A step response variable duration fopdt model parameter identification method and system

Abstract

This invention discloses a method for parameter identification of a FOPDT model with a variable step response duration, comprising the following steps: S1: Initializing a custom matrix accumulation structure; S2: Real-time acquisition of the step response sampling time t, current output data y_current, and step input signal u_step of the FOPDT model, calculating the integral increment of the output data based on the trapezoidal integral formula, and updating the response integral value in the custom matrix accumulation structure in real time; S3: Constructing a 3D feature vector using the response integral value, the product of the step input signal and the sampling time, and a constant 1, and incrementally updating the 3×3 matrix elements in the 3×3 matrix element storage unit through the self-multiplication operation of the 3D feature vector, thereby achieving real-time iterative update of the 3×3 matrix elements. Temperature controllers equipped with the technical solution disclosed in this invention have significant advantages in control accuracy, start-up speed, and ease of operation, exhibiting outstanding product differentiation and competitiveness, and helping enterprises gain a favorable position in market competition.

Description

Technical Field

[0001] This invention belongs to the field of embedded temperature control equipment modeling and control technology, specifically involving a method and system for parameter identification of step response variable duration FOPDT model applied to temperature controllers, which is suitable for initial parameter configuration scenarios of fuzzy PID control. Background Technology

[0002] In the field of industrial production and equipment control, the precise control of temperature parameters directly determines product quality, production efficiency, and equipment operational safety. As the core execution unit, the performance of the temperature controller has a crucial impact. Currently, mainstream industrial temperature controllers generally employ fuzzy PID control algorithms. This algorithm combines the nonlinear adaptive capability of fuzzy control with the steady-state accuracy of PID control, effectively addressing common issues in temperature control systems such as hysteresis, time-varying characteristics, and load disturbances. However, the control effect of the fuzzy PID algorithm is highly dependent on the rationality of the initial PID parameters—if the initial parameters deviate from the system's optimal value, it will not only prolong the temperature response settling time and increase overshoot, but may even lead to oscillations or instability in the temperature control system. Therefore, providing accurate initial parameter references for fuzzy PID is one of the core aspects of improving the control performance of temperature controllers.

[0003] To address the initial parameter configuration problem of temperature control systems, the industry generally adopts parameter identification methods based on mathematical models. This involves establishing a dynamic model of the temperature-controlled object to infer the optimal PID parameter range. Among these, the first-order plus pure time delay (FOPDT) model, due to its simple structure and clear physical meaning, can accurately match the dynamic characteristics of most industrial temperature-controlled objects (such as heating furnaces, reactors, and constant temperature chambers), making it the preferred model for temperature controller parameter identification. The core parameters of the FOPDT model include gain K (reflecting the amplitude relationship between input and output), time constant T (reflecting the system response speed), and pure time delay τ (reflecting signal transmission delay). The accuracy of identifying these three parameters directly determines the reliability of the subsequent fuzzy PID initial parameters.

[0004] Currently, parameter identification technology based on the least squares method is the mainstream solution for solving FOPDT model parameters. Its core principle is to construct a data matrix and response vector to find the model parameters that minimize the sum of squared errors. However, when this technology is applied to embedded temperature controllers, it faces a series of prominent problems that are incompatible with hardware resources and control requirements, which seriously restricts its engineering practicality. First, there is the problem of excessive hardware resource consumption: the traditional least squares method requires the construction of a calculation matrix of the same dimension as the amount of sampled data. For example, when the sampling period is 10ms and the identification time is 10s, a 1000×3 matrix needs to be constructed. Storing only the float data of this matrix requires 12KB of memory (1000×3×4 bytes), while the SRAM resources of industrial-grade economic temperature controllers are usually only about 20K. If the memory consumption of the fuzzy PID algorithm itself is added, memory overflow is very likely to occur, leading to system crashes. Some temperature controllers have to simplify the algorithm to adapt to this technology, which will lead to a significant decrease in identification accuracy.

[0005] Secondly, the fixed identification time leads to poor adaptability: the dynamic characteristics of temperature-controlled objects vary significantly under different loads. For example, light loads (such as small constant temperature chambers) have a fast temperature response speed, and FOPDT parameters usually stabilize within 3-5 seconds, while heavy loads (such as large heating furnaces) have a large response delay, and parameter stabilization may take 15-20 seconds. Traditional identification methods preset a fixed acquisition time (such as a uniform 10 seconds), which leads to data redundancy and prolonged parameter output time for light loads, affecting the startup efficiency of the temperature controller; for heavy loads, insufficient data will cause the identification to stop before the parameters stabilize, resulting in large errors in the output parameters. The fuzzy PID initial value configured based on these parameters will cause the temperature control system to experience significant overshoot or slow response.

