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CN-121785147-B - State coupling sliding mode control method and system for under-actuated electric heating system

CN121785147BCN 121785147 BCN121785147 BCN 121785147BCN-121785147-B

Abstract

The invention discloses a state coupling sliding mode control method and a state coupling sliding mode control system for an under-actuated electric heating system, which relate to the technical fields of electric heating engineering, thermal system modeling and intelligent control intersection and comprise the steps of constructing an electric heating system dynamic model comprising a quartz lamp temperature state, a test piece temperature state and a quartz lamp control input; the method comprises the steps of constructing a sliding mode function taking a temperature tracking error and a time derivative of a test piece as variables based on a temperature dynamic equation of the test piece and a preset temperature reference track of the test piece, deriving the constructed sliding mode function, combining the temperature dynamic equation of a quartz lamp and the temperature dynamic equation of the test piece, establishing a direct mapping relation between sliding mode dynamics and control input, designing a second-order sliding mode control law, introducing an auxiliary state, constructing a continuous second-order sliding mode arrival law, and obtaining the control input of the quartz lamp according to a linear algebraic relation. The method has clear control structure, definite physical meaning and strong engineering realizability, and is suitable for controlling the temperature of the quartz lamp electric heating system under complex working conditions.

Inventors

  • GAO PENG
  • LV XIAODONG

Assignees

  • 铜陵学院

Dates

Publication Date
20260508
Application Date
20260306

Claims (8)

