A method and system for controlling an environmental gas analyzer

Abstract

The present application belongs to the field of analyzer control, and particularly relates to an environmental gas analyzer control method and system, comprising the following steps: S1, tightening the nominal state and input constraints of each local linearization state space model by using the minimum robust positive invariance set; S2, estimating the current actual state of the environmental gas analyzer according to the sensor measurement value; generating a nominal control input sequence; S3, calculating an auxiliary control amount through a preset auxiliary control law; S4, summing the first element of the nominal control input sequence and the auxiliary control amount to obtain a control instruction and apply it to the actuator of the environmental gas analyzer. By associating the penalty weight of the control input change in the optimization problem with the current gas concentration measurement value, the control strategy focuses on fast and accurate response at low concentration and focuses on smooth operation at high concentration, thereby improving the overall measurement accuracy and stability of the analyzer.

Description

Technical Field

[0001] This invention belongs to the field of analyzer control, and particularly relates to a control method and system for an environmental gas analyzer. Background Technology

[0002] Environmental gas analyzers, especially high-precision analyzers based on tunable diode laser absorption spectroscopy technology, play an important role in industrial process control, environmental monitoring, and scientific research.

[0003] Ambient gas analyzers infer gas concentration by measuring the absorption of a specific wavelength of laser light through a gas sample. The control objective is to achieve rapid response and high stability while ensuring measurement accuracy. However, the internal optical, electronic, and thermodynamic characteristics of ambient gas analyzers cause them to exhibit varying behavior at different operating points, such as different background gas concentrations and ambient temperatures. A single linear model is insufficient to represent their characteristics across the entire operating range, leading to a decline in control performance. Furthermore, in practical deployments, analyzers are inevitably subject to external environmental disturbances, especially fluctuations in ambient temperature. These fluctuations not only directly affect the performance of core components such as lasers and detectors but also alter the absorption profile of gas molecules, constituting a major source of disturbance to the control system.

[0004] Tube-based model predictive control (Tube-based MPC) is a computationally efficient and widely used robust control strategy. It constrains the actual state trajectory of the system within a tube centered on the nominal state trajectory. The tube's cross-section is defined by offline computation of a robust positive invariant set that accommodates all uncertainties, and an auxiliary controller is designed to ensure the state error remains within this set. However, to guarantee constraint satisfaction under all conditions, the robust positive invariant set is typically designed based on worst-case assumptions about disturbances and uncertainties. This leads to an overly conservative control strategy when actual disturbances are small, sacrificing system response performance. The cost function weights of Tube-based MPC cannot adjust the control objective based on the system's current operating state (e.g., the measured gas concentration). For example, higher control accuracy is desired at low concentrations, while at high concentrations, the focus may be on stable system operation. Fixed control cannot achieve optimal performance under different operating conditions. Therefore, a control method that can adapt to the system's time-varying characteristics and changing operating conditions, and can reduce control conservatism online, is urgently needed. Summary of the Invention

[0005] To address the aforementioned problems, this invention proposes a control method and system for an environmental gas analyzer.

[0006] In a first aspect, the present invention provides a control method for an environmental gas analyzer, comprising the following steps:

[0007] S1. Obtain multiple locally linearized state-space models of the environmental gas analyzer under different gas concentrations and operating temperatures. To address the uncertainties and disturbances in the models, define an asymmetric polyhedral disturbance set parameterized by temperature. Calculate the minimum robust positive invariant set offline based on the asymmetric polyhedral disturbance set. Tighten the nominal state and input constraints of each locally linearized state-space model using the minimum robust positive invariant set.

[0008] S2, at each control moment, the current actual state of the environmental gas analyzer is estimated based on sensor measurements using a state observer; based on the current gas concentration and temperature measurements, the corresponding locally linearized spatial model is selected as the nominal prediction model for the current moment; a finite-time optimization problem is solved to generate a nominal control input sequence. The cost function of the finite-time optimization problem includes a penalty term for the rate of change of the control input, and the weight of the penalty term is a logarithmic function of the current gas concentration measurement.

