Wind power system cooperative power smoothing method based on rotor kinetic energy storage and variable pitch

Abstract

The invention discloses a wind power system cooperative power smoothing method based on rotor kinetic energy storage and variable pitch, belongs to the technical field of wind power, and solves the technical problem that in a full-wind-speed operation range, a traditional variable coefficient control method based on the rotating speed is difficult to accurately respond to wind speed changes after variable pitch control is introduced. According to the technical scheme, the method comprises the following steps that S1, according to the rotor kinetic energy principle, an active reference value of a given fan power controller is determined so as to smooth wind power fluctuation, that is, a filter GLF is cascaded after traditional maximum power tracking control reference power; s2, on the basis of power smoothing under the full wind speed, model-free self-adaptive variable pitch control is introduced, and control over the output power and the rotating speed of the draught fan in the full wind speed interval is achieved; and S3, considering the cooperative control of the kinetic energy and the variable pitch of the rotor under the full wind speed, adopting a fuzzy variable filter coefficient strategy based on wind speed estimation, and remarkably improving the power smoothing effect under the full wind speed through real-time control of the filter coefficient.

Description

Technical Field

[0001] This invention belongs to the field of wind power technology, and in particular relates to a method for coordinated power smoothing of wind power systems based on rotor kinetic energy storage and variable pitch. Background Technology

[0002] Wind energy, as a renewable energy source, has been widely applied and developed in some parts of my country in recent years. However, wind speed is highly random, and the operating environment is also subject to external disturbances. The output power of a wind power system is proportional to the cube of the wind speed, which leads to fluctuations in the output power of the wind turbine. This characteristic poses a significant challenge to the design of wind turbine controllers. An inappropriate controller often causes frequency fluctuations and voltage flicker in the power grid, thereby affecting the quality of the output power. Furthermore, considering the huge economic benefits brought by larger structural sizes, megawatt-class large-scale wind turbines are gradually becoming the mainstream. This means that the rotational inertia of the wind turbine increases accordingly, greatly increasing the potential for wind turbines to smooth power fluctuations. As the penetration rate of wind power systems in the power grid increases, studying the smoothing of the output power of individual wind turbines is of great significance for the coordinated operation of wind farms and grid dispatch.

[0003] Currently, commonly used power smoothing solutions can be divided into two main categories: energy storage-based power smoothing methods and non-energy storage-based power smoothing methods. Batteries, supercapacitors, flywheels, superconducting magnetic energy storage devices, and fuel cells are common energy storage devices used for power smoothing. Energy storage devices have significant advantages in smoothing grid power, but their inherent technical limitations (such as energy density, lifespan, safety, and cost) still need to be overcome through material innovation, intelligent control, and large-scale production. Furthermore, the limited capacity of energy storage devices and the stringent power management requirements during operation further increase the complexity of control. Therefore, non-energy storage-based methods, such as those based on rotor kinetic energy and those based on variable pitch, are gaining attention. Summary of the Invention

[0004] Purpose of the invention: The purpose of this invention is to provide a method for coordinated power smoothing of wind power systems based on rotor kinetic energy storage and variable pitch. It is a method that integrates power smoothing under all wind speeds and coordinated control of variable pitch, based on the principle of rotor rotational kinetic energy control.

[0005] To achieve the aforementioned objectives, the present invention employs the following technical solution: a method for coordinated power smoothing in wind power systems based on rotor kinetic energy storage and variable pitch, comprising the following steps: S1: Based on the rotor kinetic energy principle, determine the active power reference value for the given wind turbine power controller to smooth wind power fluctuations. That is, cascade a filter G after the reference power of the traditional maximum power point tracking (MPPT) control. LF ; S2: Based on power smoothing under all wind speeds, a model-free adaptive pitch control is introduced to achieve control of the wind turbine output power and speed across the entire wind speed range; S3: Considering the coordinated control of rotor kinetic energy and variable pitch under full wind speed, a fuzzy variable filter coefficient strategy based on wind speed estimation is adopted to achieve real-time control of the filter coefficient.

[0006] Furthermore, in step S1, under traditional maximum power point tracking (MPPT) control, the reference value for the wind turbine's generator-side power is as follows: (1) in, The reference power for traditional maximum power point tracking (MPPT) control; For optimal power coefficient; This refers to the mechanical rotational speed of the wind turbine.

