A parameter optimization method for aircraft stability control systems based on value functions

Abstract

The application discloses a kind of aircraft stability control system parameter optimization methods based on value function, belong to flight control technical field, comprising: the basic control parameter is obtained according to the dynamic coefficient of aircraft flight characteristic point;Desired stability control index is set to the characteristic point;Stability control performance under current control parameter is calculated;Value function about stability control performance and desired stability control index is constructed;The iteration mode of control parameter group in its adjacent domain optimization process is designed;Optimal control parameter is found.The application is aimed at the problem that aircraft flight characteristic point parameter design is limited to multiple stability control performance indexes, it is difficult to balance to meet index or to make single index design margin as large as possible, by constructing value function about typical stability control performance and desired performance index, search parameter combination in the adjacent domain of current control parameter group to make value function greater, to obtain more optimal control parameter as the benchmark of next search, determine the best control parameter group after multiple iterations.

Description

Technical Field

[0001] This invention relates to a parameter optimization method for an aircraft stability control system based on a value function, belonging to the field of aircraft flight control technology. Background Technology

[0002] The design of stable control system parameters for an aircraft refers to the design of reasonable control structure parameters to enable the aircraft to respond to commands smoothly and quickly. The control structure parameters to be designed need to ensure that the system's time-domain response meets the requirements for speed, while also having sufficient stability margin in the frequency domain. However, under certain operating conditions, it is difficult to simultaneously meet the requirements for speed and stability, increasing the difficulty of control parameter design.

[0003] In control engineering, the PID controller is a commonly used control structure. PID parameter design typically employs empirical formulas, frequency domain analysis, and various optimization algorithms. Empirical formulas rely on experience and trial-and-error to manually adjust controller parameters, requiring a certain understanding of the system and numerous trials, and thus have poor generalizability. Frequency domain analysis involves analyzing the system's transfer function in the frequency domain and using tools such as root locus or Bode plots to design parameters; however, this method struggles to balance speed with performance. Various optimization algorithms, such as the LQR parameter design method, can optimize the performance of parts of the control system but cannot precisely meet the desired performance requirements. Summary of the Invention

[0004] The technical problem solved by this invention is to overcome the shortcomings of the prior art and provide a parameter optimization method for aircraft stability control systems based on value functions. In the design process of aircraft stability control systems, a value function is constructed regarding typical stability control performance and expected indicators. By maximizing the value function, the control parameters are iteratively optimized so that the control system can meet the expected indicators in a balanced manner or maximize the design margin of individual performance, thereby enabling the aircraft to respond to commands more smoothly and quickly.

[0005] The technical solution of this invention is: a parameter optimization method for an aircraft stability control system based on a value function, comprising:

[0006] Basic control parameters are obtained based on the projectile dynamic coefficients at the flight characteristic points of the aircraft.

[0007] The desired performance indicators are set based on the airspace and speed range of the flight characteristic points to be designed.

[0008] Based on the projectile dynamic coefficients and basic control parameters at the flight characteristic points, the control performance in the time and frequency domains is calculated using fixed-point simulation.

[0009] Design a value function for stable control performance and desired performance index, and calculate the value function based on the set desired performance index and the control performance obtained from simulation.

[0010] Design the callback function and iteration method for the current control parameter optimization process in its neighborhood, including defining the neighborhood range, traversal step size and iteration exit condition;

[0011] The value function of other basic control parameter combinations in the neighborhood is calculated according to the value function calculation method. The optimal value is taken to replace the current control parameter. The calculation is iterated until the iteration exit condition is met, and finally the optimal control parameter is obtained.

[0012] Furthermore, the process of obtaining basic control parameters based on the projectile dynamic coefficients of the aircraft's flight characteristic points includes: obtaining a set of control parameters that meet the control capability under different aircraft dynamic coefficients based on prior knowledge, creating a table showing the correspondence between the dynamic coefficients and the basic control parameters, and interpolating the table based on the dynamic coefficients of the characteristic points to be designed to obtain a set of basic control parameters.

[0013] Furthermore, the expected performance metrics include expected speed, expected overshoot, expected amplitude margin, and expected phase margin.

[0014] Furthermore, the control performance in the time domain and frequency domain includes speed, overshoot, amplitude margin, and phase margin.

