Event-triggered intermittent control method for pitch angle of wind generating set

Abstract

The invention discloses an event-triggered intermittent control method for a pitch angle of a wind generating set, and belongs to the technical field of wind motor control. The method is characterized by comprising the following steps: step 1, constructing a dynamic model of the wind driven generator; step 2, setting a control target as a full-load region in which the wind driven generator operates, and defining an adjustment error conversion control target; 3, designing a neural network adaptive estimation law based on the converted control target; 4, constructing a self-adaptive neural network controller, and estimating an unknown dynamic part and nonlinear function compensation of the wind driven generator in real time; and 5, carrying out interval division on the control process to realize real-time tracking control on the pitch angle of the wind generating set. According to the technical scheme, the control interval and the rest interval are reasonably divided, and the neural network estimation law is utilized, so that the control cost and the communication resource consumption are reduced, and meanwhile, the stable operation of the wind driven generator system and the improvement of the control performance are ensured.

Description

TECHNICAL FIELD

[0001] The application relates to an event-triggered intermittent control method for the pitch angle of a wind turbine, and belongs to the technical field of wind motor control. BACKGROUND

[0002] With the rapid development of wind power technology, the research on wind turbine control methods has also been increasingly in-depth. At present, there are various control methods for variable speed wind turbines (VSWTs), including traditional PID control, fuzzy logic control and advanced adaptive neural network control. These methods have improved the control performance of wind turbines to some extent, but there are still many challenges when facing the nonlinear characteristics of the dynamic model of the wind turbine and the problem of unknown dynamics estimation and compensation. For example, although the sliding mode control can handle nonlinear problems, it is easy to cause chattering and high gain problems; and although the adaptive neural network control has good adaptability and learning ability, it may face the problems of overfitting and high computational complexity.

[0003] In the existing wind turbine control strategies, the problem of nonlinear compensation and estimation is always a key technical difficulty. The nonlinear characteristics of the wind turbine make it difficult for traditional linear control methods to achieve ideal control effects, and the existing nonlinear control methods often need a large amount of real-time computing resources when dealing with the complex nonlinear dynamic characteristics of the wind turbine, resulting in high control cost. For example, the Chinese invention patent with the patent name of "a predefined space-time pitch angle control method for a variable speed wind turbine" (application number 202511425080.X) submitted by the applicant of the present application on September 30, 2025, discloses a technical solution. In the technical solution, the unknown smooth nonlinear function in the dynamic model of the variable speed wind turbine pitch angle control is compensated by using the neural network method, and a controller and an adaptive law are proposed in combination with the neural network. However, the defects of this scheme are that the adaptive neural network control needs to adjust the network parameters online, which involves a large amount of matrix operations and gradient calculations, which not only increases the burden of the processor, but also may cause waste of control resources.

[0004] In addition, although the existing event-triggered control reduces the control update frequency to some extent, the application research in the wind turbine system is relatively less, especially the research on combining intermittent control to further reduce control cost and communication resources is still in the exploratory stage. SUMMARY

[0005] The technical problem to be solved by this invention is to overcome the shortcomings of the prior art and provide an event-triggered intermittent control method for the pitch angle of a wind turbine generator set. This method achieves stable operation and improved control performance of the wind turbine generator system by rationally dividing the control interval and rest interval and utilizing neural network estimation laws, thereby reducing control costs and communication resource consumption.

[0006] The technical solution adopted by this invention to solve its technical problem is: an event-triggered intermittent control method for the pitch angle of a wind turbine generator set, characterized by the following steps: Step 1: Establish dynamic models of the wind turbine rotor side and the wind turbine generator side, and construct a dynamic model of the wind turbine. Step 2: Set the control objective to maintain the rotor speed and generator power at rated values ​​in the full-load operating range of the wind turbine, using the pitch angle as the control input, and define the regulation error conversion control objective. Step 3: Based on the transformed control objective, design an adaptive estimation law for the neural network; Step 4: Based on the neural network adaptive estimation law, construct an adaptive neural network controller to estimate the unknown dynamic components and nonlinear function compensation of the wind turbine in real time; Step 5: Divide the control process into intervals and use different estimation laws in different intervals to achieve real-time tracking control of the wind turbine pitch angle.