[0007] To make the output power smoother, a filter is cascaded after the aforementioned reference power. The reference power becomes: (2) in, For the improved reference power; For a second-order SOF filter, its expression is as follows: (3) In equation (3), It is a complex variable. These are adjustable filter coefficients. and yes The two corner frequencies can be selected with appropriate values ​​based on different filtering effects. << ,0< <1; Its own amplitude-frequency characteristics, such as Figure 1 As shown, It has 3 transition frequencies, which correspond to the following frequencies from smallest to largest: , ,as well as ;in, The value needs to be small to attenuate power fluctuations in the low-frequency range; however, a parameter that is too small... This will lead to an excessive decrease in the overall output power, resulting in reduced revenue for wind turbine units; As the final turning point, it is responsible for filtering out high-frequency fluctuations, therefore It is not advisable to set the value too high; turning point frequency and The selection is related. The larger the value, the closer the distance between ω2 and ω3, resulting in a worse mid-frequency filtering effect and better wind speed tracking; conversely, The smaller, and The greater the distance, the better the mid-frequency filtering effect.

[0008] Furthermore, in step S2, as a response to the power command, compared to traditional maximum power point tracking (MPPT) control, by introducing... After that, reduce To make the wind turbine's output power smoother, the dimensionless transfer function from wind speed to engine speed at the rated operating point is analyzed. As shown in equation (4), different [formulas] can be drawn. Bode plot of the downwind speed to rotational speed transfer function (e.g.) Figure 2 As shown), the smaller [wind speed] is a response to changes in wind speed. Although it has a better effect on suppressing high-frequency fluctuations, it increases the speed amplitude in the low-frequency range, thus increasing the speed fluctuation. When the wind speed approaches the rated value, the rotor speed will exceed the rated value. The power and speed of the wind turbine can be controlled by introducing model-free adaptive pitch control.

[0009] (4) in, For wind speed, The operating point speed; Pitch angle This is a crucial parameter for wind turbine power capture. The actual blade pitch action is driven by the pitch mechanism using a pitch angle command as the input signal. The pitch mechanism can be considered as a first-order inertial system with amplitude and speed limiting elements: (5) in, The pitch angle command output by the pitch controller. The equivalent time constant of the pitch mechanism; Considering the actual pitch control system of a wind turbine, if the pitch control system inputs a pitch control command... Since the change in speed is finite, the resulting change in the mechanical rotational speed of the wind turbine is clearly not infinite. Therefore, there exists a maximum proportionality factor between the two, namely: (6) in, This is a pseudo-partial derivative of the pitch system; It is a system pitch command. exist Time and Time difference, ; Rotational speed tracking is an important tracking objective; therefore, consider the following performance metric function: (7) in, It is a weighting factor; yes Reference value for the mechanical rotation speed of the wind turbine at any time; Substituting equation (6) into equation (7), we can obtain the value of J with respect to... Taking the derivative and setting it to zero yields the optimal pitch control command under model-free adaptive control (MFAC): (8) in, It is the step size factor. A larger step size factor results in faster tracking, but a larger step size factor also increases overshoot. for The estimate is expressed as: (9) in, Step size factor; It is a weighting factor; ; ; Furthermore, the specific method for step S3 is as follows: Step 3.1) Wind speed can be measured using an anemometer, but due to the enormous blade area of ​​large wind turbines, it is difficult to accurately measure the effective wind speed. To estimate the effective wind speed of a wind turbine, the turbine itself can be used as a sensor. By estimating the mechanical power captured by the rotor, the wind speed can be estimated using the Newton-Raphson method.

[0010] The mechanical power captured by the wind turbine can be estimated from the transmission system equations: (10) in, For estimated mechanical power; The moment of inertia of the wind turbine; Electromagnetic torque; It is the coefficient of viscous friction; yes The derivative; According to the Newton-Lager method, the iterative formula for the estimator is written as: (11) in, (12) (13) in, It is the first The wind speed estimate for the next iteration; It is the first The wind speed estimate for the next iteration; It is the first The next iteration Corrections; The radius of the wind turbine; air density; For the tip speed ratio, ; The wind energy utilization coefficient is and propeller pitch angle The function, The expression is as follows: (14) in, for The fitting parameters for the curve, in this invention, =0.5176, =116, =0.4, =5, =21, =0.0068, =0.08, =0.035.