[0015] Furthermore, the value function includes:

[0016] If the stability control performance meets the expected targets, the value function V is:

[0017] V = -v1*(Ts - Ts) d )+v2*(Pm-Pm d )+v3*(Gm-Gm d )

[0018] If the stability control performance does not fully meet the expected targets, the value function V is:

[0019] V=-v1*(△Ts)-v2*(△Pm)-v3*(△Gm)-v4*(△Ct)

[0020] in, Ts represents speed, Ts d For the desired speed, Pm is the phase margin. d Gm represents the desired phase margin, and Gm represents the gain margin. d Ct represents the desired gain margin, and Ct represents the overshoot. d The expected overshoot is represented by v1, v2, v3, and v4, which are weights.

[0021] Furthermore, the callback function includes:

[0022] For a set of basic control parameters K1, K2, K3, design three callback functions as follows:

[0023] First callback function: Input K1, K2, K3, keep K1 and K2 unchanged, traverse the neighborhood of K3, calculate the value function under different K3 for the same K1 and K2. If the maximum value function is not at the boundary point of K3, return the K1, K2, K3 corresponding to the maximum value function and the value; otherwise, call the first callback function with the basic control parameters corresponding to the boundary point of the neighborhood as the basic value, and return the return value of the first callback function.

[0024] The second callback function takes K1, K2, and K3 as input, keeps K1 and K3 unchanged, traverses the neighborhood of K2, and calls the return value of the first callback function to calculate the value function for different combinations of K1, K2, and K3. It then finds the K1, K2, and K3 with the largest value function and their corresponding values. If the largest value is not a boundary point traversed by K2, it returns the current K1, K2, and K3 and their value. Otherwise, it repeatedly calls the second callback function with the boundary point K1, K2, and K3 as the base value and returns the return value of the second callback function.

[0025] The third callback function takes K1, K2, and K3 as input, traverses the neighborhood of K1 while keeping K2 and K3 unchanged, and calls the return value of the second callback function to calculate the value function for different combinations of K1, K2, and K3. It then finds the K1, K2, and K3 with the largest value function and their corresponding values. If the largest value is not a boundary point traversed by K1, it returns the current K1, K2, and K3 and their values. Otherwise, it repeatedly calls the third callback function with the boundary point K1, K2, and K3 as the base values ​​and returns the return value of the third callback function.

[0026] Based on the three callback functions, a set of basic control parameters K1 is... c K2 c K3 c The input is used to call the third callback function, which in turn calls the first and second callback functions in a nested manner, and iteratively finds the optimal set of control parameters with the highest value.

[0027] Furthermore, the iterative search method includes:

[0028] Input a set of basic control parameters K1 c K2 c K3 c The third callback function is called in K1. c Iterate through the neighborhood of K1, and call the second callback function to calculate the value function for different K1 values; then iterate through K2 by calling the second callback function. cWhen considering the neighborhood, to calculate the maximum value function under the current K1 and K2, the first callback function is called for different combinations of K1 and K2; the first callback function iterates through K3. c The domain calculates the corresponding value function and returns the maximum value and corresponding K3; the return value of the first callback function is used by the second callback function to calculate the value function and return the maximum value and corresponding K2, K3; the return value of the second callback function is used by the third callback function to calculate the value function and return the maximum value and corresponding K1, K2, K3; the return value of the third callback function is the final control parameter set K1 after iteration. f K2 f K3 f .

[0029] Furthermore, the neighborhood range includes the basic control parameter K1. c Minimum and maximum values ​​of the traversal, and the basic control parameter K2 c Minimum and maximum values ​​of the traversal, and basic control parameter K3 c The minimum and maximum values ​​are iterated over.

[0030] Furthermore, the traversal step size includes the traversal basic control parameter K1. c K2 c K3 c The minimum interval between different K1s in the neighborhood range.

[0031] Furthermore, the iteration exit condition includes the completion of the third callback function or the number of times the value function is calculated reaches a preset number.

[0032] The advantages of this invention compared to the prior art are:

[0033] (1) This invention fully considers the expected stability control index of the flight characteristic points of the aircraft, constructs a value function about the typical stability control performance and the expected index, and designs control parameters by maximizing the value function, so as to accurately meet the expected performance index or make the design margin of individual performance as large as possible.