[0006] Furthermore, existing technologies suffer from issues such as parameter output lag and insufficient solution stability: traditional methods require all preset data to be collected before performing a one-time matrix solution, making it impossible to output parameters in real time. Fuzzy PID can only obtain initial parameters after identification is completed, resulting in a control "window period" during the start-up phase of the temperature controller. At the same time, most methods use fixed regularization coefficients to suppress matrix ill-conditioning. When there is noise interference in the temperature control system (such as temperature sampling errors caused by power fluctuations), the fixed coefficients are difficult to adapt to different operating conditions, easily leading to solution divergence. The output K, T, and τ parameters fluctuate wildly and cannot be used as a reliable reference for fuzzy PID.

[0007] To address the aforementioned issues, the industry urgently needs a FOPDT model identification technology that can adapt to the hardware resources of embedded temperature controllers (especially those with limited SRAM), possess load adaptability, and output stable parameters in real time. Summary of the Invention

[0008] The purpose of this invention is to provide a method and system for identifying parameters of a FOPDT model with a variable step response duration, in order to solve at least one of the following technical problems existing in the prior art.

[0009] The existing technologies have the following technical problems: 1. Traditional least squares methods require the construction of a matrix proportional to the amount of sampled data, resulting in excessive SRAM usage (easily exceeding the 20K SRAM limit of the temperature controller) and causing system memory overflow; 2. The preset fixed identification time cannot adapt to the difference in the stabilization time of the temperature control object parameters under light / heavy loads, resulting in data redundancy under light loads and insufficient parameter accuracy under heavy loads; 3. The parameter solution is only performed after all data acquisition is completed, resulting in parameter output lag and a control "window period" during the fuzzy PID startup phase; 4. The use of fixed regularization coefficients makes the solution prone to divergence when facing noise interference from the temperature control system, causing drastic parameter fluctuations and failing to provide a reliable initial reference for the fuzzy PID.

[0010] The technical solution adopted by this invention to solve its technical problem is: a method for identifying parameters of a FOPDT model with variable step response duration, comprising the following steps: S1: Initialize the custom matrix accumulation structure, which includes a 3×3 matrix element storage unit, a response integral value storage unit, and a data counting unit; initialize the 3×3 matrix elements in the 3×3 matrix element storage unit to 0; initialize the response integral value in the response integral value storage unit to a preset reference value; initialize the data counting unit to a preset reference value; S2: Real-time acquisition of the step response sampling time t, current output data y_current, and step input signal u_step of the FOPDT model; calculation of the integral increment of the output data based on the trapezoidal integral formula; and real-time acquisition of the response integral value in the newly defined matrix accumulation structure. S3: Construct a 3D feature vector using the response integral value, the product of the step input signal and the sampling time, and a constant 1. Incrementally update the 3D matrix elements in the 3D matrix element storage unit through the self-multiplication operation of the 3D feature vector to achieve real-time iterative update of the 3D matrix elements. S4: Calculate the dynamic regularization coefficient Lambda based on the numerical values ​​of the data counting units, and superimpose it onto the diagonal elements of a 3×3 matrix to construct a regularization matrix. Use the SVD decomposition algorithm with column pivoting to solve the system of equations formed by the regularization matrix and the response data vector to obtain the intermediate values ​​of the model parameters. S5: The three parameters of the FOPDT model, namely gain K, time constant T, and pure time delay τ, are obtained by converting intermediate values. These parameters are updated synchronously with the control cycle of the temperature controller. The parameter changes are monitored in real time for multiple consecutive cycles. When the parameter changes meet the stability condition, the dynamic update is stopped, and the stable parameters at this time are used as the initial parameter calculation reference for the fuzzy PID algorithm of the temperature controller.

[0011] In the custom matrix accumulation structure described in step S1, the 3×3 matrix element storage unit includes matrix upper triangular element storage variables sum00, sum01, sum02, sum11, sum12, sum22 and response data association and storage variables sumR0, sumR1, sumR2; the response integral value storage unit includes the response integral value storage variable y_integral; and the data counting unit includes the data counting variable count.

[0012] The trapezoidal integral formula described in step S2 is: dy_int = 0.5×(last_y + y_current)×dt, where dy_int is the integral increment of the output data, last_y is the output data of the previous sampling period, dt is the time interval between the current and the previous sampling period, and y_current is the current output data; when dt≤0, its value is the reciprocal of the sampling frequency.

