A method and system for non-matching disturbance rejection control of an underactuated electrothermal system based on a second-order hyperlocal model

Abstract

The application discloses a kind of second-order superlocal model's underactuated electrothermal system non-matching disturbance suppression control method and system, it is related to electrothermal engineering, thermal system modeling and intelligent control cross technical field, including based on the energy transmission relationship between quartz lamp and test piece, carry out high-order time derivation to test piece output variable, introduce the control input item of quartz lamp, establish target dynamic relationship;According to target dynamic relationship, the total disturbance item is structured and decomposed into structured disturbance component and unstructured remaining disturbance component, and the total disturbance compensation is obtained using measurable state information;Based on the expected output variable tracking error dynamics, combined with the total disturbance compensation, construct the nominal control equation, convert it into the constrained optimization allocation of quartz lamp, and solve to obtain each quartz lamp control input result.The method disclosed in the application breaks through the underactuated control bottleneck, realizes the accurate compensation and decoupling of disturbance, and significantly improves the steady-state accuracy and dynamic performance.

Description

Technical Field

[0001] This invention relates to the interdisciplinary fields of electrothermal engineering, thermal system modeling and intelligent control, specifically to a method and system for suppressing unmatched disturbances in an underdriven electrothermal system based on a second-order hyperlocal model. Background Technology

[0002] With the development of aerospace materials, high-end equipment manufacturing, and new functional materials, quartz lamp electrothermal systems are widely used in materials heat treatment, heat loading tests, and environmental simulation tests due to their advantages such as rapid heating, high heating power density, and compact structure. In typical applications, multiple quartz lamps act as heating sources to simultaneously heat multiple test pieces through radiation, convection, and conduction, thereby achieving precise temperature control of the test pieces.

[0003] However, in practical engineering systems, quartz lamp electrothermal systems typically exhibit significant underactuated characteristics: the number of adjustable control inputs in the system is inconsistent with the number of output variables requiring precise control. The quartz lamp, as the controlled object, has its input power directly adjustable, while the test specimen, as the heated object, has its temperature changes dependent on the quartz lamp's temperature state and various complex heat transfer processes; the dynamic equation for the test specimen's temperature does not directly include control inputs. This structural characteristic naturally introduces mismatched disturbances in the system's output path, significantly increasing the difficulty of controlling system design.

[0004] Furthermore, the quartz lamp electrothermal system exhibits significant multi-field coupling and strong nonlinear characteristics. Radiation, convection, and conduction heat transfer processes occur simultaneously within the system. The radiation heat transfer term is typically related to the fourth power of temperature, while the convection and conduction heat transfer terms are influenced by environmental conditions and structural parameters. Simultaneously, complex thermal coupling relationships exist between quartz lamps, between test specimens, and between quartz lamps and test specimens. Based on this, the material's thermal properties change with temperature, environmental fluctuations, and external disturbances, further leading to uncertainties in the system model parameters and time-varying dynamic characteristics.

[0005] To address the aforementioned control problems in electrothermal systems, existing technologies often employ proportional-integral-derivative (PID) control, model predictive control, or disturbance suppression control methods based on extended state observers. However, most existing methods assume a matching relationship between the control input and the controlled output, or only perform disturbance compensation design within a first-order dynamic model framework, making it difficult to effectively handle the mismatched disturbance problem prevalent in underdriven electrothermal systems. When the system output is not directly affected by the control input, traditional control methods often can only improve control performance through indirect adjustment, making it difficult to theoretically guarantee disturbance suppression effects and multi-objective coordinated control performance.

[0006] Therefore, there is an urgent need for a new control method that can transform the mismatched disturbances in the underdriven electrothermal system into a form that is in the same channel as the control input through system structure reconstruction without increasing the number of system actuators. Based on this, it can achieve coordinated control and disturbance suppression of the temperature of multiple test pieces to meet the requirements of control accuracy and robustness for complex engineering applications. Summary of the Invention

[0007] In view of the above-mentioned problems, the present invention is proposed.

[0008] Therefore, the technical problem solved by the present invention is that existing quartz lamp electrothermal systems have problems such as low temperature tracking accuracy in complex thermal coupling environments, difficulty in overcoming model uncertainty, strong nonlinear interference, and how to achieve multi-objective cooperative control under underactuated constraints where the number of actuators and controlled targets is inconsistent.

[0009] To address the aforementioned technical problems, this invention provides the following technical solution: a method for suppressing unmatched disturbances in an underdriven electrothermal system based on a second-order hyperlocal model, comprising: performing high-order time derivatives on the output variables of the test specimen based on the energy transfer relationship between the quartz lamp and the test specimen; introducing control input terms of the quartz lamp to establish a target dynamic relationship; decomposing the total disturbance term into structured disturbance components and unstructured residual disturbance components according to the target dynamic relationship; obtaining the total disturbance compensation amount using measurable state information; constructing a nominal control equation based on the expected output variable tracking error dynamics and the total disturbance compensation amount, transforming it into a constraint optimization allocation of the quartz lamp, and solving it to obtain the control input results of each quartz lamp.