[0009] S3. Estimate the statistical characteristics of the measurement noise online, adjust the size of the minimum robust positive invariant set according to the statistical characteristics to obtain the time-varying control domain; calculate the error vector between the current actual state and the nominal state, and calculate an auxiliary control quantity according to the position of the error vector in the time-varying control domain through a preset auxiliary control law.

[0010] S4, sum the first element of the nominal control input sequence with the auxiliary control quantity to obtain a control command and apply it to the actuator of the environmental gas analyzer.

[0011] Furthermore, the nominal state and input constraints of each local model are tightened using the minimum robust positive invariant set, including the following steps:

[0012] For the original state constraint set and the original input constraint set The constraint set of the nominal state Z is tightened to The constraint set of the nominal input V is tightened to ,in This is the minimum robust positive invariant set. Let be the feedback gain matrix of the auxiliary control law. This represents the Pontryagin subtraction operation.

[0013] Furthermore, the minimum robust positive invariant set S is calculated based on a combined perturbation set, which is the Minkowski sum of the temperature-parameterized asymmetric polyhedral perturbation set and the normalized measurement noise perturbation set.

[0014] Furthermore, in S2, a Kalman filter is used as the state observer. In each control cycle, a prediction step and an update step are performed to obtain the posterior state estimate at the current time.

[0015] Furthermore, the weight of the penalty term It is a scalar value, which is determined by the formula The calculation yielded, where This represents the measured gas concentration at the current moment. , , These are preset positive integers.

[0016] Furthermore, the temperature value measured by the temperature sensor and the gas concentration value derived from the ambient gas analyzer at the current moment are compared with the operating point corresponding to each local model in the model library. Using the criterion of minimum Euclidean distance, the local linearized state-space model that best matches the current operating condition is retrieved from the model library and selected as the prediction model for model predictive control at that moment.

[0017] Furthermore, in S3, the process of adjusting the size of the minimum robust positive invariant set includes the following steps:

[0018] Within a sliding window of fixed length N, calculate the sample variance of the prediction error output by the state observer;

[0019] A scaling factor proportional to the noise standard deviation is calculated based on the sample variance. ;

[0020] Multiply the minimum robust positive invariant set S by the scaling factor. Thus, the time-varying regulatory domain is obtained. .

[0021] Furthermore, when calculating an auxiliary control quantity using a preset auxiliary control law, the error vector is multiplied by a feedback gain matrix of a linear quadratic regulator obtained through pre-calculated offline calculation. The auxiliary control quantity is obtained.

[0022] Furthermore, in S4, the first control vector in the nominal control input sequence is added to the auxiliary control quantity calculated by the auxiliary control law to synthesize a control command; the control command is converted into an analog voltage or current quantity by a digital-to-analog converter and applied to the current drive module or temperature control module of the laser.

[0023] Secondly, the present invention provides a temperature regulation system for a carbonizer drying equipment, including a memory and a processor. The memory stores computer program instructions, and when the computer program instructions are executed by the processor, the above-mentioned temperature regulation method for the carbonizer drying equipment is implemented.

[0024] The beneficial effects are as follows: By employing multiple locally linearized models corresponding to different operating conditions, nonlinear behavior over a wide temperature and concentration range can be expressed. Designing a robust controller by constructing an asymmetric perturbation set associated with temperature parameters better reflects the actual process compared to conservative designs based on worst-case scenarios. Furthermore, by adjusting the range of the regulating pipe region in real time based on the online estimated measurement noise level, higher control performance can be achieved by breaking free from the constraints of traditional fixed pipe regions when actual perturbations are small. In addition, by associating the penalty weight for changes in control input in the optimization problem with the current gas concentration measurement value, the control strategy emphasizes fast and accurate response at low concentrations and stable operation at high concentrations, achieving good control performance at different operating points and improving the overall measurement accuracy and stability of the analyzer. Attached Figure Description

[0025] Figure 1 This is a schematic diagram of the local model working point network partitioning;

[0026] Figure 2 A schematic diagram of the temperature parameterization set;

[0027] Figure 3 This is a schematic diagram of state constraint tightening;

[0028] Figure 4 This is a schematic diagram of Kalman filter state estimation.