[0013] The expression for the 3D feature vector in step S3 is [φ0, φ1, φ2]ᵀ, where φ0 = -y_integral, φ1 = u_step×t, φ2 = 1.0, where y_integral is the cumulative response integral value stored in the response integral value storage unit in the custom matrix accumulation structure, u_step is the step input signal, t is the step response sampling time, and the matrix update rule is: sum00 += φ0×φ0, sum01 += φ0×φ1, sum02 += φ0×φ2, sum11 += φ1×φ1, sum12 += φ1×φ2, sum22 += φ2×φ2, and at the same time update sumR0 += φ0×y_current, sumR1 += φ1×y_current, sumR2 += φ2×y_current, where y_current is the current output data.

[0014] The formula for calculating the dynamic regularization coefficient in step S4 is: dynamic_lambda = LAMBDA × exp(-0.001×count), where dynamic_lambda is the dynamic regularization coefficient, LAMBDA is the preset initial regularization value, which takes the value 1000.0; count is the data counting variable in the data counting unit, and the dynamic regularization coefficient is only superimposed on the diagonal elements sum00, sum11, and sum22 of the 3×3 matrix.

[0015] Step S4, the SVD decomposition solution, includes the following sub-steps: S41: Construct a 3×4 augmented matrix based on the regularization matrix. The first 3 columns of the 3×4 augmented matrix are the 3×3 matrix elements of the regularization matrix, and the 4th column consists of the response data association and storage variables sumR0, sumR1, and sumR2. S42: Perform column pivoting on the 3×4 augmented matrix in step S41, locate the row containing the element with the largest absolute value in each column and swap them to the main diagonal position; S43: Based on step S42, the 3×4 augmented matrix is ​​transformed into an upper triangular matrix by Gaussian elimination, and then the intermediate values ​​of the three model parameters θ0, θ1, and θ2 are obtained by back substitution along the main diagonal.

[0016] 7. The FOPDT model parameter identification method with variable step response duration according to claim 6, characterized in that: the model parameter conversion formula in step S5 is: T = 1.0 / θ0, K = θ1 / θ0, τ = (y0 - θ2) / (θ1×u_step), where y0 is the initial output reference value of the FOPDT model, and θ0, θ1, and θ2 are the intermediate values ​​obtained in step S4.

[0017] The parameter changes mentioned in step S5 satisfy the stability condition as follows: within three consecutive temperature control cycles, the absolute value of the change in gain K of the FOPDT model is ≤5%, the absolute value of the change in time constant T is ≤5%, and the absolute value of the change in pure time delay τ is ≤5%.

[0018] A parameter identification system for a FOPDT model with variable step response duration includes an initialization module, a data acquisition module, a matrix update module, a parameter solving module, and a control and scheduling module. Initialization module: Used to trigger the Matrix_Init() function. After receiving the initial output baseline value of the FOPDT model, it resets the 3×3 matrix element storage unit, response integral value storage unit, and data counting unit of the custom matrix accumulation structure to the initial state. Data acquisition module: Acquires real-time output data Get_RealTemp(), step input signal Output, and sampling time count mTs of the FOPDT model according to the set sampling period DT, and outputs them to the matrix update module; Matrix update module: It has a built-in custom matrix accumulation structure, executes the Matrix_Update() function to complete the real-time calculation of the integral increment of the output data, the incremental update of the 3×3 matrix elements, and the accumulation of the data counting unit; The parameter solving module calls the Solve_Matrix() function to calculate the dynamic regularization coefficient Lambda, and uses the Solve_SVD_3x3 function to perform column pivot SVD decomposition to obtain the FOPDT model parameters K, T, and τ. Control and scheduling module: The SecondMul_Caculation() function is used to implement the periodic scheduling of initialization triggering, sampling counting, matrix updating and parameter solving, and outputs the final stable parameters K, T and τ of the FOPDT model.

[0019] The execution frequency of the matrix update module and the parameter solving module is consistent with the fuzzy PID control frequency of the temperature controller, and the parameter update cycle is synchronized with the temperature control cycle of the temperature controller. The logic for determining the FOPDT model parameters K, T, and τ obtained by the parameter solving module as stable parameters is as follows: the absolute value of the change in K, T, and τ within three consecutive cycles is ≤5%. When the stability condition is not met, the FOPDT model parameters K, T, and τ are dynamically updated with the cycle. After the condition is met, a stability signal is triggered, the control scheduling module stops the duration extension, and the final stable parameters of the FOPDT model are output.

[0020] The beneficial effects of the present invention are as follows: (1) The present invention uses a custom matrix accumulation structure and incremental update mechanism, so the memory usage of the entire identification process is ≤200 bytes, which only accounts for 1% of the 20K SRAM resources of the temperature controller, completely avoiding the problem of hardware upgrades due to memory overflow in traditional algorithms. On the one hand, the FLASH usage is ≤5K, which is compatible with 128K FLASH resources; the temperature controller can continue to use the more economical 128K FLASH and 20K SRAM chip solution, without the need to select high-specification hardware for the identification function, and the hardware cost of a single device is reduced by 15%-20%; on the other hand, the algorithm code is simplified (FLASH usage is ≤5K), without the need to occupy the storage resources of core control programs such as fuzzy PID, reducing the workload of software and hardware compatibility debugging, shortening the R&D cycle by more than 25%, and significantly improving the product launch efficiency.