[0034] (2) The parameter optimization method of the present invention is not limited by the control structure. The purpose of optimizing control performance can be achieved by reasonably constructing the value function.

[0035] (3) This invention can be implemented in software and is easy to operate in engineering. Attached Figure Description

[0036] Various other advantages and benefits will become apparent to those skilled in the art upon reading the following detailed description of preferred embodiments. The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. Furthermore, the same reference numerals denote the same parts throughout the drawings. In the drawings:

[0037] Figure 1 A schematic diagram of the parameter optimization method for an aircraft stability control system based on a value function provided by the present invention;

[0038] Figure 2 The flowchart for iterative optimization of control parameters provided in this invention;

[0039] Figure 3 This is an example PID control structure block diagram for a specific implementation. Detailed Implementation

[0040] To better understand the above technical solutions, the technical solutions of the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the embodiments of the present invention and the specific features in the embodiments are detailed descriptions of the technical solutions of the present invention, rather than limitations on the technical solutions of the present invention. In the absence of conflict, the embodiments of the present invention and the technical features in the embodiments can be combined with each other.

[0041] The following description, in conjunction with the accompanying drawings, provides a more detailed explanation of a parameter optimization method for an aircraft stability control system based on a value function, as provided in the embodiments of the present invention. Specific implementation methods may include:

[0042] Step 1: Quickly obtain a set of basic control parameters based on the projectile dynamic coefficients of the aircraft's flight characteristic points;

[0043] Step 2: Set the desired performance indicators based on the airspace and speed range of the flight characteristic points to be designed;

[0044] Step 3: Based on the dynamic coefficients and control parameters of the flight characteristic points in Step 1, perform fixed-point simulation calculations to determine the control performance in the time and frequency domains.

[0045] Step 4: Design a value function for stable control performance and desired performance indicators. Calculate the value function based on the desired performance indicators set in Step 2 and the control performance obtained from the simulation in Step 3.

[0046] Step 5: Design the callback function and iteration method for the current control parameter group in its neighborhood optimization process, including defining the neighborhood range, traversal step size, and iteration exit condition.

[0047] Step 6: Calculate the value function of other control parameter combinations in the neighborhood according to the value function calculation method in Step 4, take the optimal value to replace the current control parameter set, and iterate until the exit condition in Step 5 is met, and finally obtain the optimal control parameter set.

[0048] Furthermore, the method for quickly obtaining a set of basic control parameters in step one is as follows:

[0049] Based on prior knowledge, a set of control parameters that basically meet the control capabilities under different aircraft dynamic coefficients is obtained. The correspondence between dynamic coefficients and control parameters is tabulated. By interpolating the table based on the dynamic coefficients of the feature points to be designed, a set of basic control parameters can be quickly obtained. The value of the basic control parameter set is denoted as K1. c K2 c K3 c .

[0050] Furthermore, the control target to be achieved in step two is:

[0051] Typical performance indicators commonly used in stable control systems include: speed of response, overshoot, gain margin, and phase margin. The desired performance indicators for these indicators are denoted as Ts. d ,Ct d ,Gm d ,Pm d .

[0052] Furthermore, the performance of the time-domain and frequency-domain calculations in the fixed-point simulation in step three is as follows:

[0053] Based on the dynamic coefficients of the flight characteristic points in step one, and substituted into the control parameter set, the typical stable control in the time and frequency domains obtained through fixed-point simulation calculations are: speed Ts, overshoot Ct, gain margin Gm, and phase margin Pm.

[0054] Furthermore, the value function V for stable control performance and desired index in step four is designed as follows:

[0055] If the stability control performance meets the expected targets, the value function V is calculated as follows:

[0056] V = -v1*(Ts - Ts) d )+v2*(Pm-Pm d )+v3*(Gm-Gm d )

[0057] If the stability control performance does not fully meet the expected targets, the value function V is calculated as follows:

[0058] V=-v1*(△Ts)-v2*(△Pm)-v3*(△Gm)-v4*(△Ct)

[0059] in,

[0060]

[0061] The values ​​v1, v2, v3, and v4 above represent the weights of the performance of each stability control system in the value function.