[0011] Step 3.2) The wind speed estimated in step 3.1) above. and the time parameter that reflects its change Filter coefficients used as inputs to a fuzzy controller For output; The block diagram is as follows Figure 4 As shown, where Sampling time, This is the acceleration threshold. yes The duration of acceleration is determined by timing when the absolute value of the acceleration exceeds a threshold acceleration. >0 indicates that the wind speed is increasing; the larger the value, the faster the wind speed is increasing. A value less than 0 indicates that the wind speed is decreasing; the smaller the value, the faster the wind speed is decreasing. =0 indicates a small range of wind speed variation.

[0012] Membership functions can be set according to the specifications of the generator and wind turbine. This invention uses common triangular (trimf), z-shaped (zmf), and sigmoid (smf) functions as membership functions. Input and output membership functions are described below. Figure 5The linguistic variables are represented by S (small), M (medium), L (large), NL (negative large), NM (negative medium), NS (negative small), ZE (zero), PS (positive small), PM (positive medium), and PL (positive large). The fuzzy rules are shown in Table 1 below. The design should be as simple as possible to avoid overly complex rules that could negatively impact the filter coefficients k. w Drastic changes in power levels can affect the smoothing effect.

[0013] Table 1 shows the coefficients. , , Fuzzy rule table

[0014] In step 3.2), the filter coefficients The design process includes the following steps: Step 3.2.1) The range below the rated wind speed: When wind speed varies within a small range, it mainly consists of low-frequency components with small amplitudes and high-frequency components with even smaller amplitudes. Therefore, a smaller [measurement / method] is used. The fan speed will vary over a wider range, thus fully utilizing the rotor's kinetic energy while the decrease in power output efficiency is relatively small. Considering scenarios with rapidly fluctuating wind speeds, when the wind speed increases rapidly, if a smaller... The fan's output power cannot effectively track changes in wind speed, resulting in lower system efficiency. Furthermore, when wind speed decreases rapidly, the wind contains high-amplitude low-frequency components, reducing... This can cause larger fluctuations in wind speed, which may push the fan into an unstable region and lead to system instability. Therefore, in situations with rapidly fluctuating wind speeds, a larger filter coefficient should be selected to ensure system stability and efficiency.

[0015] Step 3.2.2) Transition zone and zone above rated wind speed: In the transition zone and zone above rated wind speed, increase... This is to avoid frequent adjustments to the filter coefficient and ensure smooth output power.

[0016] Compared with the prior art, the beneficial effects of the present invention are as follows: 1. This invention proposes a cooperative power smoothing strategy for wind turbines applicable across the entire wind speed range. This strategy combines rotor kinetic energy storage with variable pitch control, utilizing the inherent inertia of megawatt-class wind turbines as the energy storage medium, eliminating the need for additional energy storage devices and thus significantly reducing system costs.

[0017] 2. The model-free adaptive pitch control strategy employed in this invention is not only used for constant power control, but also effectively limits rotor overspeed. Compared to traditional PI control, this method significantly reduces rotor speed deviation.

[0018] 3. This invention proposes a collaborative power smoothing method for wind turbines based on rotor kinetic energy and pitch variation under all wind conditions. Traditional fuzzy controllers use rotor speed as input; however, considering the effect of pitch variation, rotor speed cannot reflect wind speed changes across the entire wind speed range. This invention proposes a fuzzy variable filter coefficient strategy based on real-time wind speed estimation, which dynamically adjusts the filter coefficient according to the estimated wind speed, significantly improving power smoothing performance while maintaining high power capture efficiency. The estimated wind speed does not require extremely high precision, exhibiting good robustness to estimation errors. This strategy effectively avoids turbine instability caused by fixed or improperly tuned filter coefficients. Furthermore, the filter coefficient design solves the coordination problem between power commands and pitch angle controllers in the wind speed transition region, significantly improving the smoothness of power output during mode switching, demonstrating high feasibility and application value. Attached Figure Description

[0019] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used together with the embodiments of the invention to explain the invention and do not constitute a limitation thereof.