[0029] Figure 5 This is a schematic diagram illustrating the relationship between penalty weight and gas concentration.

[0030] Figure 6 This is a schematic diagram of a time-varying control zone;

[0031] Figure 7 This is a schematic diagram for calculating auxiliary control quantities. Detailed Implementation

[0032] The following is a brief explanation of the terminology involved in this invention:

[0033] Locally linearized state-space model: Select a point in the system under a specific operating state, and use a simple linear mathematical model in the vicinity of this point to approximate the dynamic behavior of the system.

[0034] Polyhedral perturbation set: Similar to a polyhedral uncertainty set, a polyhedral perturbation set is a set of perturbations affected by external and / or internal influences. Optionally, in this invention, a polyhedral perturbation set is a collection of multiple perturbations, including internal and external perturbations, aggregated into a polyhedral perturbation set.

[0035] Nominal: In control theory, this specifically refers to data unaffected by any disturbances or uncertainties. The nominal state is the ideal state of the system under conditions free from noise and model errors, while the nominal input is the control command calculated for the ideal system. In practical control, the nominal planned path is typically calculated first, and then an additional controller is designed to handle unavoidable deviations.

[0036] Minimal Robust Positive Invariant Set: A robust positive invariant set describes the set of all possible states of a system under the presence of bounded disturbances. The minimum robust positive invariant set is the smallest set that satisfies the robust positive invariant set. Using the minimum robust positive invariant set to limit the disturbance range can reduce or even avoid the conservatism of the disturbance boundary description.

[0037] Tube: Also known as a pipe or tubular region, it is a concept in Tube-based Model Predictive Control (Tube-based MPC). By considering the uncertainty of the system state and representing it as a tubular region, a controller is designed to ensure that the system state is within the tubular region.

[0038] In the first embodiment, the present invention proposes a control method for an environmental gas analyzer, comprising the following steps:

[0039] S1. Obtain multiple locally linearized state-space models of the environmental gas analyzer at different gas concentrations and operating temperatures. To address the uncertainties and disturbances in the models, define an asymmetric polyhedral disturbance set parameterized by temperature. Calculate the minimum robust positive invariant set offline based on the asymmetric polyhedral disturbance set. Tighten the nominal state and input constraints of each locally linearized state-space model using the minimum robust positive invariant set.

[0040] A grid is created on the concentration-temperature plane, and multiple operating points are selected, for example, points with temperatures of 10°C, 25°C, and 40°C, and concentrations of 10ppm, 100ppm, and 1000ppm. At each operating point, a pseudo-random binary sequence is applied as an excitation signal to the environmental gas analyzer, and the input and output data of the analyzer are collected. The N4SID subspace identification algorithm is used to identify the linearized state-space model corresponding to each operating point, forming a local model library, such as... Figure 1 As shown.

[0041] To analyze the main impacts of temperature fluctuations on the status of an environmental gas analyzer, a polyhedron describing the disturbance boundary is constructed, where the vertex coordinates are functions of temperature, such as... Figure 2 As shown, for example, disturbance satisfy ,in This is a vector that varies with temperature T, thus defining the asymmetric perturbation set. An offline solution to the linear matrix inequality (LMI) is used to calculate the minimum robust positive invariant set corresponding to the asymmetric perturbation set. Using the Pontryagin difference operation, the minimum robust positive invariant set is subtracted from the original state constraint set and input constraint set respectively, yielding the tightened nominal state and input constraints, as shown below. Figure 3 As shown.

[0042] S2, at each control moment, the current actual state of the ambient gas analyzer is estimated based on sensor measurements using a state observer; based on the current gas concentration and temperature measurements, the corresponding locally linearized spatial model is selected as the nominal prediction model for the current moment; a finite-time optimization problem is solved to generate a nominal control input sequence. The cost function of the finite-time optimization problem includes a penalty term for the rate of change of the control input, and the weight of the penalty term is a logarithmic function of the current gas concentration measurement.