  1. 1. The state coupling sliding mode control method of the under-actuated electric heating system is characterized by comprising the following steps of: Constructing an electrothermal system dynamic model (100) comprising a quartz lamp temperature state, a test piece temperature state and a quartz lamp control input, wherein a quartz lamp temperature dynamic equation comprises an electric power input item and a heat exchange nonlinear item, and the test piece temperature dynamic equation comprises nonlinear coupling heat transfer of the quartz lamp and the test piece temperature; Constructing a sliding mode function (200) taking a test piece temperature tracking error and a time derivative as variables based on the test piece temperature dynamic equation and a preset test piece temperature reference track (T), and introducing a state dependence coefficient related to the quartz lamp temperature state so as to reflect a nonlinear coupling relation between the test piece temperature dynamic equation and the preset test piece temperature reference track (T); The constructed sliding mode function (200) is derived and combined with a quartz lamp temperature dynamic equation and a test piece temperature dynamic equation to establish a direct mapping relation (300) between the sliding mode dynamic and the control input; On the basis of a sliding mode function (200), a second-order sliding mode control law (400) is designed, an auxiliary state is introduced, a continuous second-order sliding mode arrival law (C) is constructed, so that sliding mode variables and derivatives are converged in a limited time, quartz lamp control input is reversely obtained according to a linear algebraic relation, and a test piece is enabled to track a temperature reference track (T) under disturbance; wherein the constructing a sliding mode function (200) taking the temperature tracking error and time derivative of the test piece as variables comprises, Setting a continuous and at least second-order-derivative temperature reference track (T) for each test piece, defining a temperature tracking error of each test piece according to the actual temperature state of the test piece and the temperature reference track (T), carrying out time derivation on the temperature tracking error according to a test piece temperature dynamic equation to obtain a first derivative of the error, and constructing a corresponding sliding mode function (200) of each test piece on the basis of the first derivative, wherein the sliding mode function is expressed as: , Wherein, the Is the first The sliding mode variable of each test piece, Is the first The first derivative of the temperature tracking error of each test piece, As a sliding mode coefficient function related to the system state, Is the first Temperature tracking errors of the individual test pieces; the establishing a direct mapping relationship (300) between sliding mode dynamics and control inputs includes, Carrying out time derivation on the sliding mode function (200), expressing the second derivative of the temperature of the test piece into a form containing the change rate of the temperature of the quartz lamp by utilizing the partial derivative relation of the temperature dynamic equation of the test piece to the temperature of the quartz lamp, substituting the second derivative into the time derivative of the sliding mode function (200) to obtain a sliding mode dynamic expression containing the change rate of the temperature of the quartz lamp, and converting the sliding mode dynamic expression into a linear algebraic relation related to the control input of the quartz lamp by combining the temperature dynamic equation of the quartz lamp, wherein the linear algebraic relation is expressed as follows: , Wherein, the As the first derivative of the sliding mode variable, To couple gain from the state The coupling matrix is formed by the steps of, For an input vector consisting of the individual quartz lamp control inputs, Is a vector term composed of system state, reference track and disturbance term.
  2. 2. The method for controlling a state-coupled sliding mode of an under-actuated electric heating system as claimed in claim 1, wherein said electric heating system dynamic model (100) comprises, The electric heating system of the under-actuated quartz lamp test piece consists of Cup quartz lamp The temperature of all quartz lamps is formed into a temperature vector, the temperature of all the test lamps is formed into a temperature vector, control input in an electrothermal system is only applied to a quartz lamp channel, and all quartz lamp control input is formed into an input vector; the electrothermal system dynamic model (100) constructs a temperature change mechanism based on the common decision of electrothermal energy conversion and heat transfer, and comprises a plurality of heat exchange mechanisms and corresponding physical coefficients.
  3. 3. The method for controlling a state-coupled sliding mode of an under-actuated electric heating system as claimed in claim 1 or 2, wherein said quartz lamp temperature dynamic equation comprises, , Wherein, the Is the first derivative of the quartz lamp temperature with respect to time, Wen Shengxiang resulting from the electrical power input to the quartz lamp, In order to achieve the electric heating energy conversion efficiency, In order to achieve an equivalent heat capacity, Is the first A control input to the cup of quartz lamp, Is a nonlinear item generated by heat exchange between the quartz lamp and the quartz lamp, between the quartz lamp and the test piece and between the quartz lamp and the environment, Is a quartz lamp temperature state vector, As a temperature state vector of the test piece, Is the first Total disturbance term of the temperature channel of the cup quartz lamp.
  4. 4. The method for controlling a state-coupled sliding mode of an under-actuated electric heating system as claimed in claim 3, wherein said test piece temperature dynamic equation comprises, , Wherein, the For the first derivative of the test piece temperature with respect to time, For the nonlinear coupling heat transfer term determined by the quartz lamp temperature state and the test piece temperature state, Is the first Total disturbance term of each test piece temperature channel.
  5. 5. The method for state-coupled sliding mode control of an under-actuated thermoelectric system as claimed in claim 1, 2 or 4, wherein said second-order sliding mode control law (400) comprises, Introducing auxiliary state variables corresponding to each sliding mode variable, forming auxiliary state vectors, and constructing a continuous second-order sliding mode arrival law (C) for the sliding mode variable corresponding to each test piece; the second order sliding mode arrival law (C) takes a continuous form containing fractional order terms and sets a control gain function that is dependent on the system state.
  6. 6. The method for state-coupled sliding mode control of an under-actuated thermoelectric system as recited in claim 5, wherein said second order sliding mode control law (400) comprises, The second order sliding mode arrival law (C) is expressed as a vector form: , , Wherein, the As the first derivative of the sliding mode variable, For a diagonal matrix of corresponding gains for each test piece, As a vector function consisting of components, As an auxiliary state vector for the device, For the auxiliary state vector time derivative, Is a sliding mode vector consisting of sliding mode variables of each test piece.
  7. 7. The state coupling sliding mode control system of the under-actuated electric heating system adopts the state coupling sliding mode control method of the under-actuated electric heating system as claimed in any one of claims 1 to 6, and is characterized by comprising a dynamic modeling module, a sliding mode function construction module, a mapping relation construction module and a control law design and implementation module; The dynamic modeling module is used for constructing an electric heating system dynamic model (100) comprising a quartz lamp temperature state, a test piece temperature state and a quartz lamp control input, wherein an electric power input item and a nonlinear item generated by heat exchange among the quartz lamp, the test piece and the environment are contained in a quartz lamp temperature dynamic equation, and a nonlinear coupling heat transfer item determined by the quartz lamp temperature and the test piece temperature is contained in the test piece temperature dynamic equation; The sliding mode function construction module is used for constructing a sliding mode function (200) taking a test piece temperature tracking error and a time derivative thereof as variables according to a test piece temperature dynamic equation and a preset test piece temperature reference track (T), and introducing a state dependence coefficient related to a quartz lamp temperature state into the sliding mode function (200) so that the structure of the sliding mode function (200) reflects a nonlinear coupling relation between the quartz lamp temperature and the test piece temperature; The mapping relation construction module is used for conducting time derivation on the sliding mode function (200), obtaining a sliding mode dynamic expression containing the quartz lamp temperature change rate by utilizing the dependence of the test piece temperature dynamic equation on the quartz lamp temperature, and further converting the sliding mode dynamic expression into a linear algebraic relation related to quartz lamp control input by combining the quartz lamp temperature dynamic equation; The control law design and implementation module is used for designing a second-order sliding mode control law (400) on the basis of a sliding mode dynamic equation, leading in an auxiliary state and constructing a continuous second-order sliding mode arrival law (C) to enable sliding mode variables and derivatives to be converged, and meanwhile, reversely solving a quartz lamp control input according to a linear algebraic relation and applying the quartz lamp control input to an electrothermal system.
  8. 8. A computer readable storage medium having stored thereon a computer program, wherein the computer program when executed by a processor implements the steps of the state-coupled sliding mode control method of an under-actuated electrical heating system as claimed in any one of claims 1 to 6.