[0021] (2) The combination of dynamic regularization and column pivot SVD decomposition reduces the parameter identification error of the FOPDT model, providing accurate initial parameter references for fuzzy PID and significantly improving identification accuracy. It solves the problems of large overshoot and long adjustment time caused by "blind parameter matching" in the startup stage of traditional temperature controllers from the source. In light load scenarios (such as small constant temperature chambers), the temperature controller can quickly enter the precise control state after startup. In heavy load scenarios (such as large heating furnaces), by adaptively extending the identification time, the fuzzy PID based on this parameter configuration can effectively suppress temperature fluctuations caused by load lag, and the steady-state temperature error is controlled within ±0.2℃. At the same time, the dynamic regularization coefficient design enables the algorithm to output stable parameters under complex working conditions such as power fluctuations and environmental interference, significantly enhancing the anti-interference capability of the temperature controller and making it suitable for harsh industrial environments such as chemical and electronic manufacturing.

[0022] (3) In this invention, the parameter changes over multiple consecutive cycles are monitored in real time. When the parameter changes meet the stability condition, dynamic updates are stopped, and the stable parameters at this time are used as the initial parameter calculation reference for the fuzzy PID algorithm of the temperature controller. Because the parameter stabilization time varies for different loads, the duration of the entire stable parameter identification process is dynamically adapted to the load characteristics, achieving variable duration identification. The load adaptability is extremely strong: the identification duration is dynamically adjusted with the load, reducing data redundancy for light loads and ensuring parameter stability for heavy loads, adapting to various industrial temperature control objects. This variable duration identification mechanism completely eliminates the traditional algorithm's "manually preset identification duration" operation process. The temperature controller can automatically adjust the identification cycle according to the temperature response characteristics of different loads. It automatically shortens the duration when facing light loads such as small heating modules and automatically extends the duration when facing heavy loads such as reactor jacket heating. The entire process does not require operators to manually set parameters according to the load type, greatly reducing the dependence on the professional skills of operators, and is especially suitable for multi-specification load switching scenarios on production lines.

[0023] In addition, the parameters are updated in real time with the temperature control cycle. The fuzzy PID can obtain reference parameters during the identification process, eliminating the "window period" of fuzzy PID startup. This avoids the risk of temperature runaway during the startup phase caused by the traditional solution of "identification before control", and reduces the product scrap rate caused by temperature fluctuations. Taking the temperature control scenario of electronic component welding as an example, it significantly reduces the enterprise's operation and maintenance costs.

[0024] (4) The core algorithm of this invention adopts a modular design. The initialization module, data acquisition module, matrix update module, parameter solving module, and control scheduling module are compatible with fuzzy PID temperature controllers of different brands and models. Only minor adjustments to the data interface are needed for porting, making it highly adaptable. Furthermore, the algorithm's lightweight nature allows it to be applied not only to industrial-grade temperature controllers but also to miniaturized scenarios such as household smart temperature controllers and laboratory precision temperature control equipment, broadening the product's application scope. Compared to competing products using traditional identification technologies, temperature controllers equipped with this invention have significant advantages in control accuracy, startup speed, and ease of operation, resulting in outstanding product differentiation and competitiveness, helping companies gain a favorable position in market competition.

[0025] The present invention will be described in more detail below with reference to the embodiments. Detailed Implementation

[0026] Example: A parameter identification method for a FOPDT model with a variable step response duration, applied to a temperature controller configured with 128K FLASH and 20K SRAM, can be used to provide initial parameter references for fuzzy PID control, including the following steps: S1: Initialize the custom matrix accumulation structure, which includes a 3×3 matrix element storage unit, a response integral value storage unit, and a data counting unit; initialize the 3×3 matrix elements in the 3×3 matrix element storage unit to 0; initialize the response integral value in the response integral value storage unit to a preset reference value; initialize the data counting unit to a preset reference value; S2: Real-time acquisition of the step response sampling time t, current output data y_current, and step input signal u_step of the FOPDT model; calculation of the integral increment of the output data based on the trapezoidal integral formula; and real-time acquisition of the response integral value in the newly defined matrix accumulation structure. S3: Construct a 3D feature vector using the response integral value, the product of the step input signal and the sampling time, and a constant 1. Incrementally update the 3D matrix elements in the 3D matrix element storage unit through the self-multiplication operation of the 3D feature vector, thereby realizing the real-time iterative update of the 3D matrix elements; the update process only depends on the current sampled data and the historical accumulation results. S4: Calculate the dynamic regularization coefficient Lambda based on the numerical values ​​of the data counting units, and superimpose it onto the diagonal elements of a 3×3 matrix to construct a regularization matrix. Use the SVD decomposition algorithm with column pivoting to solve the system of equations formed by the regularization matrix and the response data vector to obtain the intermediate values ​​of the model parameters. S5: The three parameters of the FOPDT model, namely gain K, time constant T, and pure time delay τ, are obtained by converting intermediate values. These parameters are updated synchronously with the control cycle of the temperature controller. The parameter changes over multiple consecutive cycles are monitored in real time. When the parameter changes meet the stability condition, the dynamic update stops, and the stable parameters at this time are used as the initial parameter calculation reference for the fuzzy PID algorithm of the temperature controller. Since the acquisition time of stable parameters varies for different loads, the duration of the entire stable parameter identification process is dynamically adapted to the load characteristics to achieve variable duration identification.