[0007] Preferably, in step 2, the adjustment error e is the adjusted error after filtering, which is r. The derivative of the filtered adjusted error r is obtained as follows: in, Let v be the first derivative of the wind speed. J is the first derivative of the pitch angle β. r For rotor inertia, The rotor angular velocity ω r angular acceleration, K t For total damping, J t T is the total inertia of the transmission system. g For the equivalent electromagnetic torque, T α Where is the aerodynamic torque, and c is the filter coefficient. Equivalent electromagnetic torque T g The first derivative, , It is a nonlinear function that includes wind speed, rotor angular velocity, and blade pitch angle; The control objective is translated into control inputs. This allows for the control of the adjustment error e.

[0008] Preferably, nonlinear functions Represented as: nonlinear functions Represented as: in, Let v be the first derivative of the wind speed. The first derivative of the pitch angle β. The rotor angular velocity ω r angular acceleration, K t For total damping, J t T is the total inertia of the transmission system. g For the equivalent electromagnetic torque, T α Where is the aerodynamic torque, and c is the filter coefficient. Equivalent electromagnetic torque T g The first derivative.

[0009] Preferably, in step 3, the adaptive estimation law of the neural network is: Combining nonlinear functions , The unknown dynamics neural network estimate is: in, For ideal weights The estimated value, express The first derivative, denoted by , where g is the learning rate of the neural network; g is the learning rate coefficient for weight estimation. This represents the sigmoid activation function, where Z is the intermediate variable. To estimate the error, v is the wind speed, ω r β is the rotor angular velocity, β is the propeller pitch angle, and the superscript T indicates transpose.

[0010] Preferably, in step 4, the adaptive neural network controller is: in, Let represent the control input at time t; K represents the feedback error gain, which is a real number; and r is the filtered adjustment error. The first derivative of the pitch angle β. For ideal weights The estimated value, where the superscript T indicates transpose. This represents the sigmoid activation function, with Z being the intermediate variable.

[0011] Preferably, in step 1, the overall control process is divided into control intervals and rest intervals, with each control interval followed by a rest interval. Event-triggered control strategies and intermittent control strategies are introduced into the adaptive neural network controller. An intermittent event-triggered adaptive neural network controller is designed, and different estimation laws are used in the control intervals and rest intervals to adjust the control strategies in real time.

[0012] The preferred intermittent control strategy is expressed as follows: Where U(t) represents the control input under intermittent control at time t, t k t k+1 Let s represent the start times of the k-th and (k+1)-th control intervals, respectively. k Indicates the start time of the k-th rest area; Indicates an adjustable parameter; The event triggering control strategy is as follows: in, , representing the trigger measurement error at time t; Indicates the controller that triggers the event within the control zone; express Time-based control input; , These represent the i-th and (i+1)-th trigger times within the k-th control interval, respectively. Represents the space of real numbers; Let f be the positive definite constant to be set; inf represents the infimum; After the event-triggered control strategy is triggered, then Updated to , express Time-based control input.

[0013] Preferably, for rest areas, the ideal weights are applied within the rest area. The estimated value That is, at the end of the previous control interval between rest areas, maintain the ideal weight at that time. The estimated value constant.

[0014] Compared with the prior art, the beneficial effects of this invention are: In the event-triggered intermittent control method for the pitch angle of a wind turbine generator set in this application, by reasonably dividing the control interval and rest interval, and using the neural network estimation law, the stable operation of the wind turbine generator system and the improvement of control performance are ensured while reducing control costs and communication resource consumption.

[0015] This invention converts a non-affine model into an affine model, successfully determines the form of the control input by introducing adjustment error technology, and effectively solves nonlinear problems by using the method of designing estimation laws in intervals, thus reducing the real-time computation burden. On the other hand, it cleverly divides the overall control process into control intervals and rest intervals, and establishes the quantitative relationship between the two by using upper and lower bounds technology, thereby realizing the organic combination of event-triggered control and intermittent control, significantly reducing control costs and effectively avoiding the need for real-time updates of control information.