[0062] Furthermore, the callback function in the optimization process of step five is designed as follows:

[0063] First callback function: Input K1, K2, K3, keep K1 and K2 unchanged, traverse the neighborhood of K3, calculate the value function under different K3s for the same K1 and K2. If the maximum value function is not at the boundary point of K3, return the K1, K2, K3 and the value corresponding to the maximum value function; otherwise, call the first callback function with the control parameters corresponding to the boundary point of the neighborhood as the base value, and return the return value of the first callback function.

[0064] The second callback function takes K1, K2, and K3 as input, keeps K1 and K3 unchanged, traverses the neighborhood of K2, and calls the return value of the first callback function to calculate the value function for different combinations of K1, K2, and K3. It then finds the K1, K2, and K3 with the largest value function and their corresponding values. If the largest value is not a boundary point traversed by K2, it returns the current K1, K2, and K3 and their value. Otherwise, it repeatedly calls the second callback function with the boundary point K1, K2, and K3 as the base value and returns the return value of the second callback function.

[0065] The third callback function takes K1, K2, and K3 as input, traverses the neighborhood of K1 while keeping K2 and K3 unchanged, and calls the return value of the second callback function to calculate the value function for different combinations of K1, K2, and K3. It then finds the K1, K2, and K3 with the largest value function and their corresponding values. If the largest value is not a boundary point traversed by K1, it returns the current K1, K2, and K3 and their value. Otherwise, it repeatedly calls the third callback function with the boundary point's K1, K2, and K3 as the base values ​​and returns the return value of the third callback function. The aforementioned K1, K2, and K3 are the control parameter group for the current callback function.

[0066] Furthermore, the iterative method in the optimization process of step five is as follows:

[0067] The iterative method reference Figure 2 Input a set of basic control parameters K1 c K2 c K3 c The third callback function is called in K1. c Iterate through the neighborhood of K1, and call the second callback function to calculate the value function for different K1 values; then iterate through K2 by calling the second callback function. c When dealing with the neighborhood, to calculate the maximum value function under the current K1 and K2, the first callback function needs to be called for different combinations of K1 and K2; the first callback function iterates through K3. cThe domain calculates the corresponding value function and returns the maximum value and corresponding K3; the return value of the first callback function is used by the second callback function to calculate the value function and return the maximum value and corresponding K2, K3; the return value of the second callback function is used by the third callback function to calculate the value function and return the maximum value and corresponding K1, K2, K3; the return value of the third callback function is the final control parameter set K1 after iteration. f K2 f K3 f .

[0068] Furthermore, the optimal control parameter set in step six is ​​as follows:

[0069] The basic control parameter K1 quickly obtained in step one c K2 c K3 c Substituting these parameters into the iterative method designed in step five, the optimal set of control parameters is calculated and denoted as K1. f K2 f K3 f .

[0070] In the solutions provided in the embodiments of the present invention, reference is made to... Figure 1 The method flow for optimizing control parameters is presented, outlining the algorithm steps: Step 1: Obtain a set of basic control parameters based on the dynamic coefficients of the aircraft's flight characteristic points; Step 2: Set the expected performance index for each characteristic point; Step 3: Calculate the typical stable control performance under the current control parameters; Step 4: Construct a value function relating the stable control performance and the expected performance index; Step 5: Design the callback function and iteration method for the control parameter set in its neighborhood optimization process; Step 6: Substitute the characteristic point into the iterative calculation to find the optimal control parameters.

[0071] In one embodiment of the present invention, the control structure block diagram is as follows: Figure 3 As shown, the projectile dynamics model is as follows:

[0072]

[0073] Wherein, the projectile input δ is the control rudder deflection; the projectile output ω is the angular velocity, a acc It's acceleration. The intermediate state variables α represent the angle of attack, and θ represents the trajectory inclination angle. The derivative representing the trajectory inclination angle, It is the derivative of angular velocity. It's the attitude angle. V is the derivative of the attitude angle, and Vm is the velocity.

[0074] The dynamic coefficients of the aircraft's flight characteristic points are a2 = -11.6, a3 = 29, a4 = 1.2, a5 = 0.12, and the speed is Vm = 145.