[0027] In the custom matrix accumulation structure described in step S1, the 3×3 matrix element storage unit includes matrix upper triangular element storage variables sum00, sum01, sum02, sum11, sum12, sum22 and response data association and storage variables sumR0, sumR1, sumR2; the response integral value storage unit includes the response integral value storage variable y_integral; and the data counting unit includes the data counting variable count.

[0028] The trapezoidal integral formula described in step S2 is: dy_int = 0.5×(last_y + y_current)×dt, where dy_int is the integral increment of the output data, last_y is the output data of the previous sampling period, dt is the time interval between the current and the previous sampling period, and y_current is the current output data; when dt≤0, its value is the reciprocal of the sampling frequency.

[0029] The expression for the 3D feature vector in step S3 is [φ0, φ1, φ2]ᵀ, where φ0 = -y_integral, φ1 = u_step×t, φ2 = 1.0, where y_integral is the cumulative response integral value stored in the response integral value storage unit in the custom matrix accumulation structure, u_step is the step input signal, t is the step response sampling time, and the matrix update rule is: sum00 += φ0×φ0, sum01 += φ0×φ1, sum02 += φ0×φ2, sum11 += φ1×φ1, sum12 += φ1×φ2, sum22 += φ2×φ2, and at the same time update sumR0 += φ0×y_current, sumR1 += φ1×y_current, sumR2 += φ2×y_current, where y_current is the current output data.

[0030] The formula for calculating the dynamic regularization coefficient in step S4 is: dynamic_lambda = LAMBDA × exp(-0.001×count), where dynamic_lambda is the dynamic regularization coefficient, LAMBDA is the preset initial regularization value, which takes the value 1000.0; count is the data counting variable in the data counting unit, and the dynamic regularization coefficient is only superimposed on the diagonal elements sum00, sum11, and sum22 of the 3×3 matrix.

[0031] Step S4, the SVD decomposition solution, includes the following sub-steps: S41: Construct a 3×4 augmented matrix based on the regularization matrix. The first 3 columns of the 3×4 augmented matrix are the 3×3 matrix elements of the regularization matrix, and the 4th column consists of the response data association and storage variables sumR0, sumR1, and sumR2. ; S42: Perform column pivoting on the 3×4 augmented matrix in step S41, locate the row containing the element with the largest absolute value in each column and swap them to the main diagonal position; S43: Based on step S42, the 3×4 augmented matrix is ​​transformed into an upper triangular matrix by Gaussian elimination, and then the intermediate values ​​of the three model parameters θ0, θ1, and θ2 are obtained by back substitution along the main diagonal.

[0032] The model parameter conversion formula mentioned in step S5 is: T = 1.0 / θ0, K = θ1 / θ0, τ = (y0 - θ2) / (θ1×u_step), where y0 is the initial output baseline value of the FOPDT model, and θ0, θ1, and θ2 are the intermediate values ​​obtained in step S4.

[0033] The parameter changes mentioned in step S5 meet the stability conditions as follows: within three consecutive temperature control cycles, the absolute value of the change in gain K of the FOPDT model is ≤5%, the absolute value of the change in time constant T is ≤5%, and the absolute value of the change in pure time delay τ is ≤5%, and this stable trend continues for more than three temperature control cycles.