[0043] Using a Kalman filter as the state observer, such as Figure 4 As shown, in each control cycle, the measured values ​​of the sensors (photodetector and temperature sensor) are input into the Kalman filter. The Kalman filter uses the state estimate of the previous moment and the current measured value to obtain the optimal estimate of the current internal state of the environmental gas analyzer through two steps: prediction and update.

[0044] The temperature value measured by the temperature sensor and the gas concentration value derived from the ambient gas analyzer at the current moment are compared with the operating point corresponding to each local model in the model library. The local linearized state-space model that best matches the current operating condition is retrieved from the model library and selected as the prediction model for model predictive control at that moment, based on the criterion of minimum Euclidean distance.

[0045] The finite-time optimization problem is constructed as a quadratic programming problem. Its cost function includes a penalty term for the nominal state and nominal input, as well as a term for the change in the control input. The penalty term. The weighting coefficient of the penalty term. The logarithmic function of the current gas concentration measurement C, for example ,in For calibration coefficients, To prevent tiny positive numbers from being zeroed, such as Figure 5 As shown, numerical optimization algorithms such as the interior point method or the effective set method are used to quickly solve this quadratic programming problem.

[0046] S3. Estimate the statistical characteristics of the measurement noise online, adjust the size of the minimum robust positive invariant set according to the statistical characteristics to obtain the time-varying control domain; calculate the error vector between the current actual state and the nominal state, and calculate an auxiliary control quantity according to the position of the error vector in the time-varying control domain through a preset auxiliary control law.

[0047] By calculating the measurement residuals output by the state observer, and then calculating the variance of the measurement residuals within a sliding time window, the intensity of measurement noise is estimated online. The measurement residuals are the difference between the actual and predicted measurements. A scaling factor is then set based on the variance value. This scaling factor approaches 1 as the noise variance increases and decreases as the measurement residual variance decreases. Multiplying the scaling factor by the offline-calculated minimum robust positive invariant set yields a real-time variable control domain, such as... Figure 6 As shown.

[0048] The state error vector is obtained by subtracting the current actual state estimated by the state observer from the nominal state of the nominal prediction model at the current time. Then, the state error vector is substituted into a pre-calculated linear state feedback control law. Among them The auxiliary feedback gain matrix is ​​obtained offline during the calculation of the minimum robust positive invariant set; e represents the state error vector. From this, the auxiliary control quantity used to eliminate the state error is calculated, such as... Figure 7 As shown.

[0049] S4, sum the first element of the nominal control input sequence with the auxiliary control quantity to obtain a control command and apply it to the actuator of the environmental gas analyzer.

[0050] The first control vector in the nominal control input sequence obtained from solving the finite-time optimization problem is vector-added with the auxiliary control quantity calculated by the auxiliary control law to synthesize a control command. This control command is then converted into analog voltage or current by a digital-to-analog converter and applied to the laser's current drive module or temperature control module.

[0051] In an optional embodiment, the nominal state and input constraints of each local model are tightened using the minimum robust positive invariant set, including the following steps:

[0052] For the original state constraint set and the original input constraint set The constraint set of the nominal state Z is tightened to The constraint set of the nominal input V is tightened to ,in This is the minimum robust positive invariant set. Let be the feedback gain matrix of the auxiliary control law. This represents the Pontryagin subtraction operation.

[0053] The control system does not directly plan the actual state trajectory, but instead plans a nominal trajectory, reserving a safety boundary. The size of the boundary is determined by the minimum robust positive invariant set. The decision is made. The Pontryagin subtraction operation is the mathematical method for implementing this reserved boundary. For example, if an original constraint set X is between 8 and 12, and the calculated height perturbation range represented by S is ±0.5, then the tightened nominal height z constraint set... It then becomes 8.5 to 11.5.