[0010] As a preferred embodiment of the underactuated electrothermal system non-matching disturbance suppression control method of the second-order hyperlocal model described in this invention, the establishment of the target dynamic relationship includes: establishing a temperature dynamic equation containing radiative heat transfer, convective heat transfer and conductive heat transfer terms based on the principle of energy conservation, so that the temperature dynamic equation of the quartz lamp contains a control input term, and the temperature dynamic equation of the test piece is coupled to the quartz lamp through the heat transfer term and does not directly contain a control input term, so that the underactuated electrothermal system has non-matching disturbances caused by the uncontrolled channel.

[0011] As a preferred embodiment of the underactuated electrothermal system non-matching disturbance suppression control method based on the second-order hyperlocal model described in this invention, the establishment of the target dynamic relationship further includes: using the output variable of the test specimen as the system output, obtaining the second derivative by performing a second-order time derivative on the output variable, expanding it using the chain rule, and substituting it into the quartz lamp temperature dynamic equation to output the second derivative expression, specifically expressed as: , , in, It is the second derivative. Let be the partial derivative matrix of the heat transfer function of the test specimen with respect to the temperature of the quartz lamp. For the temperature of the quartz lamp, For the temperature of the test piece, For time variables, To control the conversion factor from input to electrical power, The equivalent heat capacity of a quartz lamp. For input controlled by each quartz lamp The control input vector is composed of The total disturbance term is composed of the heat transfer nonlinearity of the test specimen, the heat transfer nonlinearity of the quartz lamp, the parameter uncertainty term, the external disturbance term, and its time derivative term. The input gain matrix is ​​a computable matrix determined by the system's physical parameters and the temperature state of the quartz lamp.

[0012] As a preferred embodiment of the underactuated electrothermal system non-matching disturbance suppression control method of the second-order hyperlocal model described in this invention, after the second time derivative is obtained, the control input appears explicitly in the second-order derivative of the output and is in the same channel as the total disturbance term, thereby uniformly mapping the non-matching disturbance that originally existed in the underactuated electrothermal system to the same channel as the control input through the second-order extension method.

[0013] As a preferred embodiment of the underactuated electrothermal system non-matching disturbance suppression control method based on the second-order hyperlocal model described in this invention, the output state relationship after second-order expansion reconstructs the system into a second-order hyperlocal model form, specifically expressed as follows: , in, for The control input vector is composed of the control inputs of each quartz lamp.

[0014] As a preferred embodiment of the underactuated electrothermal system non-matching disturbance suppression control method based on the second-order hyperlocal model described in this invention, the following steps are taken: the total disturbance term is further structured and decomposed into structured disturbance components and unstructured residual disturbance components constructed based on the system's physical characteristics; the structured disturbance components are parameter identified, and the parameter vector to be evaluated is estimated using the real-time feedback state of the quartz lamp and the test piece to obtain online estimated values; the unstructured residual disturbance components are dynamically observed, an extended state observer is constructed, the remaining uncertainty after deducting the structured disturbance components from the total disturbance is mapped to the extended state of the system, the extended state is corrected in real time according to the estimation error of the output variable, and the real-time observed values ​​of the unstructured residual disturbance components are obtained.

[0015] As a preferred embodiment of the underactuated electrothermal system non-matching disturbance suppression control method based on the second-order hyperlocal model described in this invention, obtaining online estimates includes estimating the parameters to be evaluated through online parameter estimation, wherein the online parameter estimation includes constructing regression residuals, expressed as: , in, To revert to residuals, The basis function regression matrix, for Online estimates, for The online estimate.

[0016] As a preferred embodiment of the underactuated electrothermal system non-matching disturbance suppression control method based on the second-order hyperlocal model described in this invention, the total disturbance compensation includes: constructing a total disturbance compensation term based on the acquired second-order hyperlocal model and, under ideal disturbance compensation conditions, utilizing the output results of online parameter estimation and the estimation results of the remaining disturbance terms by the extended state observer, and using it to compensate for the disturbance terms in the second-order hyperlocal model; under ideal disturbance compensation conditions, it is expected that the temperature tracking error of the test piece satisfies the second-order stable error dynamics, and constructing a nominal control equation.

[0017] As a preferred embodiment of the underactuated electrothermal system non-matching disturbance suppression control method based on the second-order hyperlocal model described in this invention, the method further includes: constraint optimization allocation, which transforms the nominal control equation into constraint allocation of the quartz lamp control input to address the underactuated characteristics of the underactuated electrothermal system; while satisfying the constraint conditions, the quartz lamp control input is coordinated and allocated, a weighted minimum norm optimization index function is introduced, and the constraint optimization is solved using the Lagrange multiplier method to obtain the analytical allocation result of the quartz lamp control input.

[0018] Another objective of this invention is to provide a second-order hyperlocal model-based unmatched disturbance suppression control system for underdriven electrothermal systems. This system can decompose the total disturbance term into structured disturbance components and unstructured residual disturbance components according to the target dynamic relationship, and obtain the total disturbance compensation amount using measurable state information. This solves the problem that current quartz lamp electrothermal systems have strong nonlinear interference that is difficult to accurately cancel.