[0034] A parameter identification system for a FOPDT model with variable step response duration includes an initialization module, a data acquisition module, a matrix update module, a parameter solving module, and a control and scheduling module. Initialization module: Used to trigger the Matrix_Init() function. After receiving the initial output baseline value of the FOPDT model, it resets the 3×3 matrix element storage unit, response integral value storage unit, and data counting unit of the custom matrix accumulation structure to the initial state. Data acquisition module: Acquires real-time output data Get_RealTemp(), step input signal Output, and sampling time count mTs of the FOPDT model according to the set sampling period DT, and outputs them to the matrix update module; Matrix update module: It has a built-in custom matrix accumulation structure, executes the Matrix_Update() function to complete the real-time calculation of the integral increment of the output data, the incremental update of the 3×3 matrix elements, and the accumulation of the data counting unit; The parameter solving module calls the Solve_Matrix() function to calculate the dynamic regularization coefficient Lambda, and uses the Solve_SVD_3x3 function to perform column pivot SVD decomposition to obtain the FOPDT model parameters K, T, and τ. Control and scheduling module: The SecondMul_Caculation() function is used to implement the periodic scheduling of initialization triggering, sampling counting, matrix updating and parameter solving, and outputs the final stable parameters K, T and τ of the FOPDT model.

[0035] The execution frequency of the matrix update module and the parameter solving module is consistent with the fuzzy PID control frequency of the temperature controller, and the parameter update cycle is synchronized with the temperature control cycle of the temperature controller. The logic for determining the FOPDT model parameters K, T, and τ obtained by the parameter solving module as stable parameters is as follows: the absolute value of the change in K, T, and τ is ≤5% for three consecutive cycles and lasts for more than three cycles. When the stability condition is not met, the FOPDT model parameters K, T, and τ are dynamically updated with the cycle. After the condition is met, a stability signal is triggered, the control scheduling module stops the duration extension, and the final stable parameters of the FOPDT model are output.

[0036] This invention utilizes a matrix optimization design based on a custom matrix accumulation structure to reduce hardware resource consumption. Abandoning the traditional full matrix storage mode, it designs a custom matrix accumulation structure, MatrixAccumulator, containing only 12 float variables. It achieves lightweight management of a 3×3 matrix through "upper triangular element storage + incremental update." The custom matrix accumulation structure includes 6 upper triangular elements (sum00, sum01, sum02, sum11, sum12, sum22), 3 response data association sums (sumR0, sumR1, sumR2), 1 response integral value (y_integral), and 1 data count variable (count). Leveraging matrix symmetry, it stores only the upper triangular elements, reducing redundant storage by 50%. The total memory usage of the structure is only 48 bytes (12×4 bytes). During initialization, the Matrix_Init() function resets all units of the structure to 0, requiring only minimal SRAM to complete the computational foundation, perfectly adapting to the hardware resource constraints of temperature controllers.

[0037] This invention employs a periodic iterative parameter solving mechanism to achieve real-time parameter output. The gain K, time constant T, and pure time delay τ of the FOPDT model are synchronized with the control cycle of the temperature controller's fuzzy PID, and the periodic scheduling of "data acquisition-matrix update-parameter solving" is achieved through the SecondMul_Caculation() function. Within each temperature control cycle, the data acquisition module acquires real-time temperature data (Get_RealTemp()), step input signal (Output), and sampling count (mTs) at a fixed sampling period DT, and transmits them to the matrix update module. The matrix update module executes the Matrix_Update() function, calculates the integral increment of the temperature response based on the trapezoidal integral formula (dy_int = 0.5×(last_y + y_current)×dt), updates y_integral, and constructs a 3D feature vector with "-y_integral, u_step×t, 1.0". It incrementally updates the matrix elements and associated sums in the structure through vector self-multiplication (such as sum00 += φ0×φ0, sumR0 += φ0×y_current), without needing to call the full historical data. The parameter solving module synchronously calls the Solve_Matrix() function, constructs a 3×3 regularized matrix based on the updated matrix elements, solves the FOPDT model parameters K, T, and τ in real time, and outputs them, so that the fuzzy PID can obtain parameter references during the identification process, eliminating the control "window period".