[0020] Figure 1 The second-order filter in this invention Its own amplitude-frequency characteristic diagram.

[0021] Figure 2 Added to this invention Later different Bode plot of the transfer function from downwind speed to rotational speed.

[0022] Figure 3 This is a block diagram of the modelless pitch control in this invention.

[0023] Figure 4 This is a block diagram of fuzzy control in this invention.

[0024] Figure 5 This is a system block diagram of the wind power system cooperative power smoothing method based on rotor kinetic energy storage and variable pitch in this invention.

[0025] Figure 6 For each fuzzy variable in this invention , , A diagram showing the corresponding membership function.

[0026] Figure 7 This is a schematic diagram of the wind speed waveform used in this invention.

[0027] Figure 8 This is a comparison diagram of the output power waveforms of the method of the present invention and the methods without filters and with fixed filter coefficients.

[0028] Figure 9 This is a comparison diagram of the rotational speed waveforms of the method of the present invention and the methods without filters and with fixed filter coefficients.

[0029] Figure 10 This is a comparison diagram of the pitch angle waveforms of the method of the present invention and the methods without filters and with fixed filter coefficients.

[0030] Figure 11 The output of the fuzzy controller in this invention The waveform diagram.

[0031] Figure 12 This is a comparison diagram of the transition range waveforms of the method of this invention and the conventional method combined with pitch control.

[0032] Figure 13 This is a comparison of simulation waveforms above the rated wind speed range for model-free pitch control and PI pitch control in this invention.

[0033] Figure 14 This is a comparison chart of the standard deviation of rotational speeds for model-free pitch control and PI pitch control under different wind speeds in this invention.

[0034] Figure 15 This is a comparison diagram of the power waveform of the present invention and that considering wind speed estimation error noise.

[0035] Figure 16 This is a comparison diagram of the rotational speed waveform of the present invention and that taking into account wind speed estimation error noise. Detailed Implementation

[0036] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. Of course, the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0037] Example 1: This example verifies smoothing under all wind speeds as follows: This embodiment provides a method for coordinated power smoothing of wind power systems based on rotor kinetic energy storage and variable pitch, including the following steps: S1: The parameters of the fan in the example used are as follows: =1.225, R=75, =0.48, =8.1, =4124283, =5140000. Filter coefficient =2.0633, =0.05.

[0038] S2: Design a model-free adaptive pitch controller, such as Figure 3 As shown. Among them It is a weighting factor. A larger value indicates more frequent pitch changes, thus resulting in better tracking performance. It is the step size factor. A larger step size factor results in faster tracking, but a larger step size factor can also increase overshoot. yes The weighting factors of the estimated cost function, This is the step size factor; its value should not be too large, otherwise it will cause speed fluctuations. (Considering all factors...) =0.01, =140, =0.7, =0.07. The initial value is set to -0.01. The pitch speed is limited to ±12° / s, and the pitch time constant is 0.5s.