[0019] As a preferred embodiment of the mismatched disturbance suppression control system for an underdriven electrothermal system based on a second-order hyperlocal model as described in this invention, the system includes: a physical characteristic modeling and expansion module, a hyperlocal model reconstruction module, a structured disturbance estimation module, and a coordinated control and compensation execution module. The physical characteristic modeling and expansion module is used to construct a dynamic model of the underdriven electrothermal system, perform second-order time derivative calculation on the temperature output of the test specimen, substitute the dynamic equations of the lamp layer using the chain rule, and explicitly introduce the control input into the second-order derivative of the output, performing second-order expansion mapping. The hyperlocal model reconstruction module is used to reconstruct the system into a second-order hyperlocal model form based on the expanded output dynamic relationship, and through the temperature of the test specimen... The partial derivative relationship between the degree of heat and the quartz lamp temperature is used to calculate the input gain term and define the total disturbance term to uniformly characterize the uncertainties inside and outside the system. The structured disturbance estimation module is used to decompose the total disturbance term into structured disturbance components and unstructured residual disturbance components, and calculates them using online parameter estimation methods. At the same time, an extended state observer is constructed to observe the unstructured residual disturbance components. The coordinated control and compensation execution module is used to construct a fixed gain proportional differential control law based on a second-order hyperlocal model and perform joint compensation. For underactuated characteristics, the nominal control equation is transformed into constraint allocation through weighted minimum norm optimization, and the quartz lamp control input allocation result that satisfies the constraints is calculated and applied.

[0020] The beneficial effects of this invention are:

[0021] The non-matching disturbance suppression control method for underdriven electrothermal systems using a second-order hyperlocal model provided by this invention addresses the common underdriven characteristics and non-matching disturbance problems in multi-quartz lamp, multi-test-piece electrothermal systems. By performing a second-order extension of the dynamic relationship of the test piece temperature output, the original test piece temperature output, which was not directly affected by the control input, is transformed into a second-order hyperlocal model form explicitly related to the quartz lamp control input, structurally eliminating the constraints of non-matching disturbances on control design. Furthermore, the method structurally decomposes the disturbance terms with clear physical characteristics caused by radiative heat transfer, convective heat transfer, ambient heat transfer, and the extended-order product relationship in the system, and compensates for these disturbances through basis function regression and online parameter estimation. Simultaneously, the unstructured residual disturbance component is used as an extension... The state is estimated in real time by introducing an extended state observer, which effectively reduces the observer's estimation burden on system structure terms and improves disturbance estimation accuracy and response speed. Furthermore, based on the reconstructed second-order hyperlocal model, a fixed-gain proportional-differential control law combined with a weighted minimum norm control input allocation method is adopted to achieve coordinated control of multiple test specimen temperature targets under finite quartz lamp control channels. This not only avoids the strong dependence of traditional control methods on accurate system models, but also ensures good dynamic performance and steady-state accuracy under complex conditions such as uncertain system parameters, external disturbances, and multiple objective requirements. This invention achieves better results in terms of temperature tracking accuracy, system response stability, and multi-objective coordinated control flexibility. Attached Figure Description

[0022] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the following description of the embodiments will be briefly introduced. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0023] Figure 1 The above is an overall flowchart of a method for suppressing unmatched disturbances in an underdriven electrothermal system based on a second-order hyperlocal model, as provided in Embodiment 1 of the present invention.

[0024] Figure 2 The temperature tracking simulation result of the test piece 1 is shown in Embodiment 2 of the present invention, which is a second-order hyperlocal model for suppressing unmatched disturbances in an underdriven electrothermal system.

[0025] Figure 3 The temperature tracking simulation results of the test piece 2 are provided in Embodiment 2 of the present invention for a second-order hyperlocal model of an underdriven electrothermal system with unmatched disturbance suppression control method.

[0026] Figure 4The temperature tracking simulation results of test piece 1 are shown in Embodiment 2 of the present invention, which is a comparative method for suppressing unmatched disturbances in an underdriven electrothermal system using a second-order hyperlocal model.

[0027] Figure 5 The temperature tracking simulation results of test piece 2 are shown in Embodiment 2 of the present invention, which is a comparative method for suppressing unmatched disturbances in an underdriven electrothermal system using a second-order hyperlocal model. Detailed Implementation

[0028] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. 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 protection scope of the present invention.

[0029] Example 1, referring to Figure 1 As an embodiment of the present invention, a method for suppressing and controlling mismatched disturbances in an underdriven electrothermal system based on a second-order hyperlocal model is provided, comprising: Specifically, a dynamic model of an underactuated electrothermal system is established. The underactuated electrothermal system includes multiple quartz lamps 100 and multiple test pieces 200, where the quartz lamps 100 are the controlled objects and the test pieces 200 are the objects being heated. Based on the principle of energy conservation, a dynamic equation for the lamp layer temperature is established for each quartz lamp 100, including an electrical power input term and terms related to radiative heat transfer, convective heat transfer, and conductive heat transfer between quartz lamps 100 and test pieces 200, between quartz lamps 100, and between quartz lamps 100 and the environment. Simultaneously, a dynamic equation for the temperature of each test piece 200 is established, including terms related to radiative heat transfer, convective heat transfer, and conductive heat transfer between test pieces 200 and quartz lamps 100, between test pieces 200, and between test pieces 200 and the environment. The dynamic equation for the lamp layer temperature includes a control input, while the dynamic equation for the temperature of the test pieces 200 does not directly include a control input, thus causing a mismatch disturbance in the underactuated electrothermal system. Using the temperature of each test piece 200 as the system output, and based on the temperature dynamic equation of the test piece 200, the temperature output of the test piece 200 is differentiated once in time to obtain the first derivative expression of the output without control input. On this basis, the first derivative of the output is further differentiated twice in time, and the temperature dynamic equation of the quartz lamp 100 is substituted into it through the chain rule, thereby explicitly introducing the control input term into the second derivative expression of the output. Thus, the non-matching disturbance that originally existed in the system is uniformly mapped to the same channel as the control input through the second-order extension method.