Description

State coupling sliding mode control method and system for under-actuated electric heating system Technical Field The invention relates to the technical fields of electrothermal engineering, thermal system modeling and intelligent control intersection, in particular to a state coupling sliding mode control method and system of an under-actuated electrothermal system. Background The quartz lamp electric heating system is widely applied to material heat treatment, aerospace component heating, advanced manufacturing test platforms and various thermal experimental devices due to the advantages of high heating speed, high power density, compact structure, easiness in modularized arrangement and the like. In the system, a plurality of quartz lamps are generally adopted as heating execution units, and heat is transferred to a heated test piece in a radiation, convection, heat conduction and other modes, so that the temperature of the test piece is regulated and controlled. Along with the complicating and refined development of engineering application scenes, the practical quartz lamp electric heating system often has the characteristics of multiple inputs, multiple outputs, strong nonlinearity and strong coupling. On one hand, the heat transfer process between the quartz lamps and the test pieces is influenced by the common effects of a plurality of physical mechanisms such as temperature square term, convection heat transfer, contact heat conduction and the like in radiation heat transfer, so that the system dynamics shows remarkable nonlinear characteristics, and on the other hand, complex space coupling relations are formed between a plurality of quartz lamps and a plurality of test pieces through heat radiation and heat conduction, so that all channels are mutually influenced, and simple decoupling control is difficult to realize. Furthermore, in practical systems, quartz lamps are usually used as the only actuator unit to which a control input can be directly applied, whereas the test piece itself is not provided with a separate heating actuator, the temperature variation of which is entirely dependent on the quartz lamp temperature and its heat exchange process with the surrounding environment. This structural characteristic results in a quartz lamp electrothermal system that is essentially an under-actuated system, i.e., the control input dimension of the system is smaller than the controlled state dimension, making conventional control methods based on the full drive assumption difficult to apply directly. In the prior control method for quartz lamps or similar electrothermal systems, proportional-integral-derivative control, feedforward-feedback composite control or a control strategy based on a linearization model is mostly adopted. Such methods typically rely on a simplified linear model or linear approximation around a specific operating point, and it is difficult to adequately characterize the strong nonlinear coupling relationship between the quartz lamp and the test piece caused by radiative heat transfer. When the working condition of the system changes, the uncertainty exists in the parameters or the disturbance of the external environment is strong, the control performance is often obviously reduced, and even the problems of temperature overshoot, oscillation or steady-state error increase and the like can be caused. On the other hand, some researches have been attempted to introduce nonlinear control methods such as sliding mode control, robust control and the like into the field of thermal system control, but most existing schemes still tend to treat nonlinear terms in the system as uncertain disturbances uniformly or indirectly achieve control targets by introducing virtual control amounts and multilayer back-off designs. Although the method has certain robustness in theory, in an under-actuated quartz lamp electric heating system, the problems of complex control structure, difficult parameter design, unclear physical meaning and large actual implementation difficulty often exist, and particularly, the method is difficult to directly construct an efficient control law by utilizing the known physical coupling relation between the temperature of the quartz lamp and the temperature of a test piece. In addition, in practical engineering application, the quartz lamp electric heating system is inevitably influenced by factors such as parameter uncertainty, heat radiation coefficient change, convection heat exchange condition fluctuation, ambient temperature disturbance and the like, and higher requirements are put on the stability and the robustness of the control system. In the prior art, a control method which can construct a control law directly based on a system physical model and by utilizing a nonlinear coupling relation between a quartz lamp and a test piece and realize accurate temperature tracking of the test piece under the condition of ensuring physical constraint of the system is not yet