[0038] This invention employs dynamic regularization and high-precision solution to improve parameter stability. To avoid solution divergence caused by matrix ill-conditioning, a regularization coefficient is designed that dynamically adjusts with the sampling count. The calculation formula is dynamic_lambda = 1000.0 × exp(-0.001 × count). Through exponential decay, the coefficient gradually decreases during the identification process, balancing stability in the initial stage with identification accuracy in the later stage. This coefficient is only added to the diagonal elements (sum00, sum11, sum22) of the 3×3 matrix, further simplifying the calculation. In the solution stage, an SVD decomposition algorithm based on column pivoting is used. By constructing a 3×4 augmented matrix (the first 3 columns are the regularization matrix, and the 4th column is the response vector), the element with the largest absolute value in each column is first located and swapped to the main diagonal. Then, Gaussian elimination is used to transform it into an upper triangular matrix. Finally, the intermediate values ​​θ0, θ1, and θ2 are solved by reverse substitution, effectively suppressing temperature sampling noise interference and ensuring the stability of parameter output. The variable-duration identification with load adaptation matches the characteristics of different temperature-controlled objects. It abandons the mode of preset fixed identification duration, using parameter stability as the stopping criterion to achieve dynamic adaptation of the identification duration to the load. The parameter solving module has a built-in stability monitoring unit that calculates the changes in parameters K, T, and τ in real time over three consecutive temperature control cycles. When the absolute value of the changes in the three parameters is ≤5% and this trend continues for more than two cycles, the parameters are determined to have reached a stable state, triggering a stability signal to the control scheduling module. The control scheduling module then stops the duration extension and transmits the stable parameters to the fuzzy PID module as the basis for initial parameter calculation. This design compresses the identification duration for light loads (such as small constant temperature chambers) to 3-5 seconds, and adaptively extends the identification duration for heavy loads (such as large heating furnaces) to 15-20 seconds, avoiding data redundancy while ensuring parameter accuracy. The system seamlessly integrates with fuzzy PID control, supporting initial parameter configuration. The control scheduling module of the identification system communicates directly with the fuzzy PID module of the temperature controller via an internal data bus. The stabilized K, T, and τ parameters are transmitted according to a preset protocol. Based on these parameters, the fuzzy PID controller quickly calculates the initial PID parameters using empirical formulas (such as the proportional coefficient KP being positively correlated with K, and the integral time TI being positively correlated with T), without manual intervention, significantly improving the start-up control performance of the temperature controller.

[0039] The above description is merely illustrative. Clearly, the specific implementation of the present invention is not limited to the above-described manner. Any non-substantial improvements made using the inventive concept and technical solution of the present invention; or the direct application of the inventive concept and technical solution to other situations without modification, are all within the protection scope of the present invention.

Claims

1. A method for parameter identification of a FOPDT model with variable duration of step response, characterized in that: Includes the following steps: S1: Initialize the custom matrix accumulation structure, which includes a 3×3 matrix element storage unit, a response integral value storage unit, and a data counting unit; Initialize the 3×3 matrix elements in the 3×3 matrix element storage unit to 0; Initialize the response integral value in the response integral value storage unit to the preset reference value; initialize the data counting unit to the preset reference value; S2: Real-time acquisition of the step response sampling time t, current output data y_current, and step input signal u_step of the FOPDT model; calculation of the integral increment of the output data based on the trapezoidal integral formula; and real-time acquisition of the response integral value in the newly defined matrix accumulation structure. S3: Construct a 3D feature vector using the response integral value, the product of the step input signal and the sampling time, and a constant 1. Incrementally update the 3D matrix elements in the 3D matrix element storage unit through the self-multiplication operation of the 3D feature vector to achieve real-time iterative update of the 3D matrix elements. S4: Calculate the dynamic regularization coefficient Lambda based on the numerical values ​​of the data counting units, and superimpose it onto the diagonal elements of a 3×3 matrix to construct a regularization matrix. Use the SVD decomposition algorithm with column pivoting to solve the system of equations formed by the regularization matrix and the response data vector to obtain the intermediate values ​​of the model parameters. S5: The three parameters of the FOPDT model, namely gain K, time constant T, and pure time delay τ, are obtained by converting intermediate values. These parameters are updated synchronously with the control cycle of the temperature controller. The parameter changes are monitored in real time for multiple consecutive cycles. When the parameter changes meet the stability condition, the dynamic update is stopped, and the stable parameters at this time are used as the initial parameter calculation reference for the fuzzy PID algorithm of the temperature controller.

2. The method for parameter identification of a FOPDT model with variable duration of step response according to claim 1, characterized in that: In the custom matrix accumulation structure described in step S1, the 3×3 matrix element storage unit includes upper triangular element storage variables sum00, sum01, sum02, sum11, sum12, sum22 and response data association and storage variables sumR0, sumR1, sumR2; the response integral value storage unit includes the response integral value storage variable y_integral, where y_integral is the cumulative response integral value stored in the response integral value storage unit of the custom matrix accumulation structure; the data counting unit includes the data counting variable count, where count is...

3. The method for identifying parameters of a FOPDT model with variable duration of step response according to claim 1 or 2, characterized in that: The trapezoidal integral formula mentioned in step S2 is: dy_int = 0.5×(last_y + y_current)×dt, where dy_int is the integral increment of the output data, last_y is the output data of the previous sampling period, dt is the time interval between the current and the previous sampling period, and y_current is the current output data; when dt≤0, its value is the reciprocal of the sampling frequency.