[0030] Furthermore, based on the output dynamic relationship after the second-order expansion, the system is reconstructed into a second-order hyperlocal model. The output second derivative consists of a computable input gain term related to the control input and a total disturbance term 300 related to the internal nonlinearity, parameter uncertainty, and external disturbance of the system. The computable input gain term is calculated from the partial derivative of the temperature of the test piece 200 with respect to the temperature of the quartz lamp 100 and the mapping relationship between the temperature of the quartz lamp 100 and the control input, and depends only on the measurable temperature state of the quartz lamp 100. The total disturbance term 300 is used to uniformly characterize all unmodeled nonlinear terms, parameter perturbation terms, and higher-order uncertainties introduced during the expansion process in the system. The total disturbance term 300 is structured and decomposed into a basis function regression term constructed based on the system's physical characteristics and an unstructured residual disturbance component 302. The basis function regression term consists of temperature polynomials and their product terms reflecting radiative heat transfer, convective heat transfer, environmental heat transfer, and extended-order product relationships, and is estimated using an online parameter estimation method. The unstructured residual disturbance component 302, as an extended state, is introduced into an extended state observer for real-time estimation, thereby reducing the observer's estimation burden on the system structure terms. Based on a second-order hyperlocal model, a fixed-gain proportional-differential control law is constructed, ensuring that the temperature tracking error of the test piece 200 satisfies the desired second-order stable error dynamics under ideal disturbance compensation conditions. For underactuated characteristics, the control law is transformed into a constraint allocation problem regarding the control input of the quartz lamp 100, and the control input allocation result satisfying the constraints is calculated using a weighted minimum norm optimization method, thereby achieving coordinated control of multiple test pieces 200 temperature targets under finite control channels. By applying control input to the underdriven electrothermal system, and through the combined compensation of basis function regression estimation and extended state observer, the system's mismatch disturbances are effectively suppressed, enabling each test piece to stably track the corresponding target temperature trajectory even under parameter uncertainties and external disturbances.

[0031] Furthermore, based on the principle of energy conservation, a target dynamic relationship R is constructed. Temperature dynamic equations, including terms for radiative heat transfer, convective heat transfer, and conductive heat transfer, are established for each quartz lamp 100 and each test piece 200, ensuring that for any time, for any numbered quartz lamp 100... With any test piece numbered 200 The following dynamic equations for lamp layer temperature and temperature 200 of the test specimen are satisfied:

[0032] The dynamic equation for lamp layer temperature is: , The dynamic equation for temperature of test specimen 200 is: , in, The number of quartz lamps. Number the quartz lamps. For the number of test pieces, For the test piece number, For time variables, To distinguish it from the label The test piece number, , The equivalent heat capacity of a quartz lamp. For the first Temperature of a quartz lamp The first time derivative, For the first The temperature state of a quartz lamp, To control the conversion factor from input to electrical power, For the first The control input for a quartz lamp, The surface emissivity of the quartz lamp. The Stefan Boltzmann constant is given. The effective heat exchange area of ​​the quartz lamp. The apparent radiation factor from the quartz lamp to the test specimen. For the first Temperature status of each test piece The convective heat transfer coefficient between the quartz lamp and the test specimen is given. The equivalent thermal resistance between the quartz lamp and the test piece. The apparent radiation factor between quartz lamps. The convective heat transfer coefficient between quartz lamps is given. The equivalent thermal resistance between quartz lamps. The apparent radiation factor of a quartz lamp to the environment. For ambient temperature, The convective heat transfer coefficient between the quartz lamp and the environment. Temperature of the quartz lamp base The equivalent thermal resistance between the quartz lamp and the base. The equivalent heat capacity of the test specimen, For the first Temperature of each test piece The first time derivative, The surface emissivity of the test specimen, The effective heat transfer area of ​​the test specimen. The apparent radiation factor between test specimens. The convective heat transfer coefficient between the test specimens is denoted as . The equivalent thermal resistance between the test specimens. The apparent radiation factor of the test specimen to the environment. The convective heat transfer coefficient between the test specimen and the environment. The temperature of the test specimen base. The equivalent thermal resistance between the test piece and the base is given, and the dynamic equation for the lamp layer temperature explicitly includes control input. The dynamic equation for the temperature of the test specimen does not directly include control input. This results in mismatched disturbances in the underdriven heating system caused by uncontrolled channels.

[0033] Taking the test specimen temperature of 200°C as the system output, the system output vector is defined as: , in, For the system output vector, For the first Temperature status of each test piece.

