Battery external liquid cooling temperature difference suppression method and system based on model predictive control

Abstract

The present application relates to the technical field of battery thermal management, and more particularly to a battery external cold liquid temperature difference suppression method and system based on model predictive control, comprising: constructing a multi-physical field coupling prior model to reflect the coupling relationship between the battery temperature field and the cold liquid flow field, providing an accurate basic model for subsequent prediction and control, and improving the overall control precision; predicting the initial temperature field prediction sequence through online rolling prediction, combining real-time data correction prediction, early insight into future temperature changes, facilitating timely discovery of potential temperature difference problems, and enhancing system response capability; identifying the maximum temperature difference value and position, locating the area where the temperature difference is too large, triggering the suppression mechanism in time, preventing the temperature difference from further expanding, and ensuring the safe and stable operation of the battery pack; constructing an optimization control objective function, comprehensively considering the temperature difference and energy consumption, and solving the optimal solution under physical constraints, continuously adjusting the cold liquid flow through rolling optimization, and realizing efficient and energy-saving temperature difference suppression.

Description

Technical Field

[0001] This invention relates to the field of battery thermal management technology, and in particular to a method and system for suppressing temperature difference in external coolant of a battery based on model predictive control. Background Technology

[0002] The safety and performance stability of current battery packs highly depend on effective thermal management technology. However, traditional control methods mostly employ open-loop flow distribution or PID control based on local temperature feedback, which have limitations under dynamic operating conditions of battery packs: when uneven local heat generation occurs inside the battery pack or the external coolant flow distribution is unbalanced, traditional control strategies lack the ability to predict future temperature field evolution and cannot identify the trend of temperature difference diffusion in advance. They can only passively respond to the already occurred local overheating or overcooling phenomena, leading to the continuous accumulation of temperature differences between battery cells, and even triggering protective derating operation, which seriously restricts the power output capability and cycle life of the battery system.

[0003] Furthermore, existing liquid cooling systems suffer from a prominent problem of singular control objectives. Most methods focus solely on controlling the upper limit of battery temperature while neglecting the energy consumption optimization of the coolant circuit. This necessitates continuously increasing the coolant flow rate to suppress local temperature differences, leading to increased pump power consumption. In large-scale energy storage scenarios, this high-energy-consumption operation mode significantly reduces the overall system efficiency and increases maintenance costs. Simultaneously, traditional control methods lack a dynamic coupling model between the battery temperature field and the coolant flow field, making it difficult to quantify the impact weight of different cooling branch flow adjustments on the overall temperature difference. This can easily lead to system oscillation due to over-adjustment or temperature difference runaway due to under-adjustment, failing to simultaneously meet the dual requirements of temperature difference suppression and system energy efficiency under complex operating conditions. Therefore, this invention proposes a battery external coolant temperature difference suppression method and system based on model predictive control. Summary of the Invention

[0004] The purpose of this invention is to solve the problems in the background art, and to propose a method and system for suppressing the temperature difference of the external coolant in a battery based on model predictive control.

[0005] To achieve the above objectives, the present invention adopts the following technical solution: The first aspect of this invention provides a method for suppressing the temperature difference of the external coolant in a battery based on model predictive control, comprising: S1. Construct a multiphysics coupled prior model to characterize the heat exchange relationship between the internal temperature distribution of the battery pack and the external coolant flow. S2. Based on the multi-physics coupling prior model, the three-dimensional temperature field distribution of the battery pack in a finite prediction time domain is predicted online to generate an initial temperature field prediction sequence. S3. Analyze the initial temperature field prediction sequence, identify the maximum temperature difference between battery cells and its location in the prediction time domain, and determine whether the maximum temperature difference exceeds the preset temperature difference safety threshold. If it does, trigger the active temperature difference suppression mechanism. S4. Under the triggered active temperature difference suppression mechanism, construct an optimized control objective function with the goal of minimizing the overall temperature difference of the battery pack and the energy consumption of the coolant circuit in the prediction time domain, and set physical constraints for the actuators, including proportional regulating valves and / or adjustable speed pumps in the coolant circuit. Use a rolling optimization algorithm to solve the optimized control objective function under the physical constraints of the actuators, and generate the optimal control command sequence for the actuators and covering the control time domain.

[0006] Furthermore, the multiphysics coupling prior model in S1 includes the following four sub-models: a battery heat generation sub-model, a heat conduction sub-model between battery cells, a convective heat transfer sub-model between the battery surface and the coolant, and a fluid dynamics sub-model of the coolant flowing in the channel. The four sub-models are numerically discretized using the finite volume method to construct a reduced-order model that reflects the coupling relationship between the battery temperature field and the coolant flow field. This reduced-order model is the multiphysics coupling prior model.

[0007] Further, S2 includes: S21. Use the real-time collected current state quantities as initial conditions and input them into the multiphysics coupling prior model; S22. Using unscented Kalman filtering, the discrete temperature monitoring point data collected in real time are fused together to correct the current state variables of the input multi-physics coupled prior model online, and the corrected state estimate is obtained. S23. Based on the corrected state estimate, starting from the current time, iteratively calculate the multiphysics coupling prior model according to the preset step size, generate Np step sizes covering the future prediction time domain, and include the initial temperature field prediction sequence within the battery pack.

[0008] Furthermore, in S3, identifying the maximum temperature difference between battery cells and its location in the prediction time domain includes: comparing the predicted temperatures of all battery cells in the generated initial temperature field prediction sequence pairwise, extracting the global maximum temperature difference value ΔTmax, and simultaneously recording the spatial coordinates of the two battery cells corresponding to the maximum temperature difference value ΔTmax and the offset steps of the maximum temperature difference value relative to the current time k.

[0009] Furthermore, the optimization control objective function in S4 is a scalar function that accumulates multiple objectives in the prediction time domain, wherein the construction process of the optimization control objective function J includes: A1. For each future moment in the prediction time domain, calculate the average predicted temperature of all battery cells at that moment; A2. For each battery cell, calculate the difference between the predicted future temperature of that cell at the current moment and the average predicted temperature of all battery cells at that moment, and then square the difference. A3. Sum the squared differences of all battery cells at all future times in the prediction time domain to obtain the first cumulative term that reflects the degree of temperature non-uniformity of the battery pack in the entire prediction time domain. A4. For each future moment in the control time domain, perform a square operation on the control quantity acting on the actuator. A5. Summing up the squared values ​​of the control quantities at all future moments in the control time domain yields the second cumulative term, which reflects the energy consumption level of the coolant circuit throughout the entire control time domain. A6. Assign a first weighting coefficient and a second weighting coefficient to the first cumulative term and the second cumulative term respectively, wherein the first weighting coefficient is used to adjust the importance of the temperature difference suppression target in the overall optimization, and the second weighting coefficient is used to adjust the importance of the energy consumption suppression target in the overall optimization. A7. Add the weighted first cumulative term to the weighted second cumulative term to obtain the value of the optimized control objective function. This value is used to evaluate the merits of different control command sequences during the rolling optimization process.

[0010] Furthermore, the actuator physical constraints in S4 include: the opening range constraint of the proportional control valve, the opening change rate constraint of the proportional control valve, the speed range constraint of the adjustable speed pump, the speed change acceleration constraint of the adjustable speed pump, and the upper limit constraint of the total flow rate of the coolant circuit.

[0011] Furthermore, in step S4, a rolling optimization algorithm is used to solve the optimization control objective function under the physical constraints of the actuator, including: S41. At the current moment, based on the real-time collected current state variables, call the multi-physics field coupled prior model to generate a prediction output of length Np in the future prediction time domain. S42. Substitute the optimized control objective function and the set actuator physical constraints into the solver, and use sequential quadratic programming to perform numerical optimization to obtain the optimal control command sequence with a future control time domain length Nc. S43. The first control instruction u(k|k) in the obtained optimal control instruction sequence is used as the actual output and sent to the actuator.

[0012] Furthermore, S4 also includes a rolling optimization control process: The first control command in the optimal control command sequence is issued and applied to the actuator to adjust the distribution of coolant flow into different cooling zones of the battery pack in real time. This process is repeated in the next control cycle to form rolling optimization control.

[0013] Furthermore, the step of issuing the first control command in the optimal control command sequence and applying it to the actuator to adjust the coolant flow distribution into different areas of the battery pack in real time includes: According to the first control command in the optimal control command sequence, the opening of multiple proportional regulating valves connected in parallel at the inlet of different cooling branches of the battery pack is adjusted to change the coolant flow rate of each branch, thereby intervening in and reducing the temperature difference between battery cells based on the future temperature field distribution indicated by the generated initial temperature field prediction sequence.

[0014] A second aspect of the present invention provides a battery external coolant temperature difference suppression system based on model predictive control, comprising: Multiphysics Prior Model Building Module: Constructs a multiphysics coupled prior model to characterize the heat exchange relationship between the internal temperature distribution of the battery pack and the external coolant flow; Battery Temperature Field Rolling Prediction Module: Based on a multi-physics coupled prior model, it performs online rolling prediction of the three-dimensional temperature field distribution of the battery pack within a finite prediction time domain in the future, and generates an initial temperature field prediction sequence. Battery temperature difference identification and judgment module: Analyzes the initial temperature field prediction sequence, identifies the maximum temperature difference between battery cells and its location in the prediction time domain, and determines whether the maximum temperature difference exceeds the preset temperature difference safety threshold. If it does, the active temperature difference suppression mechanism is triggered. Temperature difference suppression optimization control module: Under the triggered active temperature difference suppression mechanism, an optimization control objective function is constructed with the goal of minimizing the overall temperature difference of the battery pack and the energy consumption of the coolant circuit in the prediction time domain. Physical constraints of the actuators are set. The actuators include proportional regulating valves and / or adjustable speed pumps in the coolant circuit. The rolling optimization algorithm is used to solve the optimization control objective function under the physical constraints of the actuators, and the optimal control command sequence for the actuators and covering the control time domain is generated.

[0015] Compared with existing technologies, the beneficial effects of the battery external coolant temperature difference suppression method and system based on model predictive control provided by this invention are as follows: 1) By integrating four sub-models of battery heat generation, heat conduction, convective heat transfer and cold liquid fluid dynamics, and using the finite volume method to numerically discretize and construct a reduced-order model, the coupling characteristics of the battery temperature field and the cold liquid flow field can be comprehensively and accurately reflected, providing a solid foundation for subsequent temperature field prediction and temperature difference suppression, and improving prediction and control accuracy. 2) By collecting the current state variables in real time as the initial conditions input to the model, and using unscented Kalman filtering to fuse discrete temperature monitoring point data to correct the state variables, the prediction sequence is generated through iterative calculation. This can continuously correct the prediction by combining real-time data, improve the accuracy of the prediction, and comprehensively analyze the temperature changes within the limited prediction time domain in the future. Potential temperature difference problems can be detected in advance, giving time to take timely temperature difference suppression measures and enhancing the battery's response capability to temperature changes. 3) By comparing and predicting temperatures one by one, the maximum global temperature difference value is extracted, the coordinates of the corresponding battery cell and the number of offset steps are recorded, and it is determined whether the threshold is exceeded to trigger the suppression mechanism. This can accurately locate areas with excessive temperature differences, making subsequent control measures more targeted. Timely triggering of the suppression mechanism can prevent the temperature difference from expanding further, ensuring the safe and stable operation of the battery pack and avoiding the impact of excessive temperature differences on battery performance and lifespan. 4) By constructing a function with the goal of minimizing the overall temperature difference and coolant circuit energy consumption, setting actuator constraints, and using a rolling optimization algorithm to generate the optimal control command sequence, the optimal solution is sought under the condition of satisfying physical constraints by comprehensively considering temperature difference and energy consumption, thus achieving efficient and energy-saving temperature difference suppression. The rolling optimization control process continuously adjusts the coolant flow distribution, continuously optimizes the control effect, and adapts to the dynamic changes in battery temperature. Attached Figure Description

[0016] Figure 1 This is a flowchart of the battery external coolant temperature difference suppression method based on model predictive control proposed in this invention.

[0017] Figure 2 This is a block diagram of the battery external coolant temperature difference suppression system based on model predictive control proposed in this invention. Detailed Implementation

[0018] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0019] Please see Figure 1 This invention provides a method for suppressing the temperature difference of the external coolant in a battery based on model predictive control, comprising: S1. Based on the physical structure of the battery pack, the topological layout of the coolant flow channel, and the operating data of the battery cells in a preset historical period, a multi-physics coupled prior model is constructed to characterize the heat exchange relationship between the internal temperature distribution of the battery pack and the external coolant flow. S2. Based on the multi-physics coupling prior model, the three-dimensional temperature field distribution of the battery pack in a finite prediction time domain is predicted online to generate an initial temperature field prediction sequence. S3. Analyze the initial temperature field prediction sequence, identify the maximum temperature difference between battery cells and its location in the prediction time domain, and determine whether the maximum temperature difference exceeds the preset temperature difference safety threshold. If it does, trigger the active temperature difference suppression mechanism. S4. Under the triggered active temperature difference suppression mechanism, construct an optimized control objective function with the goal of minimizing the overall temperature difference of the battery pack and the energy consumption of the coolant circuit in the prediction time domain, and set physical constraints for the actuators, including proportional regulating valves and / or adjustable speed pumps in the coolant circuit. Use a rolling optimization algorithm to solve the optimized control objective function under the physical constraints of the actuators, and generate the optimal control command sequence for the actuators and covering the control time domain.

[0020] In this embodiment of the invention, the multiphysics coupling prior model in S1 includes the following four sub-models: a battery heat generation sub-model, a heat conduction sub-model between battery cells, a convective heat transfer sub-model between the battery surface and the coolant, and a fluid dynamics sub-model of the coolant flowing in the channel. The four sub-models are numerically discretized using the finite volume method to construct a reduced-order model that reflects the coupling relationship between the battery temperature field and the coolant flow field. This reduced-order model is the multiphysics coupling prior model. Specifically, a battery heat generation sub-model is established. This sub-model is based on the Bernardi heat generation rate formula and calculates the heat generated by each battery cell per unit time according to the internal resistance characteristics and current conditions of the individual cells. The input to the battery heat generation sub-model is the real-time collected current value and the open-circuit voltage and entropy-thermal coefficient corresponding to the battery's state of charge obtained through a lookup table. It can be understood that the lookup table method refers to pre-determining the open-circuit voltage and entropy-thermal coefficient values ​​of the battery under different states of charge and temperature conditions through experiments, storing these data in the memory of the battery management system in the form of a two-dimensional interpolation table, and then using this data during actual operation. The battery's state of charge (SOC) and temperature values, currently collected in real time, are used to look up and retrieve the corresponding open-circuit voltage and entropy coefficient values ​​from a two-dimensional interpolation table using linear or spline interpolation methods. The calculation formula for the battery heat generation sub-model is: heat generation power equals current multiplied by the difference between the open-circuit voltage and the terminal voltage, plus the product of battery temperature, entropy coefficient, and current. It should be noted that the difference between the open-circuit voltage and the terminal voltage is approximated by the product of the battery's internal resistance and current; the internal resistance value is obtained from a two-dimensional interpolation table that varies with battery temperature and SOC. The heat generation power output by the battery heat generation sub-model is used as a heat source term input to the subsequent heat conduction sub-model.

[0021] A heat conduction sub-model is constructed between individual battery cells. This sub-model establishes a mathematical expression characterizing the heat transfer relationship between battery cells along the solid medium based on the physical arrangement structure of the battery pack and the contact thermal resistance between adjacent battery cells. The heat conduction sub-model is based on Fourier's law of thermal conductivity, where the heat flux density between adjacent battery cells is equal to the temperature difference across the contact interface divided by the contact thermal resistance. The contact thermal resistance is a constant or a variable that changes with temperature, preset based on the contact pressure between battery cells and the properties of the contact materials. The heat conduction sub-model is used to calculate the heat transfer process in the solid medium inside the battery pack, affecting the uniformity of the temperature distribution of each battery cell.

[0022] A convective heat transfer sub-model between the battery surface and the coolant is constructed. This sub-model, based on Newton's cooling formula, characterizes the relationship between the heat transfer between the battery surface and the coolant and the temperature difference, heat transfer area, and convective heat transfer coefficient. The determination of the convective heat transfer coefficient depends on the flow state of the coolant, including laminar or turbulent flow, and the physical properties of the coolant, including viscosity, thermal conductivity, and specific heat capacity. The convective heat transfer coefficient is calculated using an empirical correlation between the Nusselt number, Reynolds number, and Prandtl number. This correlation is pre-calibrated based on the geometric characteristics of the flow channel and the flow characteristics of the coolant. The heat transfer between the battery surface and the coolant serves as the coupling boundary condition between the coolant flow field and the battery temperature field.

[0023] A fluid dynamics sub-model is constructed to represent the flow of coolant within a flow channel. This sub-model, based on the principles of mass conservation, momentum conservation, and energy conservation (i.e., the Navier-Stokes equations), describes the pressure distribution, velocity distribution, and heat exchange process between the coolant and the channel wall during the flow process. The fluid dynamics sub-model solves the continuity and momentum equations within the channel geometry to obtain the velocity and pressure fields of the coolant, and simultaneously solves the energy equation to obtain the temperature distribution of the coolant along the flow direction. The heat exchange between the coolant and the channel wall serves as the source term of the energy equation, forming a bidirectional coupling with the convective heat transfer sub-model.

[0024] Four sub-models were spatially and temporally discretized using the finite volume method to form a set of coupled algebraic equations. The finite volume method was chosen because it is suitable for numerical solutions to fluid flow and heat transfer coupled problems. During discretization, the geometric regions of the battery pack and the coolant flow channel were divided into a finite number of control volume elements. Each control volume element was assigned corresponding material properties and initial conditions, including the density, specific heat capacity, and thermal conductivity of the battery material, and the density, viscosity, thermal conductivity, and specific heat capacity of the coolant. During spatial discretization, to address the need for solving the velocity and pressure coupling in the coolant flow field, staggered meshing was used to discretize the fluid dynamics sub-models. This involved storing the velocity components at the interface center of the control volume, and storing the pressure, temperature, and other scalars at the center of the control volume, thus avoiding a checkerboard pressure field when solving the Navier-Stokes equations and ensuring the stability of the numerical calculation. A fully implicit scheme was used for temporal discretization to ensure the stability of the numerical calculation.

[0025] The process of reducing the order of a large-scale full-order model after discretization includes: performing offline simulation of the full-order model under typical working conditions to obtain a snapshot matrix, where each column of the snapshot matrix represents the numerical solution of all state variables of the full-order model at a certain moment; performing eigenorthogonal decomposition on the snapshot matrix to calculate the eigenvalues ​​and eigenvectors of its covariance matrix, extracting the top Y eigenvectors corresponding to the largest eigenvalue as basis functions reflecting the main dynamic characteristics, and simultaneously spanning a low-dimensional subspace using the basis functions to optimally reconstruct the states in the original high-dimensional state space in the least squares sense; projecting the full-order control equations in the original high-dimensional state space onto the low-dimensional subspace spanned by the basis functions, where the state variables are represented as a linear combination of basis functions, and the combination coefficients are the generalized coordinates of the reduced-order model; specifically, the projection process involves multiplying both sides of the full-order control equations by the transpose of the basis functions and integrating over the entire solution domain, using Galerkin projection to obtain the reduced-order model control equations with respect to the generalized coordinates; Understandably, the dimension of the governing equations of the reduced-order model is much lower than that of the full-order model, but it retains the main dynamic characteristics of the full-order model. It can quickly and accurately predict the coupling relationship between the battery temperature field and the coolant flow field, thus meeting the real-time requirements of model predictive control.

[0026] In this embodiment of the invention, the detailed implementation steps of S2, which is based on a multi-physics coupled prior model, to perform online rolling prediction of the three-dimensional temperature field distribution of the battery pack within a finite prediction time domain and generate an initial temperature field prediction sequence, include: S21. The real-time collected current state variables are used as initial conditions and input into the multiphysics coupling prior model. The current state variables include the current, voltage, temperature of each monitoring point, and the temperature and flow rate of the coolant at key nodes in the external coolant circuit. Specifically, a temperature sensor array is arranged inside the battery pack to collect simulated temperature signals at each monitoring point in real time; the total voltage of the battery pack and the terminal voltage of each battery cell are collected in real time through a voltage detection unit; the total current of the battery pack is collected in real time using a current transformer; temperature sensors and flow meters are installed at the inlet and outlet of the external coolant circuit to collect simulated coolant temperature and flow rate signals in real time; all the acquired simulated signals are amplified and filtered by a signal conditioning circuit and then input to an analog-to-digital converter (ADC), which converts the continuous simulated signals into discrete digital signals; the digital signals are transmitted to the main controller of the battery management system via a controller area network bus or serial peripheral interface communication method; the main controller normalizes and timestamps the received digital signals, organizing them into a data format that matches the input interface of the multiphysics coupled prior model, and inputs them into the model as the initial conditions for predicting future states.

[0027] S22. Using unscented Kalman filtering, the discrete temperature monitoring point data collected in real time are fused to correct the current state variables input to the multiphysics coupled prior model online, thereby obtaining the corrected state estimate and improving the accuracy of the multiphysics coupled prior model in predicting the future temperature field. Among them, the discrete temperature monitoring point data refers to the temperature values ​​of each monitoring point obtained by real-time collection through the temperature sensor array and analog-to-digital conversion. The temperature monitoring points are discretely distributed points in the internal space of the battery pack and belong to the same data source as the temperature data of each monitoring point in the current state variable. Specifically, the current state variables, which are collected in real time and normalized, are used as the initial state estimates for the unscented Kalman filter algorithm, and an initial state covariance matrix is ​​set. Based on the nonlinear characteristics of the multiphysics coupled prior model, an unscented transformation method is used to generate a set of weighted sigma sampling points. The number of sigma sampling points is twice the state dimension plus one. When generating sigma sampling points, the current state estimate is used as the mean, and the distribution is based on the Cholesky decomposition result of the state covariance matrix. Each sigma sampling point is assigned a corresponding mean and covariance weight coefficient, where the mean weight coefficient is used for subsequent state mean calculation, and the covariance weight coefficient is used for subsequent covariance calculation. Each sigma sampling point is substituted into the multiphysics coupled prior model for one-step prediction to obtain the predicted sigma sampling point set. When the multiphysics coupled prior model receives each sigma sampling point as input, it calculates the heat generation power of each battery cell at the current moment as the heat source term based on the battery heat generation sub-model, calculates the heat transfer process between battery cells along the solid medium based on the heat conduction sub-model, calculates the heat exchange between the battery surface and the coolant as the coupled boundary condition based on the convection heat transfer sub-model, and calculates the flow and temperature rise process of the coolant in the flow channel based on the fluid dynamics sub-model. The coupled equations are solved by the finite volume method to obtain the predicted temperature field distribution after one prediction step. The one-step prediction mean and one-step prediction covariance of the state are calculated by weighted summation of the predicted sigma sampling point set; the one-step prediction mean is obtained by weighted average of the prediction results of all sigma sampling points according to the mean weight coefficient; and the one-step prediction covariance is obtained by weighted summation of the deviations of the prediction results of all sigma sampling points from the mean according to the covariance weight coefficient and adding the process noise covariance matrix. The predicted observations and their covariance are calculated based on the one-step prediction mean and the observation equation. The observation equation is to extract the temperature values ​​of the grid nodes corresponding to the installation locations of the temperature sensors from the predicted temperature field distribution to form a predicted observation vector. The prediction results of each sigma sampling point are applied to the observation equation to obtain the sigma point set of the predicted observations. The mean of the predicted observations is obtained by weighted summation of the sigma point set. The covariance of the predicted observations is obtained by weighted summation of the deviations between the point set and the mean of the predicted observations and adding the observation noise covariance matrix. Real-time collected discrete temperature monitoring point data are used as actual observations. These data are compared with predicted observations to calculate the innovation, i.e., the deviation between the actual and predicted observations. The Kalman gain is calculated based on the innovation, the covariance of the predicted observations, and the cross-covariance between the state and the observations. The Kalman gain reflects the weight of the innovation on the state correction. The Kalman gain is used to update the one-step prediction mean to obtain the corrected state estimate, which is equal to the one-step prediction mean plus the Kalman gain multiplied by the innovation. At the same time, the state covariance matrix is ​​updated. The updated covariance matrix is ​​equal to the one-step prediction covariance minus the Kalman gain multiplied by the predicted observation covariance multiplied by the transpose of the Kalman gain. By correcting the input state variables of the multiphysics coupled prior model online, a corrected state estimate that more accurately reflects the current true state is obtained.

[0028] S23. Based on the corrected state estimate, starting from the current time, iteratively calculate the multiphysics coupled prior model according to a preset step size, generating an initial temperature field prediction sequence covering Np step sizes within the future prediction time domain, including the temperature change trajectory of each key location within the battery pack, including: The state estimate, corrected by unscented Kalman filtering, is used as the initial value for iterative calculation. This initial value includes the temperature distribution of each control volume unit within the battery pack and the temperature and velocity distribution of each control volume unit in the coolant flow field at the current moment. The prediction time domain length Np and iteration step size are set, and the iteration step size is kept consistent with the control cycle of the model predictive control to ensure matching in the time dimension. Starting from the current moment k, the corrected state estimate is substituted into the multiphysics coupled prior model as the initial condition to calculate the temperature field distribution and coolant flow field distribution at the next moment k+1 after one iteration step. During the calculation, it is assumed that execution will occur within the future prediction time domain. The controller control quantity remains unchanged or is extrapolated from a preset baseline value; the calculation result at time k+1 is used as a new input state and substituted into the multiphysics coupling prior model again to calculate the temperature field and flow field distribution at time k+2; the iterative process is repeated until the temperature field and flow field distribution at time k+Np are calculated; each iterative calculation outputs the temperature value of all control volume units in the battery pack, and the temperature field data arranged in chronological order are organized into an initial temperature field prediction sequence. This sequence covers the complete time range from the current time k to the future time k+Np, reflecting the evolution trend of the battery pack temperature field in the future under the current control action.

[0029] In this embodiment of the invention, the specific implementation of S3 identifying the maximum temperature difference between individual battery cells and its location within the prediction time domain is as follows: The predicted temperatures of all battery cells in the generated initial temperature field prediction sequence are compared one by one to extract the global maximum temperature difference value ΔTmax. At the same time, the spatial coordinates of the two battery cells corresponding to the maximum temperature difference value ΔTmax and the offset steps of the maximum temperature difference value relative to the current time k are recorded. Specifically, the temperature field distribution data corresponding to each prediction time p is extracted from the initial temperature field prediction sequence, where p ranges from k+1 to k+Np for a total of Np prediction times, and p represents the specific prediction time. For each prediction time p, the battery cell temperature values ​​corresponding to all control volume units in the temperature field distribution at that time are traversed, and the highest and lowest temperatures at that time are found using a quicksort algorithm. The instantaneous temperature difference at that time is calculated as the highest temperature minus the lowest temperature. The quicksort algorithm can efficiently sort a large amount of temperature data. While finding the highest and lowest temperatures, the spatial coordinates of the battery cell corresponding to the highest temperature and the lowest temperature are recorded. These two spatial coordinates correspond to the positions of the highest and lowest temperatures in the temperature field grid, respectively. After calculating the temperature difference for all predicted times, a temperature difference sequence containing Np instantaneous temperature difference values ​​is obtained. to ;in, This represents the instantaneous temperature difference between all individual cells in the battery pack at the predicted time k+1, which is the difference between the highest and lowest temperatures at that time. This represents the instantaneous temperature difference at the predicted time k+Np; temperature difference sequence. to It is a set of Np instantaneous temperature difference values ​​arranged in chronological order; the maximum value in this temperature difference sequence is found as the global maximum temperature difference value ΔTmax. In practice, a traversal comparison method can be used to set the initial maximum temperature difference value as ΔTmax. Then in turn with to The maximum temperature difference is updated whenever a larger temperature difference is encountered. This represents the instantaneous temperature difference at prediction time k+2; after determining the global maximum temperature difference ΔTmax, backtrack to the specific time when this value appeared, and the number of steps between this time and the current time k is the offset step number relative to the current time k; at the same time, read the spatial coordinates of the battery cell corresponding to the highest temperature and the spatial coordinates of the battery cell corresponding to the lowest temperature recorded at this time, and use the two obtained spatial coordinates as the location coordinates where the global maximum temperature difference ΔTmax appears; It is understandable that the highest and lowest temperatures may occur at different locations within the same battery cell, or at different parts of the same battery cell, but usually correspond to different battery cells. The above steps enable the identification of the maximum temperature difference and its spatiotemporal characteristics within the future prediction time domain, providing a basis for decision-making on whether to trigger the active temperature difference suppression mechanism.

[0030] In this embodiment of the invention, the optimization control objective function in S4 is a scalar function that accumulates multiple objectives in the prediction time domain, wherein the construction process of the optimization control objective function J includes: A1. For each future moment in the prediction time domain, calculate the average predicted temperature of all battery cells at that moment; A2. For each battery cell, calculate the difference between the predicted future temperature of that cell at the current moment and the average predicted temperature of all battery cells at that moment, and then square the difference. A3. Sum the squared differences of all battery cells at all future times in the prediction time domain to obtain the first cumulative term that reflects the degree of temperature non-uniformity of the battery pack in the entire prediction time domain. A4. For each future moment in the control time domain, perform a square operation on the control quantity acting on the actuator. A5. Summing up the squared values ​​of the control quantities at all future moments in the control time domain yields the second cumulative term, which reflects the energy consumption level of the coolant circuit throughout the entire control time domain. A6. Assign a first weighting coefficient and a second weighting coefficient to the first cumulative term and the second cumulative term respectively, wherein the first weighting coefficient is used to adjust the importance of the temperature difference suppression target in the overall optimization, and the second weighting coefficient is used to adjust the importance of the energy consumption suppression target in the overall optimization. A7. Add the weighted first cumulative term to the weighted second cumulative term to obtain the numerical value of the optimized control objective function. This value is used to evaluate the merits of different control command sequences during the rolling optimization process. For example, in the discrete-time domain, it is expressed as: ; In the formula, J is the objective function for optimization control; j is the step size index in the prediction time domain or control time domain, j=0 corresponds to the current time, j=1 corresponds to the first prediction time in the future, and so on; k is the current time. This represents the temperature of the i-th battery cell predicted at the current time k+j. This represents the average predicted temperature of all individual cells at the corresponding time. This represents the control quantity that will act on the actuator at the current time k+j; i is the index of the battery cell; Np is the prediction time domain length, Nc is the control time domain length, and Nc≤Np; M is the total number of battery cells; w1 and w2 are the temperature difference suppression weight and energy consumption suppression weight, respectively, used to adjust the relative importance of different objectives in the optimization process.

[0031] In this embodiment of the invention, the actuator physical constraints in S4 include: the opening range constraint of the proportional control valve, the opening change rate constraint of the proportional control valve, the rotational speed range constraint of the adjustable speed pump, the rotational speed change acceleration constraint of the adjustable speed pump, and the upper limit constraint of the total flow rate of the coolant circuit. Understandably, the opening range constraint of a proportional control valve refers to the mechanical limitation on the minimum and maximum opening of the valve core position in the physical structure of each proportional control valve. The opening range is expressed as a percentage, with the minimum opening corresponding to the valve being completely closed (0%) and the maximum opening corresponding to the valve being completely open (100%). During the model predictive control solution process, the valve opening command value in the control command sequence must always be within this closed range, i.e., greater than or equal to 0% and less than or equal to 100%. For special valve types that cannot be completely closed, the minimum opening may be greater than 0%, in which case the minimum opening value is determined according to the valve specification. The opening change rate constraint of a proportional control valve refers to the maximum allowable change in valve opening per unit time. This constraint is jointly determined by the response speed of the valve actuator, the driving capability of the motor, and the fluid impact limitation. Specifically, the expression for the opening change rate constraint is that the absolute value of the valve opening change between two adjacent control cycles is less than or equal to the product of the maximum change rate and the duration of the control cycle. This constraint is used to prevent the valve from acting too quickly, which could lead to water hammer in the pipeline or instability of the control system, while also protecting the valve actuator from excessive wear. The speed range constraint of an adjustable speed pump refers to the limitation on the pump motor speed between a minimum stable speed and a maximum rated speed. This constraint is determined by the motor's electromagnetic design, mechanical strength, and heat dissipation capacity. The expression for the speed range constraint is that the pump's speed command value is greater than or equal to the minimum stable speed and less than or equal to the maximum rated speed. For variable frequency drive adjustable speed pumps, the minimum stable speed is usually 10% to 20% of the rated speed, and the maximum rated speed is the rated speed of the motor. The speed change acceleration constraint of an adjustable speed pump refers to the second derivative limitation of the pump speed change, i.e., the limitation of the rate of change of speed per unit time. This constraint is determined by the electromagnetic inertia of the motor, the mechanical inertia of the pump, and the fluid dynamics characteristics. The expression for the speed change acceleration constraint is that the absolute value of the rate of change of speed between two adjacent control cycles is less than or equal to the product of the maximum acceleration and the square of the control cycle duration. This constraint is used to prevent drastic speed changes from causing motor overcurrent or fluid pulsation impact, ensuring the smooth operation of the pump. The upper limit constraint of total flow rate in the cold liquid circuit refers to the upper limit of the total flow rate of the entire circuit due to the limitations of pipe diameter, maximum liquid supply capacity of pump and heat dissipation capacity. The expression of this constraint is that the sum of the flow rates of each branch is less than or equal to the upper limit of the total flow rate. The flow rate of each branch is calculated by the opening degree of the proportional regulating valve and the flow resistance characteristics of the branch, and the upper limit of the total flow rate is pre-calibrated according to the system design parameters. It should be noted that the above physical constraints are the complete definition of actuator physical constraints in the model predictive control solution process. These constraints, as boundary conditions of the feasible region of the optimization problem, ensure that the optimal control command sequence obtained is physically realizable. In the model predictive control solution process, the generation of the control command sequence must satisfy all constraints. Any control command that violates the constraints will be considered an infeasible solution.

[0032] In this embodiment of the invention, the specific implementation of solving the optimization control objective function under the physical constraints of the actuator using the rolling optimization algorithm in step S4 includes: S41. At the current moment, based on the real-time acquired current state variables, the multiphysics coupling prior model is invoked to generate a predicted output of length Np in the future prediction time domain. Specifically, this includes: after correcting the state using an unscented Kalman filter based on the real-time acquired current state variables, the corrected state estimate is used as the initial condition of the multiphysics coupling prior model and substituted into the model for iterative calculation; the iterative calculation proceeds forward according to the iteration step size, and each step is based on the result of the previous step and the same control input assumptions to generate a predicted temperature field distribution covering the future time k+1 to k+Np. This predicted result is used as the initial predicted output sequence of the model predictive control.

[0033] S42. The steps of substituting the optimized control objective function and the set actuator physical constraints into the solver, and using sequential quadratic programming for numerical optimization to obtain the optimal control command sequence for the future control time domain length Nc are as follows: The optimized control objective function is used as the performance index to be minimized, and the physical constraints of each actuator are used as the constraints of the optimization problem, constructing a nonlinear constraint optimization problem. The decision variables of the nonlinear constraint optimization problem are the control quantity sequences acting on each actuator at each moment within the future control time domain, including the opening command sequence of each proportional control valve and the speed command sequence of the adjustable pump. The optimization objective is to minimize the optimized control objective function while satisfying the physical constraints, achieving multi-objective optimization of temperature difference suppression and energy consumption control. The nonlinear constrained optimization problem is input into a numerical optimization solver, which uses a sequential quadratic programming algorithm for iterative solution. The sequential quadratic programming algorithm involves performing a second Taylor expansion of the objective function at the current iteration point to construct a quadratic approximation function, while simultaneously linearizing the constraint function to construct linear constraints, thus forming a quadratic programming subproblem. Solving this subproblem yields the search direction, and a linear search determines the step size to ensure the optimal control objective function value decreases sufficiently while satisfying the constraints. After updating the optimization variables, the iterative process is repeated until convergence conditions are met, including the change in the optimal control objective function being less than a preset tolerance or the constraint violation being less than a preset tolerance. Finally, the optimal solution that minimizes the optimal control objective function is obtained. The obtained optimal solution is the optimal control command sequence acting on each actuator at each time point within the future control time domain. The control command sequence includes the target opening value of each proportional control valve and the target speed value of the adjustable pump corresponding to each control step.

[0034] S43. The first control instruction u(k|k) in the obtained optimal control instruction sequence is used as the actual output and sent to the actuator. Specifically, this includes: extracting the first control instruction vector corresponding to the current time k from the obtained optimal control instruction sequence. This vector contains the specific control quantity sent to all actuators at the current time. For the proportional control valve, the first control instruction gives the target opening percentage at this time. For the variable speed pump, the first control instruction gives the target speed value at this time. The control instruction is sent to the corresponding actuator drive unit through the controller local area network bus or analog output channel. The drive unit of the proportional control valve converts the opening instruction into a pulse width modulation signal to drive the valve core motor to rotate to the specified position. The drive unit of the variable speed pump converts the speed instruction into the frequency set value of the frequency converter to adjust the motor speed.

[0035] In this embodiment of the invention, S4 further includes a rolling optimization control process: the first control command in the optimal control command sequence is issued and applied to the actuator to adjust the distribution of coolant flow into different cooling areas of the battery pack in real time, thereby realizing the active adjustment of the battery pack temperature field, and repeating the process in the next control cycle to form rolling optimization control; Specifically, within the current control cycle, the first calculated control command u(k|k) is sent to the actuator. The actuator, based on the control command, changes the coolant flow rate of the corresponding cooling branch, directly affecting the heat exchange process between the battery pack and the coolant, thus suppressing temperature differences. After executing this control command, the system waits for the preset control cycle duration. When the next control cycle arrives, the latest current state variables are re-acquired, state estimation is performed again, a new prediction sequence is generated, the nonlinear constraint optimization problem is solved again, and a new first control command is issued. By repeating this process in each control cycle, the control time domain is continuously rolled forward, allowing the control action to be continuously updated and corrected based on the latest feedback information. This adapts to the dynamic changes in battery pack operating conditions and external disturbances, forming rolling optimization control and ensuring the continuity of the temperature difference suppression effect.

[0036] It should be noted that the real-time adjustment of the coolant flow distribution into different cooling zones of the battery pack is achieved through the following methods: According to the first control command in the optimal control command sequence, the opening of multiple proportional regulating valves connected in parallel at the inlet of different cooling branches of the battery pack is adjusted to change the coolant flow rate of each branch. Based on the future temperature field distribution indicated by the generated initial temperature field prediction sequence, the directional cooling intensity of the identified local high-temperature cooling area in the battery pack is actively increased, and the cooling intensity of the local low-temperature cooling area is correspondingly reduced, so as to intervene and reduce the temperature difference between battery cells. Specifically, the method for dividing the cooling zones of the battery pack includes: dividing the cooling zones of the battery pack according to the physical layout of the cooling channels and the spatial position of the battery cells; each cooling branch corresponds to a specific cooling zone, which contains several battery cells, and the battery cells share the coolant provided by the same cooling branch for heat exchange; the division of cooling zones is based on the series and parallel structure of the battery pack and the design of the cooling channels. For example, for a square battery pack, the cooling channel corresponding to each row of battery cells is regarded as an independent cooling zone; for a pouch battery pack, the cooling zones are divided according to the partitioning of the cooling plate; a proportional regulating valve is installed at the inlet of each cooling zone to independently control the flow rate of coolant flowing into that cooling zone (i.e., the corresponding cooling branch); The target opening value assigned to each proportional control valve is parsed from the first control command in the optimal control command sequence. All target opening values ​​are converted into corresponding control signals and sent to the proportional control valve actuators installed at the inlet of each cooling branch of the battery pack. Each proportional control valve adjusts its valve core position according to the received control signal, changing the flow cross-sectional area of ​​its cooling branch, thereby independently regulating the amount of coolant flowing into that cooling branch. For local cooling areas identified in the initial temperature field prediction sequence as areas where high temperatures are expected in the future (i.e., the predicted temperature of the battery cells corresponding to these cooling areas is significantly higher than the average), the opening of the proportional control valve on the corresponding cooling branch will be increased according to the control command, allowing more coolant to flow into the cooling area and enhancing the directional cooling effect. Conversely, for local cooling areas identified as areas where low temperatures are expected in the future (i.e., the predicted temperature of the battery cells corresponding to these cooling areas is significantly lower than the average), the opening of the proportional control valve on the corresponding cooling branch will be decreased to reduce coolant flow, reduce the cooling intensity of the cooling area, and prevent further temperature drop. Understandably, by using differentiated flow allocation based on predictive information, spatial non-uniform control of temperature distribution within the battery pack is achieved, actively intervening in the evolution of the temperature field, effectively reducing the temperature difference between individual battery cells in different cooling areas, and thus suppressing temperature differences.

[0037] Please see Figure 2 This invention provides a battery external coolant temperature difference suppression system based on model predictive control, comprising: Multiphysics Prior Model Building Module: Constructs a multiphysics coupled prior model to characterize the heat exchange relationship between the internal temperature distribution of the battery pack and the external coolant flow; Battery Temperature Field Rolling Prediction Module: Based on a multi-physics coupled prior model, it performs online rolling prediction of the three-dimensional temperature field distribution of the battery pack within a finite prediction time domain in the future, and generates an initial temperature field prediction sequence. Battery temperature difference identification and judgment module: Analyzes the initial temperature field prediction sequence, identifies the maximum temperature difference between battery cells and its location in the prediction time domain, and determines whether the maximum temperature difference exceeds the preset temperature difference safety threshold. If it does, the active temperature difference suppression mechanism is triggered. Temperature difference suppression optimization control module: Under the triggered active temperature difference suppression mechanism, an optimization control objective function is constructed with the goal of minimizing the overall temperature difference of the battery pack and the energy consumption of the coolant circuit in the prediction time domain. Physical constraints of the actuators are set, including proportional regulating valves and / or adjustable speed pumps in the coolant circuit. The optimization control objective function is solved under the physical constraints of the actuators using a rolling optimization algorithm, generating the optimal control command sequence for the actuators and covering the control time domain.

[0038] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. 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.

[0039] It should be noted that all formulas in this manual are calculated by removing dimensions and taking their numerical values. The formulas are derived from software simulations based on a large amount of collected data to obtain the most recent real-world results. The preset parameters and thresholds in the formulas are set by those skilled in the art according to the actual situation.

[0040] Although embodiments of the invention have been shown and described, those skilled in the art will understand that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the claims and their equivalents.

Claims

1. A method for suppressing the temperature difference of external coolant in a battery based on model predictive control, characterized in that, include: S1. Construct a multiphysics coupled prior model to characterize the heat exchange relationship between the internal temperature distribution of the battery pack and the external coolant flow. The multiphysics coupled prior model includes the following four sub-models: a battery heat generation sub-model, a heat conduction sub-model between battery cells, a convective heat transfer sub-model between the battery surface and the coolant, and a fluid dynamics sub-model of the coolant flow in the channel. The four sub-models are numerically discretized using the finite volume method to construct a reduced-order model that reflects the coupling relationship between the battery temperature field and the coolant flow field. This reduced-order model is the multiphysics coupled prior model. S2. Based on a multi-physics coupled prior model, online rolling prediction of the three-dimensional temperature field distribution of the battery pack within a finite prediction time domain is performed to generate an initial temperature field prediction sequence, including: S21. The real-time collected current state variables are used as initial conditions and input into the multiphysics coupling prior model. The current state variables include the current, voltage, temperature of each monitoring point, and the temperature and flow rate of the coolant at key nodes in the external coolant circuit. S22. Using unscented Kalman filtering, the discrete temperature monitoring point data collected in real time are fused together to correct the current state variables of the input multi-physics coupled prior model online, and the corrected state estimate is obtained. S23. Based on the corrected state estimate, starting from the current time, iteratively calculate the multiphysics coupling prior model according to the preset step size, generate Np step sizes covering the future prediction time domain, and include the initial temperature field prediction sequence in the battery pack. S3. Analyze the initial temperature field prediction sequence, identify the maximum temperature difference between battery cells and its location in the prediction time domain, and determine whether the maximum temperature difference exceeds the preset temperature difference safety threshold. If it does, trigger the active temperature difference suppression mechanism. Identifying the maximum temperature difference between battery cells and its location in the prediction time domain includes: comparing the predicted temperatures of all battery cells in the generated initial temperature field prediction sequence pairwise, extracting the global maximum temperature difference value ΔTmax, and simultaneously recording the spatial coordinates of the two battery cells corresponding to the maximum temperature difference value ΔTmax and the offset steps of the maximum temperature difference value relative to the current time k. S4. Under the triggered active temperature difference suppression mechanism, construct an optimized control objective function with the goal of minimizing the overall temperature difference of the battery pack and the energy consumption of the coolant circuit in the prediction time domain, and set physical constraints for the actuators, including proportional regulating valves and / or adjustable speed pumps in the coolant circuit. Use the rolling optimization algorithm to solve the optimized control objective function under the physical constraints of the actuators, and generate the optimal control command sequence for the actuators and covering the control time domain. The optimization control objective function is a scalar function that accumulates multiple objectives over the prediction time domain. The construction process of the optimization control objective function J includes: A1. For each future moment in the prediction time domain, calculate the average predicted temperature of all battery cells at that moment; A2. For each battery cell, calculate the difference between the predicted future temperature of that cell at the current moment and the average predicted temperature of all battery cells at that moment, and then square the difference. A3. Sum the squared differences of all battery cells at all future times in the prediction time domain to obtain the first cumulative term; A4. For each future moment in the control time domain, perform a square operation on the control quantity acting on the actuator. A5. Summing up the squared values ​​of the control quantities at all future times within the control time domain yields the second cumulative term; A6. Assign a first weighting coefficient and a second weighting coefficient to the first cumulative term and the second cumulative term, respectively; A7. Add the weighted first cumulative term to the weighted second cumulative term to obtain the value of the optimization control objective function; The physical constraints of the actuator include: the opening range constraint of the proportional control valve, the opening change rate constraint of the proportional control valve, the speed range constraint of the adjustable speed pump, the speed change acceleration constraint of the adjustable speed pump, and the upper limit constraint of the total flow rate of the coolant circuit. Solving the optimal control objective function under actuator physical constraints using the rolling optimization algorithm includes: S41. At the current moment, based on the real-time collected current state variables, call the multi-physics field coupled prior model to generate a prediction output of length Np in the future prediction time domain. S42. Substitute the optimized control objective function and the set actuator physical constraints into the solver, and use sequential quadratic programming to perform numerical optimization to obtain the optimal control command sequence with a future control time domain length Nc. S43. The first control instruction u(k|k) in the obtained optimal control instruction sequence is used as the actual output and sent to the actuator.

2. The battery external coolant temperature difference suppression method based on model predictive control according to claim 1, characterized in that, S4 also includes a rolling optimization control process: The first control command in the optimal control command sequence is issued and applied to the actuator to adjust the distribution of coolant flow into different cooling zones of the battery pack in real time. This process is repeated in the next control cycle to form rolling optimization control.

3. The battery external coolant temperature difference suppression method based on model predictive control according to claim 2, characterized in that, The step of issuing the first control command in the optimal control command sequence and applying it to the actuator to adjust the coolant flow distribution into different areas of the battery pack in real time includes: According to the first control command in the optimal control command sequence, the opening of multiple proportional regulating valves connected in parallel at the inlet of different cooling branches of the battery pack is adjusted to change the coolant flow rate of each branch, thereby intervening in and reducing the temperature difference between battery cells based on the future temperature field distribution indicated by the generated initial temperature field prediction sequence.

4. A battery external coolant temperature difference suppression system based on model predictive control, characterized in that, The system, applied to the battery external coolant temperature difference suppression method based on model predictive control as described in any one of claims 1-3, comprises: Multiphysics Prior Model Building Module: Constructs a multiphysics coupled prior model to characterize the heat exchange relationship between the internal temperature distribution of the battery pack and the external coolant flow; Battery Temperature Field Rolling Prediction Module: Based on a multi-physics coupled prior model, it performs online rolling prediction of the three-dimensional temperature field distribution of the battery pack within a finite prediction time domain in the future, and generates an initial temperature field prediction sequence. Battery temperature difference identification and judgment module: Analyzes the initial temperature field prediction sequence, identifies the maximum temperature difference between battery cells and its location in the prediction time domain, and determines whether the maximum temperature difference exceeds the preset temperature difference safety threshold. If it does, the active temperature difference suppression mechanism is triggered. Temperature difference suppression optimization control module: Under the triggered active temperature difference suppression mechanism, an optimization control objective function is constructed with the goal of minimizing the overall temperature difference of the battery pack and the energy consumption of the coolant circuit in the prediction time domain. Physical constraints of the actuators are set. The actuators include proportional regulating valves and / or adjustable speed pumps in the coolant circuit. The rolling optimization algorithm is used to solve the optimization control objective function under the physical constraints of the actuators, and the optimal control command sequence for the actuators and covering the control time domain is generated.

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