4. The method for parameter identification of a FOPDT model with variable duration of step response according to claim 3, characterized in that: The expression for the 3D feature vector in step S3 is [φ0, φ1, φ2]ᵀ, where φ0 = -y_integral, φ1 = u_step×t, φ2 = 1.0, where y_integral is the cumulative response integral value stored in the response integral value storage unit in the custom matrix accumulation structure, u_step is the step input signal, t is the step response sampling time, and the matrix update rule is: sum00 += φ0×φ0, sum01 += φ0×φ1, sum02 += φ0×φ2, sum11 += φ1×φ1, sum12 += φ1×φ2, sum22 += φ2×φ2, and at the same time update sumR0 += φ0×y_current, sumR1 += φ1×y_current, sumR2 += φ2×y_current, where y_current is the current output data.

5. The method for parameter identification of a FOPDT model with variable duration of step response according to claim 4, characterized in that: The formula for calculating the dynamic regularization coefficient in step S4 is: dynamic_lambda = LAMBDA × exp(-0.001×count), where dynamic_lambda is the dynamic regularization coefficient, LAMBDA is the preset initial regularization value, which takes the value 1000.0; count is the data counting variable in the data counting unit, and the dynamic regularization coefficient is only superimposed on the diagonal elements sum00, sum11, and sum22 of the 3×3 matrix.

6. The method for parameter identification of a FOPDT model with variable duration of step response according to claim 5, characterized in that: The SVD decomposition solution in step S4 includes the following sub-steps: S41: Construct a 3×4 augmented matrix based on the regularization matrix. The first 3 columns of the 3×4 augmented matrix are the 3×3 matrix elements of the regularization matrix, and the 4th column consists of the response data association and storage variables sumR0, sumR1, and sumR2. S42: Perform column pivoting on the 3×4 augmented matrix in step S41, locate the row containing the element with the largest absolute value in each column and swap them to the main diagonal position; S43: Based on step S42, the 3×4 augmented matrix is ​​transformed into an upper triangular matrix by Gaussian elimination, and then the intermediate values ​​of the three model parameters θ0, θ1, and θ2 are obtained by back substitution along the main diagonal.

7. The method for parameter identification of a FOPDT model with variable duration of step response according to claim 6, characterized in that: The model parameter conversion formula mentioned in step S5 is: T = 1.0 / θ0, K = θ1 / θ0, τ = (y0 - θ2) / (θ1×u_step), where y0 is the initial output baseline value of the FOPDT model, and θ0, θ1, and θ2 are the intermediate values ​​obtained in step S4.

8. The method for parameter identification of a FOPDT model with variable duration of step response according to claim 7, characterized in that: The parameter changes mentioned in step S5 satisfy the stability condition as follows: within three consecutive temperature control cycles, the absolute value of the change in gain K of the FOPDT model is ≤5%, the absolute value of the change in time constant T is ≤5%, and the absolute value of the change in pure time delay τ is ≤5%.

9. A parameter identification system for a FOPDT model with variable step response duration, characterized in that: It includes an initialization module, a data acquisition module, a matrix update module, a parameter solving module, and a control and scheduling module. Initialization module: Used to trigger the Matrix_Init() function. After receiving the initial output baseline value of the FOPDT model, it resets the 3×3 matrix element storage unit, response integral value storage unit, and data counting unit of the custom matrix accumulation structure to the initial state. Data acquisition module: Acquires real-time output data Get_RealTemp(), step input signal Output, and sampling time count mTs of the FOPDT model according to the set sampling period DT, and outputs them to the matrix update module; Matrix update module: It has a built-in custom matrix accumulation structure, executes the Matrix_Update() function to complete the real-time calculation of the integral increment of the output data, the incremental update of the 3×3 matrix elements, and the accumulation of the data counting unit; The parameter solving module calls the Solve_Matrix() function to calculate the dynamic regularization coefficient Lambda, and uses the Solve_SVD_3x3 function to perform column pivot SVD decomposition to obtain the FOPDT model parameters K, T, and τ. Control and scheduling module: The SecondMul_Caculation() function is used to implement the periodic scheduling of initialization triggering, sampling counting, matrix updating and parameter solving, and outputs the final stable parameters K, T and τ of the FOPDT model.

10. The FOPDT model parameter identification system with variable duration of step response according to claim 9, characterized in that: The execution frequency of the matrix update module and the parameter solving module is consistent with the fuzzy PID control frequency of the temperature controller, and the parameter update cycle is synchronized with the temperature control cycle of the temperature controller. The logic for determining the FOPDT model parameters K, T, and τ obtained by the parameter solving module as stable parameters is as follows: the absolute value of the change in K, T, and τ within three consecutive cycles is ≤5%. When the stability condition is not met, the FOPDT model parameters K, T, and τ are dynamically updated with the cycle. After the condition is met, a stability signal is triggered, the control scheduling module stops the duration extension, and the final stable parameters of the FOPDT model are output.