[0034] Based on the dynamic equation of temperature 200 for the test piece, the first time derivative of the system output is obtained by taking the first derivative of the output as follows: , in, The first derivative, The vector of nonlinear heat transfer terms is determined by the temperature of the quartz lamp and the temperature of the test specimen. The equivalent disturbance term is caused by parameter uncertainty, external disturbances, and unmodeled factors; the first derivative expression of the output does not directly contain the control input.

[0035] Based on the first derivative, performing a second time derivative yields the output second derivative, expressed as: , in, It is the second derivative. This is the first-order time derivative of the disturbance term.

[0036] Using the chain rule Expanding, we get: , in, Let be the partial derivative matrix of the heat transfer function of the test specimen with respect to the temperature of the quartz lamp. Let be the partial derivative matrix of the heat transfer function of the test specimen with respect to the temperature of the test specimen.

[0037] Substituting the temperature dynamic equation of the quartz lamp 100 into the second derivative of the output, we get: , , in, It is the second derivative. Let be the partial derivative matrix of the heat transfer function of the test specimen with respect to the temperature of the quartz lamp. For the temperature of the quartz lamp, For the temperature of the test piece, For time variables, To control the conversion factor from input to electrical power, The equivalent heat capacity of a quartz lamp. For input controlled by each quartz lamp The control input vector is composed of The total disturbance term is composed of the heat transfer nonlinearity of the test specimen, the heat transfer nonlinearity of the quartz lamp, the parameter uncertainty term, the external disturbance term, and its time derivative term. The input gain matrix is ​​a computable matrix determined by the system's physical parameters and the temperature state of the quartz lamp.

[0038] It should be noted that, based on the output dynamic relationship after the second-order extension, the system is reconstructed into a second-order hyperlocal model, expressed as: , in, for The control input vector is composed of the control inputs of each quartz lamp. This is the system output vector composed of the temperatures of each test piece.

[0039] The output second derivative is derived from the computable input gain term related to the control input. The total disturbance term 300 is composed of factors related to internal nonlinearity, parameter uncertainty, and external disturbances of the system.

[0040] The input gain matrix can be calculated. The partial derivative of the temperature of the test specimen 200 with respect to the temperature of the quartz lamp 100, and the mapping relationship between the temperature of the quartz lamp 100 and the control input, are calculated and defined as follows: , in, , For the first The algebraic sum of the heat transfer terms on the right-hand side of the energy conservation equation for each test specimen.

[0041] The first input gain matrix Line 1 Column elements Calculate using the following formula: , in, For the first The temperature of the quartz lamp is such that the input gain matrix depends only on the measurable temperature state of the quartz lamp. The known physical parameters of the system are input gain terms that can be calculated online.

[0042] The total perturbation term 300 is used to uniformly characterize all unmodeled nonlinear terms, parameter perturbation terms, and higher-order uncertainties introduced during the second-order extension process in the system, and is expressed as: , in, This is the equivalent perturbation vector for the quartz lamp temperature channel. This is the equivalent perturbation vector of the temperature channel of the test specimen. It is the first-order time derivative of the equivalent disturbance vector of the temperature channel of the test piece.

[0043] The dynamic equation for lamp layer temperature is written as: , in, This is the equivalent perturbation vector for the quartz lamp temperature channel.

[0044] Further explanation: , in, For the first The right-hand side of the energy conservation equation for a quartz lamp, excluding the input term The algebraic sum of all other heat exchange terms.

[0045] Through the above reconstruction method, the original underactuated electrothermal system is equivalently represented as a second-order hyperlocal model composed of a computable input gain term and a total disturbance term 300 after second-order expansion, thus providing a unified model basis for the subsequent controller design based on total disturbance observation and compensation.

[0046] It should also be noted that the total disturbance term 300 is structured and split into a structured disturbance component 301 and an unstructured residual disturbance component 302. The structured disturbance component 301 is a basis function regression term constructed based on the physical characteristics of the system, specifically expressed as follows: , in, The basis function regression term is constructed based on the physical characteristics of the system. This represents the unstructured residual perturbation component.

[0047] The basis function regression term consists of a temperature polynomial and its product terms reflecting the radiative heat transfer, convective heat transfer, ambient heat transfer, and the second-order extended product relationship, expressed as: , in, The basis function regression matrix, This is the vector of unknown parameters to be estimated.

[0048] The first basis function regression matrix The row basis function vector consists of temperature polynomials and their product terms, and includes at least the following basis functions characterizing radiative heat transfer terms, convective heat transfer terms, ambient heat transfer terms, and extended-order product terms: , in, For the first Row basis function vector.

[0049] And the corresponding 200 of each test piece By stacking, we get: , The basis function regression term is estimated using an online parameter estimation method, which includes constructing the regression residuals: , in, To revert to residuals, The basis function regression matrix, for Online estimates, for The online estimate.

[0050] And the following parameter update law is used to obtain : , in, It is a symmetric positive definite parameter adaptive gain matrix. A positive leakage coefficient. These are the prior values ​​of the parameters.