[0016] This invention clearly defines the practical controller design, rigorously analyzes the stability of the control interval and intermittent interval using Lyapunov theory, and fully verifies the effectiveness of the designed controller through asymptotic stabilization and mathematical induction methods, ensuring the stable operation of the wind turbine system and its eventual convergence to a bounded neighborhood. Simultaneously, theoretical analysis rigorously proves that there is a lower bound on the time for each event triggering period within the control interval, effectively avoiding Zeno behavior and further improving the system's reliability and practicality. Attached Figure Description

[0017] Figure 1 This is a flowchart of an event-triggered intermittent control method for the pitch angle of a wind turbine generator.

[0018] Figure 2 This is a graph showing the power coefficient as a function of the tip speed ratio. Figure 3 Power curves at different wind speeds; Figure 4 This is a schematic diagram of an intermittent control strategy. Detailed Implementation

[0019] Figures 1-4 This is the preferred embodiment of the present invention, which is described below in conjunction with the accompanying drawings. Figures 1-4 The present invention will be further described below.

[0020] like Figure 1 As shown, an event-triggered intermittent control method for the pitch angle of a wind turbine generator set includes the following steps: Step 1: Establish dynamic models of the wind turbine rotor side and the wind turbine generator side, and construct a dynamic model of the wind turbine. For a wind turbine structure comprising a generator, gearbox, and wind turbine, dynamic models are established on both the rotor and generator sides to construct the dynamic model of the wind turbine. The generator includes a generator rotor and a high-speed shaft, while the wind turbine includes a rotor, a low-speed shaft, and adjustable blades. The process of constructing the dynamic model of the wind turbine is as follows: The aerodynamics extracted from a wind turbine is defined as follows: (1) Among them, P α Where ρ is the aerodynamic power, ρ is the air density, R is the blade radius of the wind turbine, v is the wind speed, and C is the wind speed. P (λ, β) is the power coefficient of the wind turbine, a nonlinear function of λ and β; β is the blade pitch angle, and λ is the tip speed ratio, expressed as: (2) Where, ω r The value represents the rotor angular velocity, R is the blade radius of the wind turbine, and v is the wind speed.

[0021] Pneumatic torque T α Defined as: (3) The dynamic models for the rotor side and the generator side are described as follows: (4) Among them, J r This refers to the rotor inertia. K is the angular acceleration of the rotor. r T is the external damping constant of the low-speed shaft. ls For low-speed shaft torque; J g This refers to the generator rotor inertia. T is the angular acceleration of the generator rotor. hs For high-speed shaft torque; K g ω is the external damping constant of the high-speed shaft. g T is the angular velocity of the generator rotor. em This refers to the electromagnetic torque of the generator.

[0022] The gear ratio n of the gearbox g Represented as: (5) The dynamic model of a wind turbine is described as follows: (6) Among them, J t This is the total inertia of the transmission system. K t For total damping, T g For equivalent electromagnetic torque, .

[0023] Generator output power P g Represented as: (7) The power coefficient C of a wind turbine P The curve of (λ, β) as a function of the tip speed ratio λ is shown below. Figure 2As shown, the power coefficient C of the wind turbine P (λ, β) is represented as: (8) in, h 1. h 2. h 3. h 4. h 5. h 6 is the fitting parameter. h 1 = 0.5176 h 2=116、 h 3 = 0.4 h 4=5、 h 5=21、 h 6 = 0.0068 β The pitch angle is the propeller angle. Lambda For the tip speed ratio, Lambda x The corrected tip speed ratio is expressed as: (9) Where β is the blade pitch angle and λ is the tip speed ratio.

[0024] Depending on the wind speed, wind turbines can operate in three zones, such as Figure 3 As shown. Obviously, there are different control objectives in different operating areas. In area 2 (partial load area), the main control objective is to make the wind turbine run on its maximum power curve and capture the maximum energy from the wind. The generator torque controller is used to change the rotor speed while setting the pitch angle to the optimal value. In area 3 (full load area), the main control objective is to avoid over-generation, overspeed and large oscillation of the generator and rotor speed to ensure the safety of the entire wind energy conversion system (WECS) and obtain high-quality wind power for grid connection. Equations (6) and (8) show that the pitch system can be used to limit the generated aerodynamic torque, thereby reducing the rotor speed and output power. This application is mainly for the design of the control strategy for area 3. Therefore, the aim is to keep the rotor speed and generator power at rated values ​​by using an adaptive pitch angle controller, and to reduce system losses and reduce the occupancy of control and communication resources by designing an event-triggered intermittent pitch angle controller.

[0025] In region 3, the usual practice is to maintain the generator electromagnetic torque T. em The pitch angle β is constant, and only the control signal is used for the wind turbine. This is because the power coefficient C of the wind turbine is constant. P (λ, β) is highly sensitive to pitch angle time delay, meaning the pitch angle β has a higher control gain than other alternatives. In practice, a constant generator electromagnetic torque T emThis can be achieved through a generator and a power electronic controller. Since the time response of the electrical subsystem in a wind turbine is much faster than that of the mechanical subsystem, it can be assumed that the generator's electromagnetic torque T... em It is equal to its reference point. Therefore, as long as the rotor speed is maintained at the rated value, it is sufficient to achieve the control objective of region 3.

[0026] Step 2: Set the control objective to maintain the rotor speed and generator power at rated values ​​in the full-load operating range of the wind turbine, using the pitch angle as the control input, and define the regulation error conversion control objective.

[0027] The adjustment error e is defined as: (10) Where, ω r ω represents the rotor angular velocity. d This indicates the rotor's rated angular velocity.

[0028] At this point, the control objective becomes eliminating the regulation error e. The regulation error e is filtered, and the filtered regulation error r is defined as follows: (11) Where c is the filter coefficient, and c > 1. Taking the derivative with respect to r, based on equation (6), the dynamic of the rotor speed is represented by the filtered adjustment error: (12) in, Let r be the first derivative of the filtered adjustment error r; The second derivative of the adjustment error e; The rotor angular velocity ω r The second derivative; pneumatic torque T α The first derivative; Equivalent electromagnetic torque T g The first derivative; K t For total damping, J t This is the total inertia of the transmission system.

[0029] Combining the above formulas (3) and (6), the aerodynamic torque T α first derivative Represented as: (13) in, Let v be the first derivative of the wind speed. J is the first derivative of the pitch angle β. r For rotor inertia, The rotor angular velocity ω r angular acceleration, K tFor total damping, J t T is the total inertia of the transmission system. g For the equivalent electromagnetic torque, T α This refers to aerodynamic torque.

[0030] Substituting equation (13) into equation (12), we obtain the first derivative of the filtered adjustment error r. The expression: (14) in, Let v be the first derivative of the wind speed. J is the first derivative of the pitch angle β. r For rotor inertia, The rotor angular velocity ω r angular acceleration, K t For total damping, J t T is the total inertia of the transmission system. g For the equivalent electromagnetic torque, T α Where is the aerodynamic torque, and c is the filter coefficient. Equivalent electromagnetic torque T g The first derivative, , It is a nonlinear function that includes wind speed, rotor angular velocity, and blade pitch angle.

[0031] Ultimately, the control objective is transformed into controlling the input quantity. This allows for the control of the adjustment error e.

[0032] Clearly, by utilizing the filtered adjustment error technique, the design of the control signal becomes... Instead of β, the first derivative of the control signal appears in affine form in equation (14).

[0033] Represented as: (15) Represented as: (16) Step 3: Based on the transformed control objective, design an adaptive estimation law for the neural network; The method for designing adaptive estimation laws for neural networks is as follows: According to equation (8), the aerodynamic torque T α It is a decreasing function, which indicates that: nonlinear functions (17) Due to the physical properties of wind turbines, and It is bounded, represented as: (18) in, , It is an unknown negative constant; , It is an unknown positive number; therefore, , The constant parameters in the equation are unknown, so a neural network is used for approximate estimation. The output of the neural network is expressed as: (19) in, X represents the output of the neural network; X represents the input of the neural network. , , , They represent , The real space of dimension 1 , These represent the number of nodes in the input and output layers of the neural network, respectively. , These represent the weights of the hidden layer and the output layer of the neural network, respectively. , They represent , The real space of dimension 1 This represents the number of nodes in the hidden layer. This represents the sigmoid activation function; the superscript T indicates transpose.

[0034] Combination , The unknown dynamics neural network estimate is: (2 Among them, Z represents the ideal weights; Z is the intermediate variable. ; To estimate the error, v is the wind speed, ω r β is the rotor angular velocity, and β is the propeller pitch angle.

[0035] because It is unknown; we need to estimate it and set the following parameters: (twenty one) in, This represents the maximum ideal weight value; This indicates the maximum estimated error.

[0036] The estimated value is expressed as The neural network adaptive estimation law for equation (20) is expressed as: (twenty two) in, express The first derivative; denoted by , where g represents the learning rate of the neural network (RBFNN neural network is used in this application); g is the learning rate coefficient for weight estimation.

[0037] Step 4: Based on the neural network adaptive estimation law, construct an adaptive neural network controller to estimate the unknown dynamic components and nonlinear function compensation of the wind turbine in real time; The adaptive neural network controller is represented as: (twenty three) in, t represents the control input at time t; K represents the feedback error gain, which is a real number.

[0038] The adaptive neural network controller shown in formula (23) estimates the unknown dynamics of the wind turbine and compensates for nonlinear functions in real time.

[0039] Step 5: Divide the overall control process into a control interval and a rest interval. Introduce event-triggered control strategy and intermittent control strategy into the adaptive neural network controller. Design an intermittent event-triggered adaptive neural network controller. Use different estimation laws in the control interval and the rest interval to adjust the control strategy in real time and realize real-time tracking control of the pitch angle of the wind turbine generator.

[0040] Network control can improve control efficiency and reduce reconfiguration and maintenance costs. However, since communication networks are usually shared by different system nodes, and network resources such as communication channel bandwidth and computing power are limited, solving the energy, computation, and communication constraints is of great significance in both theory and practice. To address this issue, this application proposes an intermittent event-triggered adaptive neural network controller that reduces control cost losses and saves communication resources, combined with... Figure 4 The diagram shown illustrates an intermittent strategy. The design process for an intermittent event-triggered adaptive neural network controller is as follows: The overall control process is divided into control zones and rest zones, with each control zone followed by a rest zone. The intermittent control strategy is represented as follows: (twenty four) Where U(t) represents the control input under intermittent control at time t, t k t k+1 Let s represent the start times of the k-th and (k+1)-th control intervals, respectively. k Indicates the start time of the k-th rest area; Indicates an adjustable parameter; The event triggering control strategy is as follows: Define the triggering event in the control zone as follows: (25) in, This represents the trigger measurement error at time t; Indicates the controller that triggers the event within the control zone; express Time-based control input; , These represent the i-th and (i+1)-th trigger times within the k-th control interval, respectively. Represents the space of real numbers; is the positive definite constant to be set; inf represents the infimum.

[0041] If equation (25) is triggered, then Updated to , express Time-based control input; For the rest area, within the rest area, That is, at the end of the previous control interval between rest periods, the estimated value of the neural network at that time is maintained. constant.

[0042] For the intermittent control strategy of equation (24), there are two positive definite constants. , satisfy: (26) Where supremum represents the supremum; σ is the normal constant of the control interval; It is the set of natural numbers; μ is a constant with a value of 1.

[0043] Based on Lyapunov theory, the stability of the adaptive neural network controller and the intermittent event-triggered adaptive neural network controller in this application is verified, which enables the wind turbine system to converge asymptotically and stabilize within a bounded region, ensuring the effectiveness of the control strategy.

[0044] Meanwhile, the event triggering can generate an infinite number of events due to Zeno behavior. To avoid Zeno behavior, it is necessary to ensure that each triggering interval has a positive lower bound. The proof of avoiding Zeno behavior is as follows: For the proposed triggering condition, i.e., equation (25), there exists a time constant. Such that for any positive integer k, the trigger interval length is... There exists a lower bound of .

[0045] for ,have: (27) in, Represents a symbolic function; for The first derivative; according to ,get: (28) in, express The first derivative; This is a constant used to adjust the shape of the hyperbolic cosine function; Since all closed-loop system signals are bounded, there must exist a positive constant b such that ,because Trigger measurement error at time ,and M is the threshold, which ensures that the triggering period length must satisfy... Therefore, the designed event triggering mechanism avoids Zeno behavior.

[0046] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention in any other way. Any person skilled in the art may make changes or modifications to the above-disclosed technical content to create equivalent embodiments. However, any simple modifications, equivalent changes, and modifications made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the protection scope of the present invention.