[0039] S3: Consider the coordinated control of rotor kinetic energy and variable pitch under full wind speed. Estimated wind speed and the time parameter that reflects its change Used as input to the fuzzy controller, see the block diagram. Figure 4 ,in Sampling time, This is the acceleration threshold. yes The duration of acceleration is determined by timing when the absolute value of the acceleration exceeds a threshold acceleration. >0 indicates that the wind speed is increasing; the larger the value, the faster the wind speed is increasing. A value less than 0 indicates that the wind speed is decreasing; the smaller the value, the faster the wind speed is decreasing. =0 indicates a small range of wind speed variation. The membership function can be set according to the specifications of the generator and wind turbine. This invention uses common triangle (trimf), z-type (zmf), and sigmoid (smf) functions as membership functions. Input and output member functions are as follows... Figure 6 As shown. Language variables are represented by S (small), M (medium), L (large), NL (negative large), NM (negative medium), NS (negative small), ZE (zero), PS (positive small), PM (positive medium), and PL (positive large). The waveforms of the examples used are shown below. Figure 7 As shown, to verify the effectiveness of the power smoothing strategy described in this invention, the method of this invention is compared with methods that do not use filters and methods with a fixed number of filter coefficients. =0.9、 =0.8、 =0.7), the comparison results are as follows: Figure 8 , 9In simulations of values ​​10 and 11, over the entire 55-second simulation timeframe, compared to the method without a filter, the maximum energy function of the proposed method decreased by 3%, but the smoothing function decreased significantly by 30%, demonstrating better power smoothing performance. Compared to methods with fixed filter coefficients... =0.9, the maximum energy function of the method of the present invention decreased by 1.05%, and the smoothing function decreased by 2.22%. It is worth noting that during the period of 22-30 seconds, the maximum energy function decreased by only 0.13%, while the smoothness decreased significantly by 30%. This shows that the method of the present invention can maintain high efficiency when the wind speed changes within a small range, while significantly improving the power smoothing effect; compared with =0.8, the maximum energy function of the method of the present invention is improved by 2.5%, and the smoothing function is improved by 10.7%. Although the smoothing performance is somewhat reduced and the efficiency improvement is relatively limited, the fixed coefficient is still effective in the 0-20s range (mainly in the range above rated wind speed and the transition range). A value of 0.8 results in a significant power decrease (the maximum energy function decreases by 7.1%), which implies greater power loss over longer timescales. Further reduction... (For example If the value is less than 0.7, it will cause the fan to become unstable. During the transition range (2-25s), due to frequent wind speed changes, the fan frequently switches between wind speed tracking mode and constant power mode, resulting in significant spikes and drops in power output, such as... Figure 12 As shown, this significantly reduces the smoothness of output power. In contrast, the method of this invention effectively coordinates pitch and power control, enabling a smoother power transition during wind speed switching and effectively improving the stability and smoothness of power output.

[0040] Example 2: This example verifies the performance of model-free adaptive pitch control as follows: In this embodiment, the pitch control section employs model-free adaptive control, which offers better performance compared to a PI controller. Figure 13 The waveforms of traditional PI pitch control and model-free pitch control were compared, and the following were selected. Figure 7Simulation analysis was conducted in the 0-30s wind speed range, during which wind speeds were mainly above the rated wind speed. The results show that the rotational speed under PI control exhibits greater fluctuations and instability, especially in the high wind speed range (e.g., between 12s and 20s), where the rotational speed deviation is significantly greater than that of the model-free pitch control method. The main reason for this phenomenon is that the parameters of the PI controller are optimized only for a single operating point. Under fluctuating wind speeds, especially high wind speeds, the stable operating point of the wind turbine changes, causing the originally adjusted PI parameters to lose their optimality. In contrast, model-free pitch control can better adapt to turbulent wind speeds and effectively suppress rotational speed fluctuations, thus achieving superior control performance. Furthermore, to achieve this effect, the model-free pitch control method inevitably increases the frequency of pitch operations.

[0041] Since the effect of power smoothing mainly depends on the performance of rotor speed control, the performance of rotor speed control should be analyzed in detail. This invention uses the standard deviation of speed σ (see equation (14)) as the evaluation index. Among them, the smaller σ is, the smaller the speed deviation and the better the control effect. Figure 14 The comparison results of σ under different average wind speeds (11.5 m / s, 12.5 m / s, 13.5 m / s, 14.5 m / s, and 15.5 m / s) are presented. Calculations show that, under these wind speed conditions, the model-free pitch control method reduces the standard deviation by approximately 4.1%, 5.17%, 32.3%, 20.2%, and 16.3% compared to the traditional PI control method, respectively. This further verifies the superiority of model-free pitch control under complex wind conditions and its effect on improving the dynamic characteristics of the system.

[0042] (14) in, This represents the number of sampling points for the rotational speed curve. This represents the average of the rotational speed data; Let be the rotational speed of the i-th sample.

[0043] Example 3: The robustness verification in this example is as follows: The actual wind speed estimate has errors, so a filter is added (to address this). Figure 4 To filter out error noise after the wind speed estimator, the estimated wind speed does not need to be very accurate to achieve good control. To verify the effectiveness of the proposed method, the error is equivalent to white noise (noise power 0.01) and added to the estimated wind speed. The results are then compared with the original results in simulation. Figure 15 and Figure 16 It can be seen that the results after adding noise are similar to those without noise, thus proving that the proposed method can well reflect the actual wind speed variation. The proposed fuzzy controller can obtain appropriate output based on experience without requiring accurate wind speed.

[0044] Table 2 shows the output power statistics under different error noise levels.

[0045] This embodiment performed simulations for different error noise levels (0.005, 0.01, 0.015, 0.02, 0.025) and compiled the output power statistics under different noise levels, as shown in Table 2. The data in Table 2 shows that the output power data is not significantly different from the previous results, thus proving that the method proposed in this invention has good robustness.

[0046] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for coordinated power smoothing of wind power systems based on rotor kinetic energy storage and variable pitch, characterized in that: Includes the following steps: S1: Based on the rotor kinetic energy principle, determine the active power reference value for the given wind turbine power controller to smooth wind power fluctuations. That is, cascade a filter G after the reference power of the traditional maximum power point tracking (MPPT) control. LF ; S2: Based on power smoothing under all wind speeds, a model-free adaptive pitch control is introduced to achieve control of the wind turbine output power and speed across the entire wind speed range; S3: Due to the coordinated control of rotor kinetic energy and variable pitch under full wind speed, a fuzzy variable filter coefficient strategy based on wind speed estimation is adopted to achieve real-time control of the filter coefficient.

2. The wind power system cooperative power smoothing method based on rotor kinetic energy storage and variable pitch as described in claim 1, characterized in that: In step S1, under traditional maximum power point tracking (MPPT) control, the reference value for the wind turbine's generator-side power is as follows: (1) in, The reference power for traditional maximum power point tracking (MPPT) control; For optimal power coefficient; This refers to the mechanical rotational speed of the wind turbine; A filter is cascaded after the aforementioned reference power. The reference power becomes: (2) in, For the improved reference power; For a second-order SOF filter, its transfer function expression is as follows: (3) In equation (3), For complex variables, These are adjustable filter coefficients. and for The two corner frequencies are selected based on different filtering effects, among which... << ,0< <1.

3. The wind power system cooperative power smoothing method based on rotor kinetic energy storage and variable pitch as described in claim 1, characterized in that: In step S2, model-free adaptive pitch control is introduced to control the power and speed of the wind turbine. Pitch angle These are parameters related to the wind turbine's captured power. The actual blade pitch control is driven by the pitch mechanism using pitch angle commands as input signals. The pitch mechanism can be considered as a first-order inertial system with amplitude and speed limiting components. (4) in, The pitch angle command output by the pitch controller. The equivalent time constant of the pitch mechanism; Pitch commands input to the wind turbine pitch control system Changes in wind turbine speed There is a maximum scaling factor among the changes, namely: (5) in, This is a pseudo-partial derivative of the pitch system; It is a system pitch command. exist Time and Time difference, ; Performance metric functions: (6) in, It is a weighting factor; yes Wind turbine mechanical speed Reference value; Substituting equation (5) into equation (6), we can obtain the value of J with respect to... Taking the derivative and setting it to zero yields the optimal pitch control command under model-free adaptive control: (7) in, It is the step size factor. for The estimate is expressed as: (8) in, Step size factor; It is a weighting factor; ; .

4. The wind power system cooperative power smoothing method based on rotor kinetic energy storage and variable pitch as described in claim 1, characterized in that: Step S3 includes the following steps: Step 3.1) Using the wind turbine itself as a sensor, estimate the mechanical power captured by the wind turbine, and then estimate the wind speed using the Newton-Raphson method. ; Estimate the mechanical power captured by the wind turbine using the transmission system equations: (9) in, To estimate the mechanical power captured by the wind turbine, The moment of inertia of the wind turbine; Electromagnetic torque; It is the coefficient of viscous friction; yes The derivative; According to the Newton-Lager method, the iterative formula for the estimator is written as: (10) in, (11) (12) in, It is the first The wind speed estimate for the next iteration; It is the first The wind speed estimate for the next iteration; It is the first The next iteration Corrections; The radius of the wind turbine; air density; Wind speed; For the tip speed ratio, ; Let be the wind energy utilization coefficient, and be λ and the pitch angle. The function, The expression is as follows: (13) in, for The fitting parameters of the curve; Step 3.2) The wind speed estimated in Step 3.1) above. and the time parameter that reflects its changes Filter coefficients used as input to a fuzzy controller This is the output.

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