturbance.

For example, dividing the error into 7 regions by creating 7 membership functions is akin to attempting to cut a round cake into 7 equal pieces for 7 people. Unless a special cake-cutting mold is used, an ordinary person cannot precisely cut a round cake into 7 equal pieces. A pastry chef using a 7-piece cake divider tool is analogous to an engineer applying control theory knowledge in fuzzy control design.

Sam Chak 2024-6-26

@柯: but [the] running speed is relatively slow ... and its effect is not much different from my PID control.

Response: That's because you clamp the max output of the fuzzy controller to 1. In other words, the controller doesn't have enough "power" to cool the cabin's temperature faster. You didn't tap into the nonlinear control power of fuzzy logic. The concept is similar to charging your mobile phone: a high-power adapter delivers fast charging! Use a high-horsepower conditioner, and you should see immediate improvement.

@柯: but I found that [the] overshoot here is still a bit large, what should I do?

Response: I believe that such a response is completely normal when there is a sudden disturbance, and your controller doesn't have much "power" to compensate for it rapidly. You can try increasing the Derivative gain, but there is no guarantee it will work because the output is clamped at the max value of 1.

@柯: The result I set seems to be still some distance, here I can adjust the I parameter to achieve approximation?

Response: If you are referring to the steady-state error (the difference between black and red curves), then such a very small gap is completely normal in simulation as well as in real scenarios. The observation is similar to water tank level control, where the water level cannot be accurately regulated to the perfect desired level. For example, if the desired level is 10, the steady-state water level will probably maintain at 9.99 or 10.01.

Overall, the performance of the designed fuzzy controller looks fine, and it has the capability of rejecting the effects caused by sudden disturbances.

Sam Chak 2024-6-27

Hi @柯

A1: I cannot comment on the technical details of the revised control architecture, as I am unable to look inside the "模糊规则" subsystem. However, given that the cabin response appears to be converging sensibly to the setpoint, I believe your overall control design is acceptable.

A2: Limiting the output in a constrained control problem is considered a practical approach. There is nothing inherently wrong with that. However, you should be mindful of the limitations of what your proposed control architecture can achieve. Additionally, I'm afraid I don't fully understand the statement about the "result being unreasonable."

A3: Since you aim to reduce the overshoot, it would be natural for me to advise you to try increasing the derivative gain. However, the side effect of this approach is that it will cause the response to become slower. Ideally, the designer should seek to find the "best" derivative gain that yields the shortest settling time while producing minimal overshoot.

A4: Yes, and this will be the optimization aim as mentioned in the last sentence of A3.

Sam Chak 2024-6-28

Hi @柯

I would suggest that you start by taking the self-paced Optimization Onramp course, which is available at the following link:

https://matlabacademy.mathworks.com/details/optimization-onramp/optim?s_tid=course_opor_start1

This course should help you familiarize yourself with the basics of solving optimization problems in MATLAB. It covers topics such as defining optimization variables, implementing objective functions, and solving both unconstrained and constrained optimization problems.

If you encounter any technical issues in your optimization problem with Simulink, I would recommend posting a new, focused question. This will help prevent the current discussion on the fuzzy control topic from becoming an overly lengthy thread.

Ke 2024-6-28

Ok, thank you very much for your suggestion

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