An observer-based adaptive neural network continuous reactor control method

Abstract

This invention discloses an observer-based adaptive neural network continuous reactor control method, comprising the following steps: constructing a dynamic model for estimating the conversion rate of reactant components and the rate of change of reaction temperature inside the continuous reactor. Since the conversion rate of reactant components and the rate of change of reaction temperature are unmeasurable system states, a state observer is needed to estimate them; introducing a nonlinear mapping method to ensure that all states satisfy the designed time-varying constraints; approximating the unknown nonlinear dynamic function in the continuous reactor using a neural network, and designing an adaptive controller based on Lyapunov stability theory to cope with actuator and sensor failures. This invention enables the estimation of internal states, such as the conversion rate of reactant components, in a continuous reactor system when the system state is unknown, reducing the cost of the control system and improving efficiency.

Description

Technical Field

[0001] This invention relates to the field of chemical process control, and more specifically, to an adaptive neural network-based continuous reactor control method based on an observer. Background Technology

[0002] With the continuous development of the chemical industry, the continuous stirred tank reactor (CSTR), as a key piece of equipment in chemical processing, directly affects product quality, production efficiency, and operational safety. In actual operation, CSTR systems exhibit strong nonlinearity, parameter uncertainty, and susceptibility to external disturbances, posing significant challenges to control system design. Traditional control strategies typically rely on precise mathematical models and extensive sensor data to maintain system stability; however, these methods often fail to guarantee good dynamic response and control accuracy when faced with modeling errors, unknown disturbances, or sudden changes in operating conditions.

[0003] Neural networks possess powerful function approximation capabilities and self-learning characteristics, enabling them to effectively approximate complex nonlinear dynamic relationships and providing new ideas for the modeling and control of CSTR systems.

[0004] Introducing an observer-based adaptive neural network control method has become an important direction for improving the control performance of CSTR systems. This method achieves accurate estimation of the system's internal state by designing a high-performance state observer. Simultaneously, combined with an adaptive neural network structure, the controller can adjust network parameters online during operation, compensating for the effects of system dynamic changes and external disturbances in real time, significantly improving the system's robustness and adaptability. Summary of the Invention

[0005] The purpose of this invention is to provide an observer-based adaptive neural network continuous reactor control method to solve the problems of complex information processing and sensitivity to unknown disturbances in existing continuous stirred tank reactor (CSTR) systems.

[0006] To achieve the above objectives, the present invention adopts the following technical solution:

[0007] An observer-based adaptive neural network continuous reactor control method includes the following steps:

[0008] Step 1: Construct a kinetic model to estimate the conversion rate of the reaction components and the rate of change of the reaction temperature inside the continuous reactor, and use a state observer to estimate the unmeasurable state in the continuous reactor;

[0009] Step 2: Introduce a nonlinear mapping method to ensure that all states satisfy the time-varying constraints of the design;

[0010] Step 3: Use a neural network to approximate the unknown nonlinear dynamic function in the continuous reactor, and design an adaptive controller based on Lyapunov stability theory to estimate the conversion rate of unmeasurable reaction components and to deal with actuