Self-adaptive control method and device of instant water heater and instant water heater

Abstract

The invention discloses a self-adaptive control method and device of an instant water heater and the instant water heater. The method comprises the following steps: acquiring current operation condition data at each control sampling moment; searching in a multi-dimensional model lookup table according to the data to obtain at least two pre-calculation models; synthesizing the plurality of pre-calculation models to obtain a linear state space model; determining time-varying transport delay according to the real-time water flow, and inputting the time-varying transport delay into the linear state space model to obtain a target prediction model; determining the optimal thermal power corresponding to the current operation condition data; and the instant water heater is controlled to operate according to the optimal heat power. The technical problem that in the prior art, when an instant water heater faces complex and changeable working conditions, especially when a user suddenly changes the water flow, temperature control is prone to being unstable is solved.

Description

Technical Field

[0001] This invention relates to the field of automation control technology, and more specifically, to an adaptive control method and device for an instant water heater, and an instant water heater. Background Technology

[0002] Unlike traditional storage water heaters, instantaneous water heaters do not have a water tank. Instead, they supply hot water directly by heating the cold water flowing through them. This requires their control system to quickly and accurately adjust the heating power to cope with instantaneous changes in water flow and inlet water temperature, thereby ensuring a stable outlet water temperature.

[0003] Because the heat exchange efficiency between the heating element and water in an instant water heater varies with water flow rate and temperature, this nonlinear characteristic causes significant differences in the system's dynamic model under different operating conditions. Furthermore, there is a delay in the process of water entering the heating zone and reaching the temperature sensor, and this delay varies with water flow rate, increasing the difficulty of control.

[0004] While traditional proportional-integral-derivative (PID) control strategies are simple and reliable, their control performance is poor in nonlinear systems, especially when operating variables change significantly, making precise temperature regulation difficult. Furthermore, conventional model predictive control (MPC) typically linearizes a single operating point during design and then applies the resulting fixed model to all operating conditions. The problem with this approach is that when operating conditions change beyond the design point, the model's accuracy drops significantly, leading to deteriorated control performance. This is particularly problematic under low flow rates and extreme inlet water temperatures, potentially resulting in unstable temperature control or overshoot.

[0005] There is currently no effective solution to the above problems. Summary of the Invention

[0006] This invention provides an adaptive control method and device for an instant water heater, and an instant water heater, to at least solve the technical problem in the related art that instant water heaters are prone to unstable temperature control when facing complex and variable operating conditions, especially when users suddenly change the water flow.

[0007] According to one aspect of the present invention, an adaptive control method for an instantaneous water heater is provided, comprising: acquiring current operating condition data of the instantaneous water heater at each control sampling time; searching for at least two pre-calculated models in a multidimensional model lookup table based on the current operating condition data, wherein the multidimensional model lookup table is used to record the state-space model of the instantaneous water heater at different operating condition combinations, and the pre-calculated models are used to predict the response of the instantaneous water heater to various control actions; synthesizing the at least two pre-calculated models to obtain a linear state-space model; determining a time-varying transport delay based on the real-time water flow rate in the current operating condition data, and inputting the time-varying transport delay into the linear state-space model to obtain a target prediction model; determining the optimal thermal power corresponding to the current operating condition data through the target prediction model; and controlling the instantaneous water heater to operate according to the optimal thermal power.

[0008] The adaptive control method for instantaneous water heaters described in this invention has the following advantages compared to the prior art: Firstly, based on the nonlinear dynamic mathematical model of the instantaneous water heater and the range of key operating variables (such as water flow rate and inlet water temperature), a series of linearized state-space models are calculated offline and stored to form a multidimensional model lookup table (LUT). At each control sampling moment, the nearest pre-calculated model is quickly located and selected according to the actual operating conditions, and then the model most suitable for the current operating conditions is synthesized through an interpolation algorithm. Simultaneously, the time-varying delivery delay is calculated based on the real-time water flow rate and integrated into the interpolation model to form the final internal prediction model. Finally, the optimal thermal power calculated using the final internal prediction model is sent to the water heater's heating actuator, and the entire control process is repeated at the next sampling moment. Therefore, during online control, the prediction model under the current operating conditions can be quickly generated through model lookup and interpolation without recalculating the linearized model, significantly accelerating the control response speed. Furthermore, the delivery delay depends on the water flow rate; by calculating it in real time and integrating it into the prediction model, the time delay in the process of water reaching the temperature sensor from the heating element can be accurately reflected, avoiding control lag caused by inaccurate delay estimation.

[0009] Optionally, before searching for at least two pre-calculated models in the multidimensional model lookup table based on the current operating condition data, the adaptive control method further includes: obtaining key operating condition variables of the instantaneous water heater, wherein the key operating condition variables include at least: inlet water flow rate and inlet water temperature; selecting multiple discrete operating points in the multidimensional operating condition space corresponding to the key operating condition variables; performing point-by-point linearization processing on the multiple discrete operating points to obtain a linear state space model; and storing each linear state space model and its corresponding discrete operating point to obtain the multidimensional model lookup table.

[0010] Optionally, the plurality of discrete operating points are linearized point by point to obtain a linear state-space model, including: performing a Taylor expansion of the nonlinear differential equation at each of the plurality of discrete operating points to obtain the Taylor expansion result, wherein the nonlinear differential equation is: , This indicates the total heat capacity of the instantaneous water heater. This indicates the total temperature of the instantaneous water heater. This indicates the effective thermal power applied by the burner of the instantaneous water heater. Indicates real-time water mass flow rate. This represents the specific heat capacity of water at constant pressure. The real-time inlet water temperature is represented; the Taylor expansion result is linearized to obtain the linear state-space model.

[0011] Optionally, at least two pre-calculated models are obtained by searching a multidimensional model lookup table based on the current operating condition data, including: inserting the current operating condition data into the multidimensional model lookup table using a multilinear interpolation algorithm, and determining the position information of the current operating condition data in the multidimensional model lookup table; and selecting the at least two pre-calculated models that are adjacent to the current operating condition data based on the position information.

[0012] Optionally, the at least two pre-computation models are synthesized to obtain a linear state-space model, including: determining the weight values ​​of each of the current operating condition data on the corresponding axis; calculating the interpolation state matrix and interpolation input matrix obtained by interpolation along each of the corresponding axes based on the weight values, so as to synthesize the at least two pre-computation models to obtain the linear state-space model.

[0013] Optionally, determining the time-varying transport delay based on the real-time water flow rate in the current operating condition data, and inputting the time-varying transport delay into the linear state-space model to obtain the target prediction model, includes: calculating the time-varying transport delay based on the real-time water flow rate using a time-varying transport delay calculation formula, wherein the time-varying transport delay calculation formula is: , This indicates the time-varying transport delay. Indicates the length of the pipe. This indicates the real-time water flow rate. The pipeline radius is represented; the time-varying transport delay is discretized to obtain the discretization result; the discretization result is integrated into the linear state-space model to obtain the target prediction model.

[0014] Optionally, determining the optimal thermal power corresponding to the current operating condition data using the target prediction model includes: passing the target prediction model to a model predictive control solver, so that the model predictive control solver calculates the optimal thermal power corresponding to the current operating condition data based on the target prediction model under an optimized objective cost function, wherein the optimized objective cost function is: , This represents the sequence of operational variables within the future control time domain. This indicates the output reference tracking error term, used to penalize the deviation between the predicted outlet water temperature and the set target temperature. This represents the tracking error term for manipulated variables, used to penalize the degree to which thermal power deviates from the target value. This represents the rate of change of control action, used to suppress oscillations caused by thermal power regulation; This represents the penalty for constraint violation, which is quantified and penalized using slack variables.

[0015] Optionally, controlling the instantaneous water heater to operate according to the optimal thermal power includes: sending the first control quantity in the sequence corresponding to the optimal thermal power as the actual power command at the current moment to the heating actuator or gas proportional valve of the instantaneous water heater, so that the heating actuator or the gas proportional valve operates according to the actual power command.

[0016] According to another aspect of the present invention, an adaptive control device for an instantaneous water heater is also provided, comprising: a first acquisition unit, configured to acquire current operating condition data of the instantaneous water heater at each control sampling time; a search unit, configured to search for at least two pre-calculated models in a multidimensional model lookup table based on the current operating condition data, wherein the multidimensional model lookup table is used to record the state-space model of the instantaneous water heater at different operating condition combinations, and the pre-calculated model is used to predict the response of the instantaneous water heater to various control actions; a synthesis unit, configured to synthesize the at least two pre-calculated models to obtain a linear state-space model; a first determination unit, configured to determine a time-varying transport delay based on the real-time water flow rate in the current operating condition data, and input the time-varying transport delay into the linear state-space model to obtain a target prediction model; a second determination unit, configured to determine the optimal thermal power corresponding to the current operating condition data through the target prediction model; and a control unit, configured to control the instantaneous water heater to operate according to the optimal thermal power.

[0017] Optionally, the adaptive control device further includes: a second acquisition unit, configured to acquire key operating condition variables of the instantaneous water heater before searching for at least two pre-calculated models in a multidimensional model lookup table based on the current operating condition data, wherein the key operating condition variables include at least: inlet water flow rate and inlet water temperature; a selection unit, configured to select multiple discrete operating points in the multidimensional operating condition space corresponding to the key operating condition variables; a processing unit, configured to perform point-by-point linearization processing on the multiple discrete operating points to obtain a linear state space model; and a storage unit, configured to store each linear state space model and its corresponding discrete operating point to obtain the multidimensional model lookup table.

[0018] Optionally, the processing unit includes: a first calculation module, configured to perform Taylor expansion processing on the nonlinear differential equation at each of the plurality of discrete operating points to obtain a Taylor expansion result, wherein the nonlinear differential equation is: , This indicates the total heat capacity of the instantaneous water heater. This indicates the total temperature of the instantaneous water heater. This indicates the effective thermal power applied by the burner of the instantaneous water heater. Indicates real-time water mass flow rate. This represents the specific heat capacity of water at constant pressure. The real-time inlet water temperature is represented by the processing module, which linearizes the Taylor expansion result to obtain the linear state-space model.

[0019] Optionally, the search unit includes: an insertion module, configured to insert the current operating condition data into the multidimensional model lookup table using a multilinear interpolation algorithm, and determine the position information of the current operating condition data in the multidimensional model lookup table; and a selection module, configured to select at least two pre-calculated models adjacent to the current operating condition data based on the position information.

[0020] Optionally, the synthesis unit includes: a determination module, used to determine the weight values ​​of each of the current operating condition data on the corresponding axis; and a synthesis processing module, used to calculate the interpolation state matrix and interpolation input matrix obtained by interpolation along each of the corresponding axes based on the weight values, so as to perform synthesis processing on the at least two pre-calculated models to obtain the linear state-space model.

[0021] Optionally, the first determining unit includes: a second calculation module, configured to calculate the time-varying transport delay based on the real-time water flow using a time-varying transport delay calculation formula, wherein the time-varying transport delay calculation formula is: , This indicates the time-varying transport delay. Indicates the length of the pipe. This indicates the real-time water flow rate. The pipeline radius is represented by a discretization module, which is used to discretize the time-varying transport delay to obtain a discretization result; the integration module is used to integrate the discretization result into the linear state-space model to obtain the target prediction model.

[0022] Optionally, the second determining unit includes: a third calculation module, configured to pass the target prediction model to a model predictive control solver, so as to use the model predictive control solver to calculate the optimal thermal power corresponding to the current operating condition data based on the target prediction model under an optimized target cost function, wherein the optimized target cost function is: , This represents the sequence of operational variables within the future control time domain. This indicates the output reference tracking error term, used to penalize the deviation between the predicted outlet water temperature and the set target temperature. This represents the tracking error term for manipulated variables, used to penalize the degree to which thermal power deviates from the target value. This represents the rate of change of control action, used to suppress oscillations caused by thermal power regulation; This represents the penalty for constraint violation, which is quantified and penalized using slack variables.

[0023] Optionally, the control unit includes a sending module, configured to send the first control quantity in the sequence corresponding to the optimal thermal power as the actual power command at the current moment to the heating actuator or gas proportional valve of the instantaneous water heater, so that the heating actuator or the gas proportional valve operates according to the actual power command.

[0024] According to one aspect of the present invention, an instantaneous water heater is provided, wherein the instantaneous water heater uses the adaptive control method for instantaneous water heaters described in any one of the above embodiments.

[0025] According to one aspect of the present invention, a computer-readable storage medium is provided, the computer-readable storage medium including a stored program, wherein the program executes the adaptive control method for an instantaneous water heater as described in any one of the preceding embodiments.

[0026] According to one aspect of the present invention, a processor is provided for running a program, wherein the program executes the adaptive control method for an instantaneous water heater as described in any of the above embodiments.

[0027] According to one aspect of the present invention, a computer program product is provided, including computer instructions, which, when executed by a processor, perform the adaptive control method for an instantaneous water heater as described above. Attached Figure Description

[0028] The accompanying drawings, which are included to provide a further understanding of the invention and form part of this application, illustrate exemplary embodiments of the invention and, together with their description, serve to explain the invention and do not constitute an undue limitation thereof. In the drawings:

[0029] Figure 1 This is a hardware structure block diagram of a mobile terminal for an adaptive control method for an instant water heater according to an embodiment of the present invention.

[0030] Figure 2 This is a flowchart of an adaptive control method for an instant water heater according to an embodiment of the present invention;

[0031] Figure 3 This is a flowchart of an optional adaptive control method for an instantaneous water heater according to an embodiment of the present invention;

[0032] Figure 4 This is a schematic diagram of a multidimensional model lookup table (LUT) according to an embodiment of the present invention;

[0033] Figure 5 This is a logic flowchart of the offline pre-calculation and online interpolation control method according to an embodiment of the present invention;

[0034] Figure 6 The above is a simulation comparison of the temperature response of the adaptive control method of the instantaneous water heater according to an embodiment of the present invention with that of the traditional FFPID and fixed model MPC under the condition of sudden change in water flow.

[0035] Figure 7 The above is a simulation comparison of the temperature response of the adaptive control method of the instantaneous water heater according to an embodiment of the present invention with that of the traditional FFPID and fixed model MPC under low flow cold start conditions.

[0036] Figure 8 This is a schematic diagram of an adaptive control device for an instantaneous water heater according to an embodiment of the present invention.

[0037] The above figures include the following reference numerals:

[0038] 102. Processor; 104. Memory; 106. Transmission device; 108. Input / output device. Detailed Implementation

[0039] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. 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 should fall within the scope of protection of the present invention.

[0040] It should be noted that the terms "first," "second," etc., in the specification, claims, and accompanying drawings of this invention are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of the invention described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0041] As described in the background section, instantaneous water heaters in related technologies are prone to unstable temperature control when facing complex and variable operating conditions, especially when users suddenly change their water flow. In embodiments of the present invention, an adaptive control method and apparatus for an instantaneous water heater, an instantaneous water heater, a computer-readable storage medium, a processor, and a computer program product are provided.

[0042] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention.

[0043] The methods and embodiments provided in this invention can be executed on a mobile terminal, a computer terminal, or a similar computing device. Taking running on a mobile terminal as an example, Figure 1 This is a hardware structure block diagram of a mobile terminal for an adaptive control method of an instantaneous water heater according to an embodiment of the present invention. Figure 1 As shown, a mobile terminal may include one or more ( Figure 1 Only one is shown in the diagram. A processor 102 (which may include, but is not limited to, a microprocessor MCU or a programmable logic device FPGA, etc.) and a memory 104 for storing data are also shown. The mobile terminal may further include a transmission device 106 for communication functions and an input / output device 108. Those skilled in the art will understand that... Figure 1 The structure shown is for illustrative purposes only and does not limit the structure of the mobile terminal described above. For example, the mobile terminal may also include components that are more... Figure 1 The more or fewer components shown, or having the same Figure 1 The different configurations shown.

[0044] The memory 104 can be used to store computer programs, such as application software programs and modules, like the computer program corresponding to the adaptive control method for an instantaneous water heater in this embodiment of the invention. The processor 102 executes various functional applications and data processing by running the computer program stored in the memory 104, thereby implementing the above-described method. The memory 104 may include high-speed random access memory and non-volatile memory, such as one or more magnetic storage devices, flash memory, or other non-volatile solid-state memory. In some instances, the memory 104 may further include memory remotely located relative to the processor 102, and these remote memories can be connected to the mobile terminal via a network. Examples of the aforementioned networks include, but are not limited to, the Internet, corporate intranets, local area networks, mobile communication networks, and combinations thereof. The transmission device 106 is used to receive or send data via a network. Specific examples of the aforementioned networks may include wireless networks provided by the mobile terminal's communication provider. In one example, the transmission device 106 includes a network interface controller (NIC), which can be connected to other network devices via a base station to communicate with the Internet. In one example, the transmission device 106 may be a radio frequency (RF) module, which is used to communicate with the Internet wirelessly.

[0045] Example 1

[0046] According to an embodiment of the present invention, an adaptive control method for an instantaneous water heater is provided. It should be noted that the steps shown in the flowchart in the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions. Furthermore, although a logical order is shown in the flowchart, in some cases, the steps shown or described may be executed in a different order than that shown here.

[0047] Figure 2 This is a flowchart of an adaptive control method for an instantaneous water heater according to an embodiment of the present invention, such as... Figure 2 As shown, the method includes the following steps:

[0048] Step S202: At each control sampling moment, acquire the current operating condition data of the instantaneous water heater.

[0049] In this embodiment, to perform offline pre-calculation, a high-precision nonlinear mathematical model needs to be established first. This model is considered a true model that accurately reflects the real physical process. This embodiment uses the lumped parameter method to model the core thermal unit. For the nonlinear mathematical model of the water heater system, a set of multiple key operating condition data that have a dominant influence on the system dynamics is selected. These key operating condition data include at least water flow rate and inlet water temperature. During actual operation of the water heater, a low-computational task is executed cyclically by a low-cost microprocessor at each sampling time k. At time k, the controller reads sensor signals through an ADC (analog-to-digital converter) to obtain the current values ​​of all key operating condition variables.

[0050] In this method, the data acquisition module of the control system performs a data reading task at each predetermined control sampling time (typically a sub-second time interval) to capture the current operating status of the instantaneous water heater in real time. This task is based on real-time monitoring and feedback control theory, in which sensors and data interfaces play a crucial role. Specifically, various sensors in the system (such as temperature sensors and flow meters) continuously monitor key operating variables of the instantaneous water heater, such as water flow rate and inlet water temperature. These sensors output analog signals, which are then converted into digital signals by an analog-to-digital converter (ADC) so that the microcontroller can recognize and process them. At each control sampling time, the microcontroller calls the ADC module to read the latest data from the sensors, thereby obtaining the real-time operating status information of the instantaneous water heater at the current moment.

[0051] By implementing this control method, the control system can accurately perceive and reflect the current operating status of the instantaneous water heater in real time. This real-time data stream provides the controller with instant updates on key parameters such as water flow rate and inlet water temperature, enabling the controller to perform condition assessments and control decisions based on the latest data in each sampling cycle. This high-frequency data acquisition not only improves the response speed of the control system but also enhances its ability to make precise controls in dynamically changing environments. For example, when water flow rate or inlet water temperature changes, the controller can immediately detect these changes and quickly adjust the control strategy to compensate for anticipated temperature fluctuations in advance, thereby maintaining a stable outlet water temperature.

[0052] Step S204: Based on the current operating condition data, search the multidimensional model lookup table to obtain at least two pre-calculated models. The multidimensional model lookup table is used to record the state space model of the instantaneous water heater at different operating condition combinations, and the pre-calculated models are used to predict the response of the instantaneous water heater to various control actions.

[0053] Optionally, the above control actions may include, but are not limited to: adjusting heating power, adjusting inlet / outlet water flow, adjusting temperature setpoint, start / stop control, adjusting gas proportional valve opening, and adjusting combustion air ratio.

[0054] In this embodiment, a series of discrete operating points are selected within a multidimensional operating space spanned by a plurality of variables. At each discrete operating point, the nonlinear model is linearized, thereby pre-calculating and storing a set of high-precision linear state-space models. This large set of model data is structurally stored in the controller's non-volatile memory, forming a multidimensional model lookup table. Based on the real-time coordinates of the collected key operating data, the model is quickly located in the multidimensional model lookup table, and multiple pre-calculated models in its vicinity are retrieved.

[0055] In this method, the multidimensional model lookup table is generated offline during the product design phase. It contains a linearized state-space model of the instantaneous water heater at different operating condition combinations. These operating condition combinations cover the expected range of change for key operating condition variables (such as water flow rate and inlet water temperature). Once the current operating condition data is acquired, the positioning algorithm performs a rapid search in the multidimensional model lookup table based on this data. Because the model lookup table is structured, the nearest neighbors or interpolation points of these variable values ​​can be found by comparing the current operating condition variable values ​​with the coordinates of discrete operating points in the table. Typically, this involves at least two pre-computed models, which form the basis for interpolation synthesis of the current operating conditions.

[0056] By implementing this control method, in terms of computational efficiency, retrieving the model from a pre-built lookup table is a low-computation process compared to online real-time calculation or model identification. It only requires simple comparison and location, greatly reducing the real-time computational burden on the controller. Secondly, it enhances the adaptability of the control system. Even when operating parameters change rapidly and significantly, the controller can quickly adjust its internal model based on the multi-dimensional model lookup table, ensuring that the control strategy can accurately respond to the current operating conditions.

[0057] Step S206: Synthesize at least two pre-computed models to obtain a linear state-space model.

[0058] In this embodiment, a highly efficient multilinear interpolation algorithm is used to perform a weighted average of the retrieved neighboring models (including their state matrix, input matrix, etc.), thereby synthesizing an interpolated linear state-space model that can accurately represent the current instantaneous operating condition in real time. This interpolation process involves only a few multiplication and addition operations, with extremely low computational cost, making it perfectly suited to the computing power of low-cost microcontrollers.

[0059] This method utilizes data points in a multidimensional model lookup table. These points have already been used in the design phase to obtain a linearized model of the water heater under specific operating conditions through offline calculations. When the actual operating conditions of the water heater fall somewhere between two or more pre-calculated models, the interpolation algorithm uses the weights of these models to synthesize a new model. These weights are determined by the difference between the current operating condition variables and the corresponding operating condition variables in the pre-calculated models. For example, in a two-dimensional operating condition space, if the current water flow rate and inlet water temperature are located between two pre-calculated models, the system calculates the corresponding weights based on the relative positions of the water flow rate and inlet water temperature with the coordinate points in the model grid. Then, based on these weights, a weighted average is applied to the state matrix, input matrix, etc., to obtain a linear state-space model that best approximates the system dynamics under the current operating conditions.

[0060] By implementing this control method, a high-precision linear state-space model can be quickly generated, which can accurately predict the instantaneous water heater's response to control actions under current operating conditions. Through synthetic processing, the controller overcomes the limitations of a single pre-calculated model when operating conditions change, enabling the entire control system to maintain high accuracy and stability over a wide range of operating conditions. The generation of this adaptive model greatly enhances the flexibility of the control strategy, allowing it to effectively cope with multivariate complex disturbances, such as sudden changes in water flow and inlet water temperature.

[0061] Step S208: Determine the time-varying transport delay based on the real-time water flow rate in the current operating condition data, and input the time-varying transport delay into the linear state-space model to obtain the target prediction model.

[0062] In this embodiment, a dynamic compensation mechanism for time-varying delay is employed. Simultaneously with the synthesis of the interpolation model, the method of this invention also calculates the time-varying transport delay under the current operating condition separately and in real time based on the real-time measured water flow. This time-varying delay is then dynamically integrated into the aforementioned interpolated linear state-space model, forming a complete and accurate final internal prediction model.

[0063] The principle of this method lies in dynamically estimating and compensating for the time-varying transport delay commonly found in instantaneous water heaters. This delay originates from the transmission process of hot water from the heating element to the temperature sensor inside the water heater, and its specific value depends on the real-time water flow rate. The faster the water flow rate, the shorter the transport delay; conversely, a slower water flow rate prolongs the delay time. To accurately estimate this delay, the current transport delay time is calculated using the acquired real-time water flow data and a pre-set delay calculation formula. Once the time-varying transport delay is determined, it is then integrated into a linear state-space model to form a target prediction model. Since the transport delay directly affects the prediction of the water heater's dynamic response, neglecting it would significantly reduce the accuracy of the model's predictions and control performance. Therefore, the system corrects the model's structure by converting the time-varying delay into equivalent model parameters, ensuring that the controller can consider this important dynamic characteristic when predicting the future behavior of the water heater. Integrating the delay into the model essentially involves adjusting the model's state transition matrix to reflect the delay effect of water temperature changes in the actual system.

[0064] By implementing this control method, the predictive accuracy of the controller for the dynamic response of the water heater is significantly improved, thereby enhancing the overall performance of temperature control. By incorporating precisely calculated time-varying transport delays into the model, the controller can more accurately predict the time difference between the heating of hot water and its detection by the sensor, thus allowing for the appropriate adjustment of thermal power in the control strategy, either earlier or later. This proactive compensation mechanism is particularly suitable for scenarios involving abrupt changes in water flow, such as a rapid switch from high to low flow or vice versa, because in these cases, changes in transport delay can significantly impact water temperature stability.

[0065] Step S210: Determine the optimal thermal power corresponding to the current operating condition data through the target prediction model.

[0066] Optionally, the optimal thermal power here can refer to the most suitable thermal power level calculated by the control algorithm under given constraints (such as upper and lower limits of thermal power, physical limitations of the system, etc.) and after considering the dynamic characteristics of the system and the expected goal (usually maintaining the outlet water temperature near the set value).

[0067] In this embodiment, a rolling time-domain optimization controller based on the synthetic model is employed. At each sampling time, the controller uses the final internal prediction model formed above to predict the system's dynamic response over a future period. The controller calculates the optimal thermal power control sequence over the future period by solving a quadratic programming problem with physical constraints (e.g., upper and lower limits of thermal power).

[0068] This method involves the controller predicting the system's response over a future period (prediction window) based on a target prediction model at the current moment, while considering set constraints (such as upper and lower limits of thermal power) and expected control objectives (such as the set outlet water temperature). The controller formulates these problems as a constrained quadratic programming problem, where the objective function (loss function) is designed to minimize the deviation between the expected outlet water temperature and the set temperature, suppress the rate of change of the control action, and penalize violations of physical constraints. By solving this optimization problem, the controller can find a thermal power input sequence that will produce a system response that minimizes the objective function within the future prediction window. This sequence includes not only the control action at the current moment but also thermal power suggestions for several future sampling moments, enabling dynamic, look-ahead control of the system.

[0069] By implementing this control method, a future optimal thermal power input sequence can be generated, which can significantly improve the temperature control performance of instantaneous water heaters in practical applications. First, because a target prediction model is used, the controller can take into account dynamic characteristics such as time-varying transport delay, as well as the impact of various operating variables such as water flow rate and inlet water temperature on the system response. This allows the controller to compensate for the disturbances caused by these factors in advance in future control strategies, thus maintaining the stability of the outlet water temperature.

[0070] Step S212: Control the instantaneous water heater to operate at the optimal thermal power.

[0071] In this embodiment, the controller sends only the first control value of the sequence as the power command at the current moment to the heating actuator, and repeats the entire acquisition-interpolation-synthesis-optimization loop at the next moment, thereby achieving efficient, multi-variable adaptive closed-loop control.

[0072] This method is based on the communication protocol between the controller and the actuator, as well as the actuator's response mechanism to control signals. After determining the optimal thermal power input sequence for the future, the controller converts the first control value in the sequence (representing the optimal thermal power at the current moment) into a signal form that the actuator can understand, such as a pulse width modulation (PWM) signal or an analog voltage signal. This signal is then sent to the heating actuator or gas proportional valve of the instantaneous water heater via the actuator interface. Upon receiving the signal, the actuator adjusts the heating power or gas supply according to the signal strength to conform to the optimal thermal power command issued by the controller. This conversion process typically includes details such as signal formatting and level conversion to ensure that the digital signals generated by the microcontroller can be correctly parsed and executed by the actuator.

[0073] This control method demonstrates the advantages of efficient multivariable adaptive control in practical applications. It enables the heating actuator or gas proportional valve of the instantaneous water heater to operate precisely according to the controller's optimized instructions, thereby achieving high-quality water temperature control. By executing the first instruction of the optimal future heat power input sequence, the actuator can immediately adjust the heating power to cope with changes in operating variables such as water flow and inlet water temperature, ensuring that the outlet water temperature quickly returns to and stabilizes within the set temperature range. This method avoids the lag phenomenon common in traditional control techniques, improving the system's response speed and control accuracy.

[0074] Figure 3 This is a flowchart of an optional adaptive control method for an instantaneous water heater according to an embodiment of the present invention, such as... Figure 3 As shown, firstly, the S1 offline memory (multidimensional model lookup table) provides parameters to the S3 model synthesis module. The S2 data acquisition module obtains operating condition data such as flow rate and outlet water temperature through ADC sampling, transmitting the operating condition positioning information to S3 and the flow rate data to the S4 time-varying delay module. S3 uses a multilinear interpolation algorithm to combine the parameters and operating condition data to generate an LTI model, which is then transmitted to S4. S4 calculates the delay based on the flow rate, corrects the prediction model, and sends it to S5. The S5 MPC optimization module solves the constrained optimization problem through quadratic programming, and the generated control commands are sent to the instantaneous water heater (nonlinear thermodynamic process) in the system's physical layer via the S6 actuator interface. The outlet water temperature of the water heater is then fed back to the S2 data acquisition module, forming a closed-loop control process. This flowchart emphasizes the close relationship between the adaptability of the control strategy, computational efficiency, and actual operation, demonstrating the core technology and advantages of this invention in maintaining a stable and efficient outlet water temperature of the instantaneous water heater under complex and variable operating conditions.

[0075] As described above, in this embodiment, at each control sampling moment, the current operating condition data of the instantaneous water heater is acquired; based on the current operating condition data, at least two pre-calculated models are obtained by searching a multidimensional model lookup table, wherein the multidimensional model lookup table is used to record the state-space model of the instantaneous water heater at different operating condition combinations, and the pre-calculated models are used to predict the response of the instantaneous water heater to various control actions; the at least two pre-calculated models are synthesized to obtain a linear state-space model; the time-varying transport delay is determined based on the real-time water flow rate in the current operating condition data, and the time-varying transport delay is input into the linear state-space model to obtain a target prediction model; the optimal thermal power corresponding to the current operating condition data is determined through the target prediction model; control The instantaneous water heater operates at optimal thermal power by offline construction of a multi-dimensional model lookup table, storing a pre-calculated linear state-space model, and online real-time acquisition of key operating condition variables such as water flow and inlet water temperature. It then uses a multilinear interpolation algorithm to synthesize a linear state-space model under the current operating conditions, calculates and integrates time-varying transport delays, and solves a quadratic programming problem with physical constraints through rolling time-domain optimization to obtain the optimal thermal power input sequence for the future. Control commands are then sent to the heating actuator via the actuator interface. This achieves high-precision adaptive control on low-cost hardware, significantly improving temperature control performance and safety, especially under extreme conditions such as low flow rates. It effectively avoids water temperature overshoot and undershoot, ensuring user comfort and water safety.

[0076] Therefore, the technical solution provided by the above embodiments of the present invention solves the technical problem in the related art that instantaneous water heaters are prone to unstable temperature control when facing complex and variable operating conditions, especially when users suddenly change the water flow.

[0077] According to the above embodiments of the present invention, before searching for at least two pre-calculated models in the multidimensional model lookup table based on the current operating condition data, the adaptive control method further includes: acquiring key operating condition variables of the instantaneous water heater, wherein the key operating condition variables include at least: inlet water flow rate and inlet water temperature; selecting multiple discrete operating points in the multidimensional operating condition space corresponding to the key operating condition variables; performing point-by-point linearization processing on the multiple discrete operating points to obtain a linear state space model; and storing each linear state space model and its corresponding discrete operating point to obtain a multidimensional model lookup table.

[0078] In this embodiment, a set of multiple variables that have a dominant influence on system dynamics are identified. In this preferred embodiment, water flow rate and inlet water temperature are selected as two basic dimensions. In other embodiments, the key operating condition variables can be extended to three dimensions or higher, depending on specific needs. For example, gas pressure can be introduced as a third key operating condition variable to form a three-dimensional model lookup table.

[0079] This method collects key operating condition variables of instantaneous water heaters, including at least inlet water flow rate (water mass flow rate) and inlet water temperature, which have a decisive impact on the changes in the system's dynamic characteristics. Next, in a multi-dimensional operating condition space spanned by these key operating condition variables, a series of discrete operating points are selected according to a preset grid partitioning criterion. These operating points cover the main operating conditions that the water heater may encounter in actual operation. For each selected operating point, point-by-point linearization is performed, that is, the nonlinear mathematical model of the water heater is linearly approximated near that operating point to obtain a set of linear state-space models. These models can approximately describe the dynamic behavior of the water heater under specific operating conditions. Finally, each set of linear state-space models and its corresponding operating point information are stored together to form a multi-dimensional model lookup table. This table structure is completed during the product design phase, providing model database support for subsequent adaptive control loops.

[0080] By implementing this control method, the acquisition of key operating condition variables ensures that the controller can fully grasp the main factors affecting the dynamic characteristics of the water heater, providing necessary information for subsequent control strategy formulation. Secondly, the selection of discrete operating points in the multi-dimensional operating condition space and the linearization processing of these operating points enable the water heater to be described by corresponding linear models under a wide range of operating conditions, enhancing the broad-spectrum adaptability of the control system. Furthermore, storing the correspondence between the linear state-space model and the operating points forms a multi-dimensional model lookup table. This table structure acts as a tool for rapid model retrieval during the control process, enabling the controller to quickly locate the set of models closest to the current operating condition at any given moment, providing an efficient data source for the next step of model interpolation and synthesis.

[0081] According to the above embodiments of the present invention, a point-by-point linearization process is performed on multiple discrete operating points to obtain a linear state-space model, including: performing a Taylor expansion on the nonlinear differential equation at each of the multiple discrete operating points to obtain the Taylor expansion result, wherein the nonlinear differential equation is: , This indicates the total heat capacity of an instant water heater. This indicates the total temperature of the instantaneous water heater. This indicates the effective heat power applied by the burner of an instant water heater. Indicates real-time water mass flow rate. This represents the specific heat capacity of water at constant pressure. The real-time inlet water temperature is represented; the Taylor expansion result is linearized to obtain a linear state-space model.

[0082] In this embodiment, the operating space is divided into a grid: N×M×… discrete operating points are selected in the aforementioned multi-dimensional operating space. At each operating point (e.g., point…),… Corresponding working conditions , At point ), the above nonlinear differential equation is expanded using Taylor and linearized to obtain a set of linear state-space (LTI) model matrices. .

[0083] Figure 4 This is a schematic diagram of a multidimensional model lookup table (LUT) according to an embodiment of the present invention. This example illustrates a two-dimensional grid based on water flow rate and inlet water temperature, such as... Figure 4 As shown, in Scope (e.g.) and Scope (e.g.) Select within ) A work point, for example: , At the work site At this point, the model is obtained: Combine all these (9 sets in this example) model matrix data, along with their corresponding working condition coordinates ( , The data is structured and burned into the non-volatile memory of the water heater controller to form a multidimensional model lookup table. Figure 4 By demonstrating a preferred embodiment of a multidimensional model lookup table based on water flow rate and inlet water temperature, this invention reveals how to achieve high-precision adaptive control of instantaneous water heaters under complex and variable operating conditions without increasing the online computing burden. This provides a solid technical foundation for realizing the intelligent and efficient operation of water heaters.

[0084] This method addresses the nonlinear differential equations of a water heater system by performing Taylor expansion at each selected operating point. Taylor expansion is a method of approximating a function with a polynomial around a point, based on the function value at that point and its derivatives. In water heater control problems, local linearization of the system state and control input at the operating point is typically chosen, i.e., linear approximating all variables in the differential equation (including state variables, control inputs, and disturbance variables). This means expanding the original equation at the current operating point into a first or second-order polynomial, retaining only the first-order term and the constant term, thus obtaining a simplified linear differential equation. This linear differential equation is then transformed into a linear state-space model in state-space form, represented by a state matrix A, an input matrix B, an output matrix C, and a direct transfer matrix D. Here, A describes the endogenous changes between system states, B describes the influence of the control input on the state, C describes the influence of the system state on the output, and D describes the direct effect of the control input on the output.

[0085] By implementing this control method, the complex nonlinear dynamic characteristics of the water heater system under different operating conditions are simplified into a series of linear models that are easy to control and analyze, greatly reducing the difficulty of control strategy design. Secondly, each linear state-space model is precisely matched to its corresponding operating point, enabling the controller to obtain the model closest to the current operating condition through rapid interpolation (in subsequent steps) when facing changes in actual operating conditions, thereby making accurate control decisions. Furthermore, this linearization process enables offline pre-calculation of the system's dynamic characteristics, greatly reducing the computational burden during online control, allowing the control strategy to run efficiently on low-cost, resource-constrained microcontrollers, and improving the real-time performance and response speed of the entire system.

[0086] According to the above embodiments of the present invention, at least two pre-calculated models are obtained by searching a multidimensional model lookup table based on the current operating condition data, including: inserting the current operating condition data into the multidimensional model lookup table using a multilinear interpolation algorithm, and determining the position information of the current operating condition data in the multidimensional model lookup table; and selecting at least two pre-calculated models that are adjacent to the current operating condition data based on the position information.

[0087] In this embodiment, for example, the controller measures the current water flow rate. L / min, current inlet water temperature ℃. The controller uses the collected real-time operating coordinates. The controller performs a fast lookup in the memory's lookup table. lie in Figure 4 In the mesh shown, its four nearest pre-computed models (i.e., bounding box vertices) are: (Bottom left corner) (Bottom right corner) (Top left corner) (Top right corner).

[0088] Figure 5 This is a logic flowchart of the offline pre-calculation and online interpolation control method according to an embodiment of the present invention, as shown below. Figure 5As shown, the process is broken down into two main stages: offline pre-calculation (S1) and online adaptive loop (S2-S6). Stage 1 is executed during the product design phase. First, key operating variables such as water flow rate and inlet water temperature are determined. Multidimensional operating condition grids are divided and operating points are defined. Then, the state matrix is ​​calculated by linearizing the model point by point. Finally, a multidimensional model lookup table (LUT) is generated and stored in ROM / Flash. Stage 2 starts the online loop at each sampling time k. S2 collects data in real time. S3 retrieves neighboring models in the LUT based on these data to complete the adaptive model positioning. S4 calculates the matrix through multilinear interpolation, calculates the delay in real time, and integrates to complete the model synthesis. Then, S5 performs rolling time-domain optimization and solves the constrained quadratic programming (QP) problem. S6 outputs control commands to execute control. Then, it waits for the next time k+1. At the same time, the data is also sent back to S3 during the process, forming a continuous online adaptive closed-loop control process. Figure 5 The logic flowchart highlights how the combination of offline pre-calculation and online adaptive looping overcomes the limitations of traditional control strategies in terms of computational efficiency, model matching accuracy, and operating condition adaptability, providing an intelligent temperature regulation solution for instantaneous water heaters that is computationally efficient, highly adaptable, and highly precise in control. This flowchart provides R&D personnel and engineers with a roadmap for implementing the control strategy of this invention, facilitating precise control of complex thermodynamic processes in actual product development.

[0089] This method relies on a multilinear interpolation algorithm. When the controller collects the current values ​​of key operating variables (such as influent flow rate and influent temperature) in real time, these values ​​are treated as point coordinates in a multidimensional space. The multidimensional model lookup table is a pre-constructed grid in this space, with each grid node corresponding to a state-space model obtained through offline linearization. The goal of the multilinear interpolation algorithm is to find the model point closest to the current operating data within this multidimensional grid. In principle, the algorithm first determines the coordinate position of the current operating data in the grid, and then identifies several nearest neighbor nodes surrounding the current point based on its relative position on the grid. In a two-dimensional case, this typically means finding the four vertices of the rectangular "bounding box" containing the current point; in higher dimensions, the number of neighboring nodes surrounding the current point increases, but the principle is similar. After determining the neighboring nodes, the algorithm calculates interpolation weights based on the coordinate distances of these points. These weights reflect the proximity of the current operating data to each neighboring node model. Subsequently, these weights are used to perform a weighted average on the selected pre-calculated model, thereby obtaining a linear state-space model that accurately reflects the current operating conditions.

[0090] By implementing this control method, the interpolation algorithm significantly improves model accuracy. Even if the current operating condition is not in the offline pre-calculated set of operating points, interpolation can still obtain a model that highly approximates the current actual operating condition in real time, ensuring that the controller's decisions are based on the most accurate current dynamic description of the system. Secondly, this process improves the flexibility and robustness of control. By considering the combined changes of multiple key operating variables (such as influent flow rate and influent temperature), the controller can adapt to a wider range of operating environments and can quickly adjust the control strategy to maintain stable outlet water temperature even under sudden changes in operating conditions.

[0091] According to the above embodiments of the present invention, at least two pre-computation models are synthesized to obtain a linear state-space model, including: determining the weight values ​​of each current operating condition data on the corresponding axis; calculating the interpolation state matrix and interpolation input matrix obtained by interpolation along each corresponding axis based on each weight value, so as to synthesize at least two pre-computation models to obtain a linear state-space model.

[0092] In this embodiment, the controller invokes a multilinear interpolation algorithm; in this case, bilinear interpolation is used. The interpolation weights are calculated as follows: Axis weights: , Axis weights: Interpolation state matrix A: (along (bottom of axis interpolation) (along (axis interpolation top) (along (Axis interpolation). Interpolation input matrix B: using the exact same weights. ,right Perform the same operation to obtain This process involves only a few scalar multiplications and additions of matrices, with extremely low computational load, well within the computing power of the microprocessor.

[0093] This method determines weight values ​​on their respective control axes (i.e., operating condition variable axes) based on current operating condition data—such as real-time measured water flow and inlet water temperature. These weight values ​​are calculated based on the relative differences between the current operating condition data and the operating points of pre-stored models, reflecting how closely the current operating condition approximates each pre-calculated model. Then, these weight values ​​are used to perform a weighted average of the selected pre-calculated models, thereby performing interpolation along each operating condition variable axis. Specifically, the controller calculates a weighted average of the state matrix A and input matrix B of each pre-calculated model to synthesize the interpolated state matrix. and interpolation input matrix This process essentially treats each pre-computed model as a point in a multi-dimensional space, while the synthesis process is a linear combination of neighboring points based on the current operating condition coordinates.

[0094] By implementing this control method, the accuracy and real-time performance issues of model predictive control in nonlinear systems are effectively solved, with significant results. First, the synthesized linear state-space model can more accurately match the actual operating conditions of the water heater, significantly improving the accuracy and response speed of the control strategy, maintaining good control performance even under rapidly changing operating conditions. Second, this synthesis mechanism ensures that model predictive control can handle complex operating conditions with multiple variables, enhancing the robustness and adaptability of the control system. This allows the water heater to maintain a more stable outlet water temperature when faced with various disturbances such as water flow and inlet water temperature.

[0095] According to the above embodiments of the present invention, the time-varying transport delay is determined based on the real-time water flow rate in the current operating condition data, and the time-varying transport delay is input into a linear state-space model to obtain a target prediction model. This includes: calculating the time-varying transport delay based on the real-time water flow rate using a time-varying transport delay calculation formula, wherein the time-varying transport delay calculation formula is: , Indicates time-varying transport delay, Indicates the length of the pipe. Indicates real-time water flow. The pipeline radius is represented; the time-varying transport delay is discretized to obtain the discretization result; the discretization result is integrated into the linear state-space model to obtain the target prediction model.

[0096] In this embodiment, the delay is calculated by the controller based on the real-time water flow rate. L / min, using the formula Calculate the current transmission delay (For example, =2.1 seconds). Integrated model: The controller will reduce this delay. Discretization (e.g., (Taking a delay of d=4 sampling points), and integrating this delay into the model by expanding its dimensionality. In the end, the controller obtained a final, high-precision value that fully represents the current operating conditions. Internal prediction model .

[0097] This method is based on the explicit physical relationship between transport delay and water flow rate. Time-varying transport delay. This refers to the time required for water to travel from the heating element to the temperature sensor location; this delay value varies with the water flow rate. It changes with the changes in [the environment / conditions]. In principle, the formula for calculating time-varying transport delay [is as follows]. This physical relationship is reflected, in which and These represent the radius and length of the pipe, respectively, and are constants in the system's geometry. When the controller obtains the real-time water flow rate... Then, the time-varying transport delay τ(t) under the current operating condition can be calculated by substituting it into the above formula. Next, the calculated... Discretization is required to transform the energy state equation into a form that matches the controller's sampling time, making it easier for the controller to understand and apply. Discretization typically involves transforming the continuous-delay energy state equation into a discrete-time state equation by... Sampling time intervals divided into integer multiples The controller can determine how many sampling points of delay need to be added to the prediction model. This result will be integrated into the linear state-space model to form a target prediction model that includes time-varying delay effects.

[0098] Implementing this control method significantly improves the accuracy and stability of water temperature control in instantaneous water heaters. First, the accurate calculation and integration of time-varying transport delay allows the controller to fully consider the transmission time of water flow from heating to measurement when generating future control sequences, avoiding slow or excessive control response due to improper delay estimation. This effect is particularly evident in situations with sudden changes in water flow, such as switching from a high flow rate to a low flow rate. In such cases, the time-varying transport delay changes significantly, directly affecting the controller's ability to adjust heating power promptly to prevent overheating or undercooling. Second, by discretizing the time-varying transport delay, the controller can integrate the delay into the state-space model in a discrete form, simplifying the model's computational complexity and making it more suitable for real-time operation in low-cost microcontrollers, while retaining an accurate description of the delay effect.

[0099] According to the above embodiments of the present invention, determining the optimal thermal power corresponding to the current operating condition data through a target prediction model includes: passing the target prediction model to a model predictive control solver, so as to use the model predictive control solver to calculate the optimal thermal power corresponding to the current operating condition data based on the target prediction model under an optimized target cost function, wherein the optimized target cost function is: , This represents the sequence of operational variables within the future control time domain. This indicates the output reference tracking error term, used to penalize the deviation between the predicted outlet water temperature and the set target temperature. This represents the tracking error term for manipulated variables, used to penalize the degree to which thermal power deviates from the target value. This represents the rate of change of control action, used to suppress oscillations caused by thermal power regulation; This represents the penalty for constraint violation, which is quantified and penalized using slack variables.

[0100] In this embodiment, the controller will The data is passed to the Model Predictive Control (MPC) solver. The objective cost function is then defined. This function aims to minimize the temperature tracking error in the next P steps. ), control motion rate of change ( ) and slack variables ( Under strict physical constraints (e.g., thermal power) Must Solve this quadratic programming problem to obtain the optimal heat power sequence for the next M steps. .

[0101] In this method, the MPC solver receives the target prediction model. This model not only includes the dynamic characteristics of the water heater under the current operating conditions but also considers the impact of time-varying transport delays, thus enabling a more accurate prediction of the system's response to control actions. The optimized objective cost function is designed to comprehensively consider various control requirements and constraints. Track the deviation between the predicted temperature and the set temperature to ensure that the outlet water temperature is as close as possible to the user's expectations; The difference between the heat depletion power and the target value helps the controller maintain its efficient operating range; Controlling the speed of thermal power regulation avoids excessively frequent or drastic control actions, thus reducing unnecessary energy consumption and wear. Quantifying the degree of violation of physical constraints, such as the upper and lower limits of thermal power, ensures the safety and reliability of system operation. The task of the MPC solver is to find an optimal set of thermal power input sequences based on the above cost function within a given future control time domain. This sequence will be obtained by solving a quadratic optimization problem, in which the system's physical constraints and dynamic limitations are integrated into optimization conditions to ensure that the controller minimizes the cost function while complying with all constraints.

[0102] By implementing this control method, the thermal power input sequence is optimized based on a high-precision target prediction model using an MPC solver, achieving precise control of the dynamic characteristics of the instantaneous water heater. Even under complex and variable operating conditions, such as sudden changes in water flow and inlet water temperature, the outlet water temperature can be maintained stably, significantly improving the user's water comfort experience. Secondly, the introduced optimization objective cost function, by balancing tracking error, thermal power fluctuations, and constraint penalties, enables the controller to meet user temperature requirements while also considering energy efficiency and equipment stability, reducing unnecessary power waste, extending equipment life, and enhancing the overall system performance. Furthermore, through rolling time-domain optimization, the controller executes only the first control action in the optimal sequence at the current moment, and subsequent sequences are continuously updated over time. This strategy avoids the accumulation of uncertainty in long-term predictions, improving the real-time performance and accuracy of control.

[0103] According to the above embodiments of the present invention, controlling an instantaneous water heater to operate according to the optimal thermal power includes: sending the first control quantity in the sequence corresponding to the optimal thermal power as the actual power command at the current moment to the heating actuator or gas proportional valve of the instantaneous water heater, so that the heating actuator or gas proportional valve operates according to the actual power command.

[0104] Here, in the efficient multivariable adaptive control method for instantaneous water heaters, the optimal thermal power is the first of a series of thermal power values ​​that can minimize the control target loss function (such as the deviation between the outlet water temperature and the set target temperature, the rate of change of thermal power, the degree of violation of system constraints, etc.) in the future prediction time domain.

[0105] In this embodiment, the controller only retrieves... The first value in .Will The power command at time k is sent to the gas proportional valve or heating actuator via PWM or DAC. (Discard sequence) The rest. Waiting for the next sampling time. The arrival of this new cycle of collection, interpolation, synthesis, and optimization begins.

[0106] This method is based on the rolling optimization principle of Model Predictive Control (MPC). MPC, as an advanced control strategy, generates an optimal control sequence by predicting system behavior over a future period and solving an optimization problem. However, in actual control, MPC does not immediately execute the entire future control sequence; instead, it sends only the first control variable in the calculated sequence as the actual power command to the actuator. This is because, although MPC can predict the future system state based on current information, the prediction may change over time due to the randomness and uncertainty of the environment. Therefore, executing only the first control variable of the sequence and updating the prediction and optimization process again in the next control cycle ensures that the control strategy is always based on the latest system state, improving the real-time performance and accuracy of the control.

[0107] By implementing this control method, the accumulation of prediction errors in the control sequence is reduced. This is because only the first control input of the sequence is executed at a time, while the remaining sequences are treated as predictions. This avoids the accumulation of errors caused by long-term predictions, which is especially important when the system has time-varying characteristics and is subject to external disturbances. Secondly, the rolling optimization strategy improves the flexibility and adaptability of the control. It allows the controller to quickly update its internal model and optimization process when the system state changes, thereby adjusting the power output in a timely manner to ensure the stability and comfort of the outlet water temperature. Furthermore, by executing only the first control input of the optimal sequence, the controller can avoid over-adjustment and drastic fluctuations in control actions, reducing mechanical stress and energy waste in the equipment, extending the service life of heating actuators or gas proportional valves, and improving the system's energy efficiency.

[0108] Figure 6 The above is a simulation comparison of the temperature response of the adaptive control method for an instantaneous water heater according to an embodiment of the present invention with that of traditional FFPID and fixed model MPC under the condition of sudden change in water flow. Figure 6 As shown, the diagram illustrates the water flow rate change and outlet water temperature control effect of an instantaneous water heater under the condition of a sudden flow rate drop (from 10L / min to 4L / min) at t=5s: The upper sub-graph shows the trend of water flow rate change over time, with the flow rate stabilizing at 10L / min from 0-5s, and then dropping sharply to 4L / min at 5s and maintaining that level; The lower sub-graph compares the outlet water temperature response of three control methods: the present invention (aMPC), fixed MPC, and traditional FPID, with a target temperature of 4℃. The traditional FPID exhibits severe overshoot, and the fixed MPC also shows significant temperature fluctuations, while the control curve provided by the embodiment of the present invention always closely follows the target temperature, with almost no overshoot and rapid stabilization. Figure 6The performance comparison simulation diagrams profoundly reveal the significant advantages of the efficient multivariable adaptive control method of the instantaneous water heater provided in this embodiment of the invention compared with traditional control strategies when dealing with the complex dynamic changes of instantaneous water heaters. This provides researchers with strong evidence to optimize control strategies and improve product performance.

[0109] Figure 7 The above is a simulation comparison of the temperature response of the adaptive control method for an instantaneous water heater according to an embodiment of the present invention with that of traditional FFPID and fixed model MPC under low flow cold start conditions, as shown in the figure. Figure 7 As shown, the flow rate change and outlet water temperature control effect of the instantaneous water heater under the low flow rate start-up condition of 3L / min are presented: the upper sub-graph shows that the water flow rate suddenly increases from 0 to 3L / min and remains there; the lower sub-graph compares the outlet water temperature response of the three control methods of the present invention (aMPC), fixed MPC, and traditional FPID. The target temperature is 4℃. Among them, fixed MPC has an overshoot of about ℃, traditional FPID has a more significant overshoot, while the control curve provided by the embodiment of the present invention has no overshoot, rises steadily and stabilizes precisely at the target temperature value. Figure 7 This invention not only demonstrates the control effect of the control method provided in the embodiments of the present invention under actual complex working conditions, but also emphasizes its technical advantages over traditional control strategies, providing strong practical verification for the intelligent control of instantaneous water heaters and having important engineering guidance value.

[0110] As described above, the technical solution provided by the embodiments of the present invention involves offline pre-calculation and storage of a multidimensional model lookup table, online real-time acquisition of key operating condition variable data, synthesis of a linear state-space model of the current operating condition using a multilinear interpolation algorithm, and formation of an internal prediction model by combining real-time calculated time-varying transport delays. A quadratic programming problem with physical constraints is solved using a rolling time-domain optimization method to obtain the optimal future thermal power input sequence, thereby controlling water temperature with high precision. This solution offlineizes the computational load, significantly reducing the computational requirements during online operation.

[0111] It should be noted that, for the sake of simplicity, the foregoing method embodiments are all described as a series of actions. However, those skilled in the art should understand that this application is not limited to the described order of actions, as some steps may be performed in other orders or simultaneously according to this application. Furthermore, those skilled in the art should also understand that the embodiments described in the specification are preferred embodiments, and the actions and modules involved are not necessarily essential to this application.

[0112] Through the above description of the embodiments, those skilled in the art can clearly understand that the methods according to the above embodiments can be implemented by means of software plus necessary general-purpose hardware platforms. Of course, they can also be implemented by hardware, but in many cases the former is a better implementation method. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product is stored in a storage medium (such as ROM / RAM, magnetic disk, optical disk) and includes several instructions to cause a terminal device (which may be a mobile phone, computer, server, or network device, etc.) to execute the methods of the various embodiments of this application.

[0113] Example 2

[0114] According to embodiments of the present invention, an adaptive control device for an instant water heater for implementing the above-described adaptive control method for an instant water heater is also provided. Figure 8 This is a schematic diagram of an adaptive control device for an instantaneous water heater according to an embodiment of the present invention, such as... Figure 8 As shown, the device includes: a first acquisition unit 801, a search unit 803, a synthesis unit 805, a first determination unit 807, a second determination unit 809, and a control unit 811. The device will now be described in detail.

[0115] The first acquisition unit 801 is used to acquire the current operating condition data of the instantaneous water heater at each control sampling time.

[0116] The search unit 803 is used to search for at least two pre-calculated models in a multidimensional model lookup table based on the current operating condition data. The multidimensional model lookup table is used to record the state-space model of the instantaneous water heater at different operating condition combinations, and the pre-calculated models are used to predict the response of the instantaneous water heater to various control actions.

[0117] Synthesis unit 805 is used to synthesize at least two pre-computation models to obtain a linear state-space model.

[0118] The first determining unit 807 is used to determine the time-varying transport delay based on the real-time water flow rate in the current operating condition data, and input the time-varying transport delay into the linear state-space model to obtain the target prediction model.

[0119] The second determining unit 809 is used to determine the optimal future thermal power input sequence corresponding to the current operating condition data through the target prediction model.

[0120] The control unit 811 is used to control the instantaneous water heater to operate at the optimal thermal power.

[0121] It should be noted that the first acquisition unit 801, search unit 803, synthesis unit 805, first determination unit 807, second determination unit 809 and control unit 811 mentioned above correspond to steps S202 to S212 in the above embodiments. The six units and the corresponding steps implement the same instances and application scenarios, but are not limited to the content disclosed in the above embodiments.

[0122] As can be seen from the above, in the scheme described in the above embodiments of the present invention, a first acquisition unit is used to acquire the current operating condition data of the instantaneous water heater at each control sampling time; a search unit is used to search for at least two pre-calculated models in a multi-dimensional model lookup table based on the current operating condition data, wherein the multi-dimensional model lookup table is used to record the state space model of the instantaneous water heater at different operating condition combinations, and the pre-calculated models are used to predict the response of the instantaneous water heater to various control actions; a synthesis unit is used to synthesize the at least two pre-calculated models to obtain a linear state space model; a first determination unit is used to determine the time-varying transport delay based on the real-time water flow in the current operating condition data, and input the time-varying transport delay into the linear state space model to obtain a target prediction model; a second determination unit is used to determine the optimal thermal power corresponding to the current operating condition data through the target prediction model; and a control unit is used to control the instantaneous water heater to operate according to the optimal thermal power. The above scheme achieves the following: offline construction of a multidimensional model lookup table to store pre-calculated linear state-space models; online real-time acquisition of key operating condition variables such as water flow and inlet water temperature; synthesis of a linear state-space model under the current operating condition using a multilinear interpolation algorithm; calculation and integration of time-varying transport delays; solving a quadratic programming problem with physical constraints through rolling time-domain optimization to obtain the optimal future thermal power input sequence; and sending control commands to the heating actuator through the actuator interface. This achieves high-precision adaptive control on low-cost hardware, significantly improving temperature control performance and safety, especially under extreme operating conditions such as low flow rates, effectively avoiding water temperature overshoot and undershoot, and ensuring user comfort and water safety.

[0123] Therefore, the technical solution provided by the above embodiments of the present invention solves the technical problem in the related art that instantaneous water heaters are prone to unstable temperature control when facing complex and variable operating conditions, especially when users suddenly change the water flow.

[0124] Optionally, the adaptive control device further includes: a second acquisition unit, used to acquire key operating condition variables of the instantaneous water heater before searching for at least two pre-calculated models in a multidimensional model lookup table based on the current operating condition data, wherein the key operating condition variables include at least: inlet water flow rate and inlet water temperature; a selection unit, used to select multiple discrete operating points in the multidimensional operating condition space corresponding to the key operating condition variables; a processing unit, used to perform point-by-point linearization processing on the multiple discrete operating points to obtain a linear state space model; and a storage unit, used to store each linear state space model and its corresponding discrete operating point to obtain a multidimensional model lookup table.

[0125] Optionally, the processing unit includes: a first calculation module, used to perform Taylor expansion processing on the nonlinear differential equation at each of the multiple discrete operating points to obtain the Taylor expansion result, wherein the nonlinear differential equation is: , This indicates the total heat capacity of an instant water heater. This indicates the total temperature of the instantaneous water heater. This indicates the effective heat power applied by the burner of an instant water heater. Indicates real-time water mass flow rate. This represents the specific heat capacity of water at constant pressure. This represents the real-time inlet water temperature; the processing module is used to linearize the Taylor expansion results to obtain a linear state-space model.

[0126] Optionally, the search unit includes: an insertion module, used to insert the current operating condition data into the multidimensional model lookup table using a multilinear interpolation algorithm, and to determine the position information of the current operating condition data in the multidimensional model lookup table; and a selection module, used to select at least two pre-calculated models that are adjacent to the current operating condition data based on the position information.

[0127] Optionally, the synthesis unit includes: a determination module, used to determine the weight values ​​of each current operating condition data on the corresponding axis; and a synthesis processing module, used to calculate the interpolation state matrix and interpolation input matrix obtained by interpolation along each corresponding axis based on each weight value, so as to perform synthesis processing on at least two pre-calculated models to obtain a linear state-space model.

[0128] Optionally, the first determining unit includes: a second calculation module, used to calculate the time-varying transport delay based on the real-time water flow using a time-varying transport delay calculation formula, wherein the time-varying transport delay calculation formula is: , Indicates time-varying transport delay, Indicates the length of the pipe. Indicates real-time water flow. The module represents the pipeline radius; the discretization module is used to discretize the time-varying transport delay to obtain the discretization result; the integration module is used to integrate the discretization result into the linear state-space model to obtain the target prediction model.

[0129] Optionally, the second determining unit includes: a third calculation module, used to pass the target prediction model to the model predictive control solver, so as to use the model predictive control solver to calculate the optimal thermal power corresponding to the current operating condition data based on the target prediction model under the optimized target cost function, wherein the optimized target cost function is: , This represents the sequence of operational variables within the future control time domain. This indicates the output reference tracking error term, used to penalize the deviation between the predicted outlet water temperature and the set target temperature. This represents the tracking error term for manipulated variables, used to penalize the degree to which thermal power deviates from the target value. This represents the rate of change of control action, used to suppress oscillations caused by thermal power regulation; This represents the penalty for constraint violation, which is quantified and penalized using slack variables.

[0130] Optionally, the control unit includes: a sending module, used to send the first control quantity in the sequence corresponding to the optimal thermal power as the actual power command at the current moment to the heating actuator or gas proportional valve of the instantaneous water heater, so that the heating actuator or gas proportional valve operates according to the actual power command.

[0131] According to one aspect of the present invention, an instantaneous water heater is provided, which uses the adaptive control method of any of the above-described instantaneous water heaters.

[0132] According to one aspect of the present invention, a computer-readable storage medium is provided, the computer-readable storage medium including a stored program, wherein the program executes the adaptive control method for an instantaneous water heater as described above.

[0133] According to one aspect of the present invention, a processor is provided for running a program, wherein the program executes the adaptive control method for an instantaneous water heater described above.

[0134] According to one aspect of the present invention, a computer program product is provided, including computer instructions, which, when executed by a processor, perform an adaptive control method for an instantaneous water heater as described above.

[0135] Optionally, in this embodiment, the computer-readable storage medium may be located in any computer terminal in a group of computer terminals in a computer network, or in any communication device in a group of communication devices.

[0136] Optionally, in this embodiment, the computer-readable storage medium is configured to store program code for performing the following steps: at each control sampling moment, acquiring the current operating condition data of the instantaneous water heater; searching for at least two pre-calculated models in a multidimensional model lookup table based on the current operating condition data, wherein the multidimensional model lookup table is used to record the state-space model of the instantaneous water heater at different operating condition combinations, and the pre-calculated models are used to predict the response of the instantaneous water heater to various control actions; synthesizing the at least two pre-calculated models to obtain a linear state-space model; determining the time-varying transport delay based on the real-time water flow in the current operating condition data, and inputting the time-varying transport delay into the linear state-space model to obtain a target prediction model; determining the optimal thermal power corresponding to the current operating condition data through the target prediction model; and controlling the instantaneous water heater to operate according to the optimal thermal power.

[0137] Optionally, in this embodiment, the computer-readable storage medium is configured to store program code for performing the following steps: influent flow rate and influent temperature; selecting multiple discrete operating points in the multidimensional operating space corresponding to key operating condition variables; performing point-by-point linearization processing on the multiple discrete operating points to obtain a linear state-space model; and storing each linear state-space model and its corresponding discrete operating point to obtain a multidimensional model lookup table.

[0138] Optionally, in this embodiment, the computer-readable storage medium is configured to store program code for performing the following steps: performing a Taylor expansion of the nonlinear differential equation at each of a plurality of discrete operating points to obtain a Taylor expansion result, wherein the nonlinear differential equation is: , This indicates the total heat capacity of an instant water heater. This indicates the total temperature of the instantaneous water heater. This indicates the effective heat power applied by the burner of an instant water heater. Indicates real-time water mass flow rate. This represents the specific heat capacity of water at constant pressure. The real-time inlet water temperature is represented; the Taylor expansion result is linearized to obtain a linear state-space model.

[0139] Optionally, in this embodiment, the computer-readable storage medium is configured to store program code for performing the following steps: inserting the current operating condition data into a multidimensional model lookup table using a multilinear interpolation algorithm, and determining the position information of the current operating condition data in the multidimensional model lookup table; selecting at least two pre-calculated models adjacent to the current operating condition data based on the position information.

[0140] Optionally, in this embodiment, the computer-readable storage medium is configured to store program code for performing the following steps: determining the weight values ​​of each current operating condition data on the corresponding axis; calculating the interpolation state matrix and interpolation input matrix obtained by interpolation along each corresponding axis based on each weight value, so as to synthesize at least two pre-calculated models to obtain a linear state-space model.

[0141] Optionally, in this embodiment, the computer-readable storage medium is configured to store program code for performing the following steps: calculating the time-varying transport delay based on the real-time water flow using a time-varying transport delay calculation formula, wherein the time-varying transport delay calculation formula is: , Indicates time-varying transport delay, Indicates the length of the pipe. Indicates real-time water flow. The pipeline radius is represented; the time-varying transport delay is discretized to obtain the discretization result; the discretization result is integrated into the linear state-space model to obtain the target prediction model.

[0142] Optionally, in this embodiment, the computer-readable storage medium is configured to store program code for performing the following steps: passing the target prediction model to the model predictive control solver, so as to use the model predictive control solver to calculate the optimal thermal power corresponding to the current operating condition data based on the target prediction model under the optimized target cost function, wherein the optimized target cost function is: , This represents the sequence of operational variables within the future control time domain. This indicates the output reference tracking error term, used to penalize the deviation between the predicted outlet water temperature and the set target temperature. This represents the tracking error term for manipulated variables, used to penalize the degree to which thermal power deviates from the target value. This represents the rate of change of control action, used to suppress oscillations caused by thermal power regulation; This represents the penalty for constraint violation, which is quantified and penalized using slack variables.

[0143] Optionally, in this embodiment, the computer-readable storage medium is configured to store program code for performing the following steps: sending a first control quantity in the optimal thermal power as the actual power command at the current moment to the heating actuator or gas proportional valve of the instantaneous water heater, so that the heating actuator or gas proportional valve operates according to the actual power command.

[0144] In the above embodiments of the present invention, the descriptions of each embodiment have different focuses. For parts not described in detail in a certain embodiment, please refer to the relevant descriptions of other embodiments.

[0145] In the several embodiments provided in this application, it should be understood that the disclosed technical content can be implemented in other ways. The device embodiments described above are merely illustrative; for example, the division of units can be a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the displayed or discussed mutual couplings, direct couplings, or communication connections may be through some interfaces; indirect couplings or communication connections between units or modules may be electrical or other forms.

[0146] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0147] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0148] Furthermore, the functional units in the various embodiments of the present invention can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0149] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods of the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, read-only memory (ROM), random access memory (RAM), portable hard drives, magnetic disks, or optical disks.

[0150] The above are merely preferred embodiments of the present invention. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. An adaptive control method for an instantaneous water heater, characterized in that, include: At each control sampling moment, the current operating condition data of the instantaneous water heater is acquired; Based on the current operating condition data, at least two pre-calculated models are obtained by searching a multidimensional model lookup table. The multidimensional model lookup table is used to record the state-space model of the instantaneous water heater at different operating condition combinations, and the pre-calculated models are used to predict the response of the instantaneous water heater to various control actions. The at least two pre-computation models are synthesized to obtain a linear state-space model; The time-varying transport delay is determined based on the real-time water flow rate in the current operating condition data, and the time-varying transport delay is input into the linear state-space model to obtain the target prediction model; The optimal thermal power corresponding to the current operating condition data is determined using the target prediction model. The instantaneous water heater is controlled to operate at the optimal thermal power.

2. The adaptive control method for an instantaneous water heater according to claim 1, characterized in that, Before searching for at least two pre-calculated models in a multidimensional model lookup table based on the current operating condition data, the adaptive control method further includes: The key operating condition variables of the instantaneous water heater are obtained, wherein the key operating condition variables include at least: inlet water flow rate and inlet water temperature; Select multiple discrete operating points in the multidimensional operating space corresponding to the key operating condition variables; The multiple discrete operating points are linearized point by point to obtain a linear state-space model; Each linear state-space model is stored in relation to its corresponding discrete operating point to obtain the multidimensional model lookup table.

3. The adaptive control method for an instantaneous water heater according to claim 2, characterized in that, The multiple discrete operating points are linearized point by point to obtain a linear state-space model, including: At each of the plurality of discrete operating points, the nonlinear differential equation is subjected to a Taylor expansion to obtain the Taylor expansion result, wherein the nonlinear differential equation is: , This indicates the total heat capacity of the instantaneous water heater. This indicates the total temperature of the instantaneous water heater. This indicates the effective thermal power applied by the burner of the instantaneous water heater. Indicates real-time water mass flow rate. This represents the specific heat capacity of water at constant pressure. Indicates the real-time inlet water temperature; The Taylor expansion result is linearized to obtain the linear state-space model.

4. The adaptive control method for an instantaneous water heater according to claim 1, characterized in that, Based on the current operating condition data, at least two pre-calculated models are obtained by searching the multidimensional model lookup table, including: The current operating condition data is inserted into the multidimensional model lookup table using a multilinear interpolation algorithm, and the position information of the current operating condition data in the multidimensional model lookup table is determined. Based on the location information, at least two pre-calculated models that are adjacent to the current operating condition data are selected.

5. The adaptive control method for an instantaneous water heater according to claim 4, characterized in that, The at least two pre-computation models are synthesized to obtain a linear state-space model, including: Determine the weight value of each of the current operating condition data on the corresponding axis; Based on the weight values, interpolation state matrices and interpolation input matrices are calculated along the corresponding axes to synthesize the at least two pre-calculated models and obtain the linear state-space model.

6. The adaptive control method for an instantaneous water heater according to claim 1, characterized in that, The time-varying transport delay is determined based on the real-time water flow rate in the current operating condition data, and the time-varying transport delay is input into the linear state-space model to obtain the target prediction model, including: The time-varying transport delay is calculated based on the real-time water flow using the time-varying transport delay calculation formula, wherein the time-varying transport delay calculation formula is: , This indicates the time-varying transport delay. Indicates the length of the pipe. This indicates the real-time water flow rate. Indicates the pipe radius; The time-varying transport delay is discretized to obtain the discretization result; The discretization result is integrated into the linear state-space model to obtain the target prediction model.

7. The adaptive control method for an instantaneous water heater according to any one of claims 1 to 6, characterized in that, The optimal thermal power corresponding to the current operating condition data is determined using the target prediction model, including: The target prediction model is passed to the model predictive control solver, which calculates the optimal thermal power corresponding to the current operating condition data based on the target prediction model under the optimized objective cost function. The optimized objective cost function is: , This represents the sequence of operational variables within the future control time domain. This indicates the output reference tracking error term, used to penalize the deviation between the predicted outlet water temperature and the set target temperature. This represents the tracking error term for manipulated variables, used to penalize the degree to which thermal power deviates from the target value. This represents the rate of change of control action, used to suppress oscillations caused by thermal power regulation; This represents the penalty for constraint violation, which is quantified and penalized using slack variables.

8. The adaptive control method for an instantaneous water heater according to any one of claims 1 to 6, characterized in that, Controlling the instantaneous water heater to operate according to the optimal thermal power includes: The first control quantity in the sequence corresponding to the optimal thermal power is sent as the actual power command at the current moment to the heating actuator or gas proportional valve of the instantaneous water heater, so that the heating actuator or the gas proportional valve operates according to the actual power command.

9. An adaptive control device for an instantaneous water heater, characterized in that, include: The first acquisition unit is used to acquire the current operating condition data of the instantaneous water heater at each control sampling moment; The search unit is used to search for at least two pre-calculated models in a multidimensional model lookup table based on the current operating condition data. The multidimensional model lookup table is used to record the state-space model of the instantaneous water heater at different operating condition combinations, and the pre-calculated models are used to predict the response of the instantaneous water heater to various control actions. A synthesis unit is used to synthesize the at least two pre-computed models to obtain a linear state-space model; The first determining unit is used to determine the time-varying transport delay based on the real-time water flow rate in the current operating condition data, and input the time-varying transport delay into the linear state-space model to obtain the target prediction model; The second determining unit is used to determine the optimal thermal power corresponding to the current operating condition data through the target prediction model; The control unit is used to control the instantaneous water heater to operate according to the optimal thermal power.

10. An instantaneous water heater, characterized in that, The instantaneous water heater uses the adaptive control method for instantaneous water heaters as described in any one of claims 1 to 8.

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