[0054] By imposing stricter constraints on the nominal state and nominal input, leeway is provided for potential errors and disturbances. Similarly, for input constraints, assuming the original input voltage U is between 0 and 5V, the maximum possible correction voltage KS generated by multiplying the feedback gain matrix K of the auxiliary control law by the state error is 0.2V. Therefore, the constraint set for the nominal input v... The voltage is then tightened to 0 to 4.8V. In this way, when the model predictive controller calculates the optimal nominal input, the selection range is limited to within 4.8V, ensuring that even with the addition of an auxiliary correction control quantity of up to 0.2V, the total voltage applied to the motor will not exceed the physical limit of 5V, thus guaranteeing the stability and safety of the entire closed-loop system.

[0055] In an optional embodiment, when using a state observer to estimate the current actual state of the system based on sensor measurements, a Kalman filter is used as the state observer. In each control cycle, a prediction step and an update step are performed to obtain the posterior state estimate at the current moment.

[0056] In many real-world systems, not all state variables can be directly and accurately measured, or the sensors themselves may be noisy. The Kalman filter provides an optimal estimation algorithm that fuses system model predictions and noisy sensor measurements. In each control cycle, for example, every 20 ms, the Kalman filter performs a prediction step. It uses the state estimate from the previous time step and the system dynamics model to predict the current state of the system. For example, it predicts the current position based on the previous position and velocity.

[0057] In the update step, the Kalman filter acquires actual measurements from the sensors. These actual measurements typically differ from the predicted values; this difference is called innovation. The Kalman filter selectively trusts the predicted and actual measurements based on their respective degrees of uncertainty (i.e., noise covariance). If the sensor accuracy is high, it will more readily adopt the actual measurements to correct the prediction; otherwise, it will trust the model prediction more. Through this weighted fusion process, it outputs a posterior state estimate that is closer to the true state of the system than either a simple prediction or a simple measurement, providing a reliable basis for subsequent control calculations.

[0058] In an optional embodiment, the weight of the penalty term It is based on the formula The calculated scalar value, where This represents the measured gas concentration at the current moment. , , These are preset positive integers.

[0059] Weight To punish drastic changes in control input, a larger weight results in a smoother, more conservative control behavior; a smaller weight allows for more aggressive control actions. The formula utilizes the logarithmic function property to represent gas concentration... This environmental information is dynamically mapped to weights. Above. For example, when the distance from the leak source is relatively far, the measured gas concentration... Very low, close to 0.

[0060] Assuming preset parameters It is 20. For 1000, It is 5. In the far field, At 0.1 parts per million, at this time Approximately 25.2. The relatively small weighting value encourages large maneuvers for rapid exploration over a wide area. When approaching the leak source, the concentration... When it increases significantly to 10%, This will increase to approximately 190. This much larger weight will suppress aggressive actions by the controller, resulting in smoother and more precise movements, preventing the controller from missing the target due to excessive actions.

[0061] In an optional embodiment, a minimum robust positive invariant set S is computed offline based on a combined perturbation set, which is the Minkowski sum of a temperature-parameterized asymmetric polyhedral perturbation set and a normalized measurement noise perturbation set.

[0062] To ensure reliable system operation in the real world, calculating the safety boundary, i.e., the minimum robust positive invariant set S, requires considering all sources of disturbance that could cause the system to deviate from the ideal model. This embodiment clarifies two key disturbances: modeling uncertainty and measurement noise. Modeling uncertainty stems from the fact that physical parameters change with the environment. This effect can be fitted using experimental data, confining the influence to a temperature-dependent set of disturbances, such as battery voltage or motor efficiency changing with operating temperature.

[0063] Measurement noise refers to the inherent, unavoidable random errors of the sensor itself; for example, gyroscope readings always have slight drift. Drift noise can generally be described as a statistically bounded set. To obtain a global perturbation set that covers all cases, this embodiment employs the Minkowski sum operation. Geometrically, the Minkowski sum operation is equivalent to taking all points of one set as the starting point and translating the entire other set over the swept area. By calculating the Minkowski sum of these two perturbation sets, a larger combined perturbation set is obtained, which contains the worst-case scenario under the combined effects of modeling uncertainty and measurement noise. Only the minimum robust positive invariant set S calculated based on this worst-case combined perturbation set can ensure the robustness of the controller in real-world complex environments.