Claims

1. An event-triggered intermittent control method for pitch angle of a wind turbine generator system, characterized in that: Comprising the following steps: Step 1, establish the dynamics model of wind turbine rotor side and wind turbine generator side, and construct the dynamic model of wind turbine; Step 2, set the control target as in the full load area of wind turbine operation, take the pitch angle as the control input, keep the rotor speed and generator power at the rated value, and define the regulation error conversion control target; Step 3, based on the converted control target, design a neural network adaptive estimation law; Step 4, based on the neural network adaptive estimation law, construct an adaptive neural network controller to estimate the unknown dynamics of the wind turbine and the nonlinear function compensation in real time; Step 5, divide the control process into intervals, use different estimation laws in different intervals, and realize real-time tracking control of the pitch angle of the wind turbine unit.

2. The event-triggered intermittent control method for pitch angle of a wind turbine generator system according to claim 1, characterized in that: In step 2, the regulation error e is filtered as r, and the derivative of the filtered regulation error r is obtained as: wherein is the first derivative of the wind speed v, is the first derivative of the pitch angle β, J r is the rotor inertia, is the angular acceleration of the rotor angular speed ω r K t is the total damping, J t is the total inertia of the drive train, T g is the equivalent electromagnetic torque, T α is the aerodynamic torque, c is a filter coefficient, is the first derivative of the equivalent electromagnetic torque T g , , is a non-linear function comprising the wind speed, the rotor angular speed and the pitch angle; The control target is converted into a control input quantity The control adjusts the error e further.

3. The event-triggered intermittent control method for pitch angle of a wind turbine generator system according to claim 2, characterized in that: Non-linear function is represented as: Non-linear function is represented as: wherein is the first derivative of the wind speed v, is the first derivative of the pitch angle β, is the angular acceleration of the rotor angular speed ω r K t is the total damping, J t is the total inertia of the drive train, T g is the equivalent electromagnetic torque, T α is the aerodynamic torque, c is a filter coefficient, is the first derivative of the equivalent electromagnetic torque T g .

4. The event-triggered intermittent control method for pitch angle of a wind turbine generator system according to claim 2, characterized in that: In step 3, the neural network adaptive estimation law is: Combining nonlinear functions ,The unknown dynamics neural network estimate of ​ wherein, is an ideal weight value is an estimate of the ideal weight value, denotes a first derivative of , and denotes a learning rate of the neural network; g is a learning rate coefficient for the weight estimate, denotes a sigmoid activation function, Z is an intermediate variable, is an estimation error, v is a wind speed, ω r is a rotor angular velocity, β is a pitch angle, and a superscript T denotes a transpose.

5. The event-triggered intermittent control method for pitch angle of a wind turbine generator system according to claim 1, characterized in that: In step 4, the adaptive neural network controller is: wherein, represents the control input at time t; K represents a feedback error gain, which is a real number, and r is a filtered adjustment error, is a first derivative of the pitch angle β, is an ideal weight is an estimated value of the ideal weight, and the superscript T represents transposition, represents a sigmoid activation function, and Z is an intermediate variable.

6. The event-triggered intermittent control method for pitch angle of a wind turbine generator system according to claim 1, characterized in that: In step 1, the whole control process is divided into control intervals and rest intervals, an event-triggered control strategy and an intermittent control strategy are introduced into the adaptive neural network controller, an intermittent event-triggered adaptive neural network controller is designed, and different estimation laws are used in control intervals and rest intervals to adjust the control strategy in real time.

7. The event-triggered intermittent control method for pitch angle of a wind turbine generator system according to claim 6, characterized in that: The intermittent control strategy is represented as: wherein U(t) represents the control input at time t under intermittent control, t k , tk+1 represent the start time of the kth and (k+1)th control interval, respectively k+1 s k represents the start time of the kth rest interval; represents an adjustable parameter; represents the control input at time t, and r is the filtered adjustment error; The event-triggered control strategy is: wherein, denotes the trigger measurement error at time t; denotes the controller triggered by the event within the control interval; denotes the control input at time t; , denote the ith, ith+1 trigger time within the kth control interval, respectively; denotes the real space; is a positive constant to be set; inf denotes the infimum. After the event-triggered control strategy is triggered, then is updated to , represents the control input at the moment.

8. The event-triggered intermittent control method for pitch angle of a wind turbine generator system according to claim 6, characterized in that: For the rest area, apply the ideal weights within the rest area. The estimated value That is, at the end of the previous control interval between rest areas, maintain the ideal weight at that time. The estimated value constant.

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