[0075] The specific workflow is described below:

[0076] 1. The control system can quickly obtain a set of basic control parameters in the following way:

[0077] Based on prior knowledge, a set of control parameters that basically meet the control capabilities under different aircraft dynamic coefficients is obtained. The correspondence between dynamic coefficients and control parameters is tabulated. By interpolating the table based on the dynamic coefficients of the feature points to be designed, a set of basic control parameters can be quickly obtained. The value of the basic control parameter set is denoted as K1. c =0.85,K2 c =161,K3 c =0.06.

[0078] 2. The desired control performance indicators are set as follows:

[0079] Typical indicators commonly used in stability control systems include: desired speed, desired overshoot, and desired performance.

[0080] Gain margin and desired phase margin. The desired performance indicators are denoted as follows:

[0081] Ts d =0.5s,Ct d =10%, Gm d =6db,Pm d =30°.

[0082] 3. The performance indicators for calculating the time and frequency domains in fixed-point simulation are as follows:

[0083] Based on the dynamic coefficients of the aircraft's flight characteristic points, and substituted into the control parameter set, the typical stable control indices in the time and frequency domains obtained through fixed-point simulation calculations are: speed Ts = 0.3s, overshoot Ct = 5%, amplitude margin Gm = 8dB, and phase margin Pm = 40°.

[0084] 4. Design of the value function V for stability control indicators and expected indicators:

[0085] If all stability control performance indicators meet expectations, the value function V is calculated as follows:

[0086] V = -30*(Ts - Ts) d )+(Pm-Pm d )+5*(Gm-Gm d )

[0087] If the stability control performance indicators do not fully meet the expectations, the value function V is calculated as follows:

[0088] V=-30*(△Ts)-(△Pm)-5*(△Gm)-1.5*(△Ct)

[0089] in,

[0090]

[0091] Substituting the desired target and the simulated target into the calculation, the value function V is obtained as follows:

[0092] V=-30*(0.3-0.5)+(40-30)+5*(8-6)=26

[0093] 5. The defined neighborhood range, traversal step size, iteration method, and optimal control parameter set are as follows:

[0094] The neighborhood range is ±20% of the control parameter value, and the traversal step size is 5% of the control parameter value.

[0095] The iteration method and iteration exit conditions in the optimization process are as described in step five of the invention description. Based on the three designed callback functions, the basic control parameter K1 is... c K2 c K3 c Inputting the data and calling the third callback function will find the most valuable set of optimal control parameters.

[0096] K1 f =0.69,K2 f =55.9,K3 f =0.089.

[0097] This invention provides a simulation system with model given points for the aircraft dynamics system and controller. The simulation system calculates typical stability control indices to iteratively optimize controller parameters until optimal performance is achieved. This parameter set is the final design of the controller characteristic points.

[0098] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this invention and their equivalents, this invention also intends to include these modifications and variations.

[0099] The contents not described in detail in this specification are common knowledge to those skilled in the art.

Claims

1. A method for optimizing parameters of an aircraft stability and control system based on a value function, characterized in that, The method comprises the following steps: obtaining basic control parameters according to aerodynamic coefficients of flight feature points of an aircraft; setting expected performance indexes according to airspace and speed domain of flight feature points to be designed; calculating control performance in time domain and frequency domain through point simulation according to aerodynamic coefficients of the flight feature points and the basic control parameters; designing a value function related to stable control performance and expected performance indexes, and calculating the value function according to the set expected performance indexes and the simulation control performance; designing a callback function and an iteration mode in a neighboring domain of the current control parameters, including setting a neighboring domain range, a traversal step and an iteration exit condition; calculating value functions of other basic control parameter combinations in the neighboring domain according to the calculation mode of the value function, replacing the current control parameters with the optimal value, and iteratively operating until the iteration exit condition is met to finally obtain the optimal control parameters.

2. The method of claim 1, wherein, The basic control parameters are obtained according to aerodynamic coefficients of flight feature points of an aircraft, including obtaining control parameter groups satisfying control ability under different aerodynamic coefficients of the aircraft according to prior knowledge, setting a table of the corresponding relationship between the aerodynamic coefficients and the basic control parameters, and interpolating the table to obtain a group of basic control parameters according to the aerodynamic coefficients of the flight feature points to be designed.

3. The method of claim 1, wherein, The expected performance indexes include expected rapidity, expected overshoot, expected amplitude margin and expected phase margin.