[0064] In an optional embodiment, the process of estimating the statistical properties of the measurement noise online and adjusting the size of the minimum robust positive invariant set accordingly includes the following steps:

[0065] Within a sliding window of fixed length N, calculate the sample variance of the prediction error output by the state observer;

[0066] A scaling factor proportional to the noise standard deviation is calculated based on the sample variance. ;

[0067] Multiply the minimum robust positive invariant set S by the scaling factor. The time-varying regulatory domain is obtained. .

[0068] The minimum robust positive invariant set S calculated offline is typically based on a fixed worst-case noise assumption, which may be overly conservative most of the time, limiting system performance. This embodiment adjusts the size of the minimum robust positive invariant set S online, allowing the environmental gas analyzer to adapt to the current real noise level. This is achieved by using a sliding window to continuously monitor the state observer prediction error over the most recent N time periods. The prediction error, the difference between the model prediction and the sensor measurement, directly reflects the intensity of disturbances and noise not described by the model. For example, setting the window length N to 100, the sample variance of the prediction error over the most recent 100 control cycles is continuously calculated.

[0069] Low noise results in a low sample variance of the prediction error; for example, the scaling factor calculated based on low variance. It is 0.7. At this time, the time-varying control domain This shrinks to 70% of the original minimal robust positive invariant set S. This means the safety margin reserved by the system for disturbances is smaller, increasing the controller's available operating space and allowing for the planning of better trajectories. Conversely, when the drone flies into areas with tall buildings, GPS signals are interfered with by multipath effects, increasing noise and consequently increasing the variance of the prediction error, thus affecting the calculated scaling factor. It may become 1.5. Time-varying regulation domain. It expands to 1.5 times the original minimal robust positive invariant set S, increasing the safety boundary. Although this sacrifices some performance, it ensures stability in harsh environments.

[0070] In an optional embodiment, when calculating an auxiliary control quantity using a preset auxiliary control law, the error vector is... Multiply by the feedback gain matrix of the linear quadratic regulator (LQR) calculated offline beforehand. The auxiliary control quantity is obtained.

[0071] In the tubular model predictive control framework, the master controller is responsible for calculating the long-term, economically optimal nominal trajectory and nominal control input. The sole objective of the auxiliary control law is to immediately apply a corrective force to pull the system back onto the nominal trajectory should the actual system state deviate from it due to a disturbance. This deviation is the error vector. It represents the difference between the actual state and the nominal state. For example, This could mean a deviation of 0.1 in the x-direction and a deviation of -0.05 in the y-direction.

[0072] To efficiently and stably eliminate this error, this embodiment employs an LQR controller as the auxiliary control law. The LQR can find an optimal feedback gain matrix K, eliminating the state error fastest while consuming minimal control energy. The gain matrix K can be calculated offline based on the system's linearized model and stored, resulting in minimal online computation. At each control moment, only the real-time error vector needs to be processed. By performing a multiplication operation with this fixed matrix K, the required auxiliary control quantity can be obtained. The auxiliary control quantity is added to the nominal control quantity calculated by the main controller to form the total control signal applied to the actuator, ensuring that the system can closely track the nominal trajectory and always remain within the safe control domain.

[0073] An embodiment of the environmental gas analyzer control system provided by the present invention:

[0074] The environmental gas analyzer control system includes a processor and a memory. The memory stores computer program instructions, which are executed by the processor to implement the above-described environmental gas analyzer control method.

[0075] The environmental gas analyzer control system also includes other components well known to those skilled in the art, such as communication interfaces. Their settings and functions are known in the art and will not be described in detail here.

[0076] In addition, in the description of this specification, "multiple" means at least two, such as two, three or more, etc., unless otherwise expressly and specifically defined.