[0051] The unstructured residual perturbation component 302 is introduced as an extended state into the extended state observer for real-time estimation. To reduce the estimation burden of the extended state observer on the system structure terms, the extended state observer only observes the unstructured residual perturbation component 302. The extended state observer is constructed as follows: , , , in, For output The first derivative of the observed values, For output The observed values, To output the first derivative The first derivative of the observed values, To output the first derivative The observed values, The first derivative of the observed values ​​of the unstructured residual perturbation component is given by . These are the observations of the unstructured residual perturbation components. , , The observer gain matrix is ​​selected as follows: , , , For observer bandwidth parameters, It is an identity matrix.

[0052] Through the above-mentioned structured decomposition, the structural terms constructed based on the physical characteristics of the system are obtained by online parameter estimation. The extended state observer only estimates the unstructured residual disturbance component 302 in real time, thereby reducing the estimation burden of the extended state observer on the system structural terms.

[0053] It should also be noted that, based on the obtained second-order hyperlocal model and under ideal perturbation compensation conditions, the total perturbation compensation term is constructed using the online parameter estimation results and the estimation results of the remaining perturbation term by the extended state observer. To obtain the total perturbation compensation amount D, which is then used to compensate for the perturbation terms in the second-order hyperlocal model.

[0054] Define the temperature reference trajectory of test specimen 200 as follows: , in, This serves as a reference trajectory for the temperature of the inspection piece.

[0055] Define the temperature tracking error of test piece 200 as: , , in, To account for the temperature tracking error of the test piece, This is the first derivative of the temperature tracking error of the test specimen. It is the first derivative of the temperature reference trajectory of the test piece.

[0056] Under ideal perturbation compensation conditions, the temperature tracking error of the test piece at 200°C is expected to satisfy the following second-order stable error dynamics: , in, This is the second derivative of the temperature tracking error of the test specimen. For a pre-defined proportional gain matrix, The pre-defined differential gain matrix, All are diagonal positive definite matrices, used to adjust the convergence speed and damping characteristics of the temperature error of each test piece respectively.

[0057] To achieve the desired error dynamics described above, the nominal control equation is constructed as follows: , in, The second derivative of the temperature reference trajectory of the inspection piece. The term represents the total disturbance compensation term, while the right-hand side term is the control quantity composed of the reference trajectory, the disturbance compensation term, and the fixed gain proportional-derivative feedback term.

[0058] Considering the underactuated characteristics of the underactuated electrothermal system, the above control equation is transformed into a constraint assignment problem with respect to a 100 control input, specifically expressed as: under the constraints Next, solve the controller. , To achieve coordinated allocation of the control input of the quartz lamp 100 while satisfying the aforementioned constraints, a weighted minimum norm optimization index function is introduced. ,in It is a symmetric positive definite weight matrix used to describe the energy consumption weights or usage priorities of different quartz lamp 100 control inputs.

[0059] Solving the constrained optimization problem using the Lagrange multiplier method yields the analytical allocation result of the control input of the quartz lamp 100: , The stability of the control input is demonstrated as follows: Assumption: Full order, making reversible; Bounded, satisfying: ; Bounded, satisfying: ;refer to It is twice differentiable and bounded. , , Bounded.

[0060] Get the Lyapunov function: , in, .

[0061] Further differentiation: , Substitute into the error equation: , and definition ,have to: , Substituting the regression residuals and parameter update law, we get: , For any , , Then it exists: , , , , Further calculations: , in, , , It achieves uniformly bounded convergence.

[0062] Example 2, refer to Figures 2-5 As an embodiment of the present invention, a method for suppressing unmatched disturbances in an underdriven electrothermal system based on a second-order hyperlocal model is provided. To verify the beneficial effects of the present invention, scientific demonstration is carried out through economic benefit calculations and simulation experiments.

[0063] First, three quartz lamps 100 and two test pieces 200 were selected to form an underactuated structure, where the three quartz lamps 100 were the controlled objects and the two test pieces 200 were the objects to be heated. The temperatures of the two test pieces 200 were used as the system output variables, and the target temperatures of the two test pieces 200 were set to be the same, both at 500K, to verify the control performance of the method under multi-output consistent tracking conditions. The total simulation time was set to 500s. Specific parameter settings are as follows: , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , The comparison method uses the same parameter settings for PD control.

[0064] Reference Figure 2 Under the method of this invention, the temperature of test piece 1 monotonically increases from an initial temperature of approximately 300K to a target temperature of 500K. The curve exhibits typical exponential convergence characteristics with no significant overshoot. Based on the scale in the figure, it takes approximately 60 seconds to rise to 450K and approximately 150 seconds to reach 495K, entering the steady-state range (within ±1K) in approximately 200 seconds. The steady-state temperature essentially coincides with the reference value, with a steady-state error of less than 1K and a relative error of less than 0.2%. This demonstrates that the method of this invention can achieve smooth, oscillation-free, and high-precision tracking while ensuring system stability.

[0065] Reference Figure 3 Under the method of this invention, the dynamic response of test specimen 2 is basically consistent with that of test specimen 1. There is no significant overshoot or oscillation during the rise from approximately 300K to 500K, and the settling time is also approximately 150~200s. The steady-state error is close to 0K. Both test specimens 200 achieve synchronous convergence under the same target value, and their response curves almost overlap. This indicates that the proposed underactuated coordinated allocation strategy can achieve consistent control of multiple test specimens 200 under limited control input conditions, and the system coupling effect is effectively suppressed.

[0066] Reference Figure 4 Under the comparative method, the temperature of test piece 1 failed to rise effectively to the target value of 500K. The curve only slowly rose from 300K to about 305K before stabilizing. The steady-state error was about 195K, with an error ratio as high as about 39%. There was almost no obvious heating effect during the entire adjustment process, indicating that under the current parameter settings, the traditional PD control cannot overcome the thermal coupling and nonlinear disturbance of the system, and the control input failed to be effectively transmitted to the temperature channel of test piece 200.

[0067] Reference Figure 5 Under the comparative method, the response of test piece 2 was similar to that of test piece 1. The temperature also only rose to about 305K, failing to approach the target temperature of 500K. The steady-state error was more than 195K. The system showed obvious insufficient control capability, indicating that under underactuated structure and complex thermal coupling conditions, it is difficult to achieve effective temperature regulation by using fixed gain PD control alone.

[0068] In summary, the method of this invention is significantly superior to the traditional PD comparison method in terms of dynamic response speed, steady-state accuracy, and coordinated control capability of multiple test pieces. The method of this invention can achieve fast, smooth, and overshoot-free tracking from 300 to 500 K with a steady-state error close to zero. In contrast, the comparison method cannot achieve effective temperature control under the same system parameters and target conditions, and has significant steady-state errors. The above results fully verify the effectiveness and superiority of the control strategy proposed by this invention for mismatched disturbances and coupling effects in underdriven electrothermal systems.

[0069] Example 3, an embodiment of the present invention, provides a second-order hyperlocal model-based unmatched disturbance suppression control system for an underdriven electrothermal system, including a physical characteristic modeling and order extension module, a hyperlocal model reconstruction module, a structured disturbance estimation module, and a coordinated control and compensation execution module.

[0070] The physical property modeling and extension module is used to construct the dynamic model of the underactuated electrothermal system. The second-order time derivative of the temperature output of the test piece 200 is calculated, and the dynamic equation of the lamp layer is substituted into it using the chain rule. The control input is explicitly introduced into the output second derivative and a second-order extension mapping is performed.

[0071] The hyperlocal model reconstruction module is used to reconstruct the system into a second-order hyperlocal model form based on the output dynamic relationship after the order expansion. It calculates the input gain term by using the partial derivative relationship between the temperature of the test piece 200 and the temperature of the quartz lamp 100, and defines the total disturbance term 300 to uniformly characterize the uncertainties inside and outside the system.

[0072] The structured disturbance estimation module is used to decompose the total disturbance term 300 into structured disturbance component 301 and unstructured residual disturbance component 302, calculate them using online parameter estimation methods, and construct an extended state observer to observe the unstructured residual disturbance component 302.

[0073] The coordinated control and compensation execution module is used to construct a fixed gain proportional-differential control law based on a second-order hyperlocal model and perform joint compensation. For underactuated characteristics, the nominal control equation is transformed into constraint allocation through weighted minimum norm optimization, and the control input allocation results of the quartz lamp 100 that satisfy the constraints are calculated and applied.

[0074] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A method for suppressing and controlling unmatched disturbances in an underdriven electrothermal system based on a second-order hyperlocal model, characterized in that, include: Based on the energy transfer relationship between the quartz lamp (100) and the test piece (200), the output variable of the test piece (200) is differentiated in a higher time order, and the control input term of the quartz lamp (100) is introduced to establish the target dynamic relationship (R). The establishment of the target dynamic relationship (R) also includes taking the output variable of the test piece (200) as the system output, obtaining the second derivative by taking the second time derivative of the output variable, expanding it using the chain rule, and substituting it into the temperature dynamic equation of the quartz lamp (100) to output the expression of the second derivative, specifically expressed as: ， ， in, It is the second derivative. Let be the partial derivative matrix of the heat transfer function of the test specimen with respect to the temperature of the quartz lamp. The temperature of the quartz lamp. For the temperature of the test piece, For time variables, To control the conversion coefficient from input to electrical power, This is the equivalent heat capacity of a quartz lamp. For input controlled by each quartz lamp The control input vector is composed of The total disturbance term is composed of the heat transfer nonlinearity of the test specimen, the heat transfer nonlinearity of the quartz lamp, the parameter uncertainty term, the external disturbance term, and its time derivative term. The total disturbance term (300) is decomposed into structured disturbance components (301) and unstructured residual disturbance components (302) according to the target dynamic relationship (R) and the total disturbance compensation amount (D) is obtained using the measurable state information. Based on the expected output variable tracking error dynamics, a nominal control equation is constructed in conjunction with the total disturbance compensation amount (D), which is then transformed into a constraint optimization allocation of the quartz lamps (100), and the control input results of each quartz lamp (100) are obtained by solving the equation.

2. The method for suppressing and controlling mismatched disturbances in an underdriven electrothermal system using a second-order hyperlocal model as described in claim 1, characterized in that: The establishment of the target dynamic relationship (R) includes, Based on the principle of energy conservation, a temperature dynamic equation is established that includes terms of radiative heat transfer, convective heat transfer, and conductive heat transfer. The temperature dynamic equation of the quartz lamp (100) includes a control input term. The temperature dynamic equation of the test piece (200) is coupled to the quartz lamp (100) through the heat transfer term and does not directly include a control input term. This causes the underdriven electrothermal system to have a mismatch disturbance caused by the uncontrolled channel.

3. The method for suppressing and controlling mismatched disturbances in an underdriven electrothermal system using a second-order hyperlocal model as described in claim 2, characterized in that: After the second time derivative is obtained, the control input appears explicitly in the second derivative of the output and is in the same channel as the total disturbance term (300). This allows the mismatch disturbance that originally existed in the underdriven electric heating system to be uniformly mapped to the same channel as the control input through the second-order extension.

4. The method for suppressing and controlling mismatched disturbances in an underdriven electrothermal system using a second-order hyperlocal model as described in claim 3, characterized in that: The second-order extended output state relationship reconstructs the system into a second-order hyperlocal model, specifically expressed as follows: ， in, for The control input vector is composed of the control inputs of each quartz lamp.

5. The method for suppressing and controlling the mismatched disturbance of an underdriven electrothermal system using a second-order hyperlocal model as described in any one of claims 1, 2, 3, and 4, characterized in that: The total disturbance term (300) is further structured and split into a structured disturbance component (301) and an unstructured residual disturbance component (302) constructed based on the physical characteristics of the system. The structured disturbance component (301) is parameter identified, and the parameter vector to be evaluated is estimated by using the real-time feedback status of the quartz lamp (100) and the test piece (200) to obtain the online estimated value; The unstructured residual disturbance component (302) is dynamically observed, and an extended state observer is constructed. The remaining uncertainty after deducting the structured disturbance component (301) from the total disturbance is mapped to the extended state of the system. The extended state is corrected in real time according to the estimation error of the output variable, and the real-time observation value of the unstructured residual disturbance component (302) is obtained.

6. The method for suppressing and controlling mismatched disturbances in an underdriven electrothermal system using a second-order hyperlocal model as described in claim 5, characterized in that: The acquisition of online estimates includes, The parameters to be evaluated are estimated through online parameter estimation, which includes constructing regression residuals, expressed as follows: ， in, To revert to residuals, The basis function regression matrix, for The online estimate, for The online estimate.

7. The method for suppressing and controlling the mismatched disturbance of an underdriven electrothermal system using a second-order hyperlocal model as described in any one of claims 1, 2, 3, 4, and 6, characterized in that: The total disturbance compensation (D) includes, Based on the acquired second-order hyperlocal model and under ideal perturbation compensation conditions, the total perturbation compensation term is constructed using the output results of online parameter estimation and the estimation results of the remaining perturbation term by the extended state observer, and is used to compensate for the perturbation term in the second-order hyperlocal model. Under ideal disturbance compensation conditions, it is expected that the temperature tracking error of the test piece (200) satisfies the second-order stable error dynamics, and the nominal control equation is constructed.

8. The method for suppressing and controlling unmatched disturbances in an underdriven electrothermal system using a second-order hyperlocal model as described in claim 7, characterized in that: It also includes constraint optimization allocation, which transforms the nominal control equation into constraint allocation of the quartz lamp (100) control input for the underactuated characteristics of the underactuated electrothermal system. While satisfying the constraints, the control input of the quartz lamp (100) is coordinated and allocated. The weighted minimum norm optimization index function is introduced, and the constraint optimization is solved by the Lagrange multiplier method to obtain the analytical allocation result of the control input of the quartz lamp (100).

9. A second-order hyperlocal model-based unmatched disturbance suppression control system for an underdriven electrothermal system, employing the second-order hyperlocal model-based unmatched disturbance suppression control method for an underdriven electrothermal system as described in any one of claims 1 to 8, characterized in that: It includes a physical property modeling and order extension module, a hyperlocal model reconstruction module, a structured disturbance estimation module, and a coordinated control and compensation execution module; The physical property modeling and extension module is used to construct the dynamic model of the underdriven electrothermal system, perform second-order time derivative of the temperature output of the test piece (200), use the chain rule to substitute the dynamic equation of the lamp layer, explicitly introduce the control input into the output second derivative, and perform second-order extension mapping. The hyperlocal model reconstruction module is used to reconstruct the system into a second-order hyperlocal model form based on the output dynamic relationship after the expansion order. It calculates the input gain term by using the partial derivative relationship between the temperature of the test piece (200) and the temperature of the quartz lamp (100), and defines the total disturbance term (300) to uniformly characterize the uncertainty inside and outside the system. The structured disturbance estimation module is used to split the total disturbance term (300) into structured disturbance components (301) and unstructured residual disturbance components (302), calculate them using online parameter estimation methods, and construct an extended state observer to observe the unstructured residual disturbance components (302). The coordinated control and compensation execution module is used to construct a fixed gain proportional differential control law based on a second-order hyperlocal model and perform joint compensation. For underactuated characteristics, the nominal control equation is transformed into constraint allocation through weighted minimum norm optimization, and the quartz lamp (100) control input allocation result that satisfies the constraints is calculated and applied.

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