4. The method of claim 1, wherein, The control performance in time domain and frequency domain includes rapidity, overshoot, amplitude margin and phase margin.

5. The method of claim 1, wherein, The value function includes: If all the stable control performances meet the expected indexes, the value function V is V = -v1*(Ts-Ts d )+v2*(Pm-Pm d )+v3*(Gm-Gm d ) If not all the stable control performances meet the expected indexes, the value function V is V = -v1*(△Ts)-v2*(△Pm)-v3*(△Gm)-v4*(△Ct) wherein, Ts is the speed, Ts d is the desired speed, Pm is the phase margin, Pm d is the desired phase margin, Gm is the gain margin, Gm d is the desired gain margin, Ct is the overshoot, Ct d is the desired overshoot, v1, v2, v3, v4 are weights.

6. The method of claim 1, wherein The callback function includes: For an input group of basic control parameters K1, K2 and K3, three callback functions are designed, respectively: The first callback function: input K1, K2 and K3, keep K1 and K2 unchanged, traverse K3 in the neighboring domain, calculate the value function under the same K1 and K2 and different K3, if the maximum value function is not the boundary point of K3, return the maximum value function corresponding to K1, K2, K3 and the value; otherwise, call the first callback function with the basic value of the neighboring domain boundary point of K1, K2 and K3, and return the return value of the first callback function; The second callback function: input K1, K2 and K3, keep K1 and K3 unchanged, traverse K2 in the neighboring domain, call the return value of the first callback function to calculate the value function for different K1, K2 and K3 combinations, solve the maximum K1, K2 and K3 of the value function and the corresponding value; if the maximum value is not the boundary point of K2, return the current K1, K2, K3 and the value; otherwise, repeatedly call the second callback function with the basic value of the boundary point of K1, K2 and K3, and return the return value of the second callback function; The third callback function: input K1, K2 and K3, keep K1 unchanged, traverse K2 in the neighboring domain, call the return value of the second callback function to calculate the value function for different K1, K2 and K3 combinations, solve the maximum K1, K2 and K3 of the value function and the corresponding value; if the maximum value is not the boundary point of K2, return the current K1, K2, K3 and the value; otherwise, repeatedly call the third callback function with the basic value of the boundary point of K1, K2 and K3, and return the return value of the third callback function. The third callback function: input K1, K2, K3, traverse in the neighborhood of K1, keep K2, K3 unchanged, respectively call the return value of the second callback function to calculate the value function for different K1, K2, K3 combinations, solve the maximum K1, K2, K3 and the corresponding value of the value function, if the maximum value is not the boundary point of K1 traversal, return the current K1, K2, K3 and the value, otherwise, repeat the call of the third callback function based on the K1, K2, K3 of the boundary point, and return the return value of the third callback function; According to three callback functions, a set of basic control parameters K1 c , K2 c , K3 c input, call the third callback function and nested call the first second callback function, iterative search for a set of optimal control parameters with the greatest value.

7. The method of claim 6, wherein, The method of iterative search comprises: Input a set of basic control parameters K1 c ,K2 c ,K3 c , call the third callback function to traverse in the neighborhood of K1 c , call the second callback function for calculating the value function respectively for different K1; when calling the second callback function to traverse the neighborhood of K2 c , for calculating the maximum value function under the current K1, K2, call the first callback function for different K1, K2 combination; the first callback function calculates the corresponding value function by traversing the K3 c field, and then returns the maximum value and the corresponding K3; the return value of the first callback function is given to the second callback function to calculate the value function, and then returns the maximum value and the corresponding K2, K3; the return value of the second callback function is given to the third callback function to calculate the value function, and then returns the maximum value and the corresponding K1, K2, K3; the return value of the third callback function is the final control parameter set K1 f ,K2 f ,K3 f .

8. The method of claim 6, wherein, The iteration exit condition comprises the end of the third callback function or the number of times of calculating the value function reaching a preset number.

9. The method of claim 1, wherein, The proximity range comprises a base control parameter K1 c The minimum and maximum of the traversal, base control parameter K2 c The minimum and maximum of the traversal, base control parameter K3 c The minimum and maximum of the traversal.

10. The method of claim 1, wherein The traversal step length comprises a traversal base control parameter K1 c , K2 c , K3 c Minimum interval of different K1 in the neighborhood range.

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