Claims

1. A control method for an environmental gas analyzer, characterized in that, Includes the following steps: S1. Obtain multiple locally linearized state-space models of the environmental gas analyzer under different gas concentrations and operating temperatures. To address the uncertainties and disturbances in the models, define an asymmetric polyhedral disturbance set parameterized by temperature. Calculate the minimum robust positive invariant set offline based on the asymmetric polyhedral disturbance set. Tighten the nominal state and input constraints of each locally linearized state-space model using the minimum robust positive invariant set. S2, at each control moment, the current actual state of the environmental gas analyzer is estimated based on sensor measurements using a state observer; based on the current gas concentration and temperature measurements, the corresponding locally linearized spatial model is selected as the nominal prediction model for the current moment; a finite-time optimization problem is solved to generate a nominal control input sequence. The cost function of the finite-time optimization problem includes a penalty term for the rate of change of the control input, and the weight of the penalty term is a logarithmic function of the current gas concentration measurement. S3, estimate the statistical characteristics of the measurement noise online, and adjust the size of the minimum robust positive invariant set according to the statistical characteristics to obtain the time-varying regulation domain; Calculate the error vector between the current actual state and the nominal state, and calculate an auxiliary control quantity based on the position of the error vector within the time-varying control domain using a preset auxiliary control law. S4, sum the first element of the nominal control input sequence with the auxiliary control quantity to obtain a control command and apply it to the actuator of the environmental gas analyzer.

2. The control method for an environmental gas analyzer according to claim 1, characterized in that, The nominal state and input constraints of each local model are tightened using the minimum robust positive invariant set, including the following steps: For the original state constraint set and the original input constraint set The constraint set of the nominal state Z is tightened to The constraint set of the nominal input V is tightened to ,in This is the minimum robust positive invariant set. Let be the feedback gain matrix of the auxiliary control law. This represents the Pontryagin subtraction operation.

3. The control method for an environmental gas analyzer according to claim 1, characterized in that, The minimum robust positive invariant set S is calculated based on a combined perturbation set, which is the Minkowski sum of the temperature-parameterized asymmetric polyhedral perturbation set and the normalized measurement noise perturbation set.

4. The control method for an environmental gas analyzer according to claim 1, characterized in that, In S2, a Kalman filter is used as the state observer. In each control cycle, a prediction step and an update step are performed to obtain the posterior state estimate at the current time.

5. The control method for an environmental gas analyzer according to claim 4, characterized in that, The weight of the penalty term It is a scalar value, which is determined by the formula The calculation yielded, where This represents the measured gas concentration at the current moment. , , These are preset positive integers.

6. The control method for an environmental gas analyzer according to claim 4, characterized in that, The temperature value measured by the temperature sensor and the gas concentration value derived from the ambient gas analyzer at the current moment are compared with the operating point corresponding to each local model in the model library. The local linearized state-space model that best matches the current operating condition is retrieved from the model library and selected as the prediction model for model predictive control at that moment, based on the criterion of minimum Euclidean distance.

7. The control method for an environmental gas analyzer according to claim 1, characterized in that, In S3, the process of adjusting the size of the minimum robust positive invariant set includes the following steps: Within a sliding window of fixed length N, calculate the sample variance of the prediction error output by the state observer; Calculate a scaling factor proportional to the noise standard deviation based on the sample variance. ; Multiply the minimum robust positive invariant set S by the scaling factor. Thus, the time-varying regulatory domain is obtained. .

8. The control method for an environmental gas analyzer according to claim 1, characterized in that, When calculating an auxiliary control quantity using a preset auxiliary control law, the error vector is multiplied by the feedback gain matrix of a linear quadratic regulator obtained through pre-calculated offline calculation. The auxiliary control quantity is obtained.

9. The control method for an environmental gas analyzer according to any one of claims 1-8, characterized in that, In S4, the first control vector in the nominal control input sequence is added to the auxiliary control quantity calculated by the auxiliary control law to synthesize a control command. The control command is converted into an analog voltage or current quantity by a digital-to-analog converter and applied to the current drive module or temperature control module of the laser.

10. A control system for an environmental gas analyzer, characterized in that, It includes a memory and a processor, wherein the memory stores computer program instructions, and when the computer program instructions are executed by the processor, the environmental gas analyzer control method according to any one of claims 1-9 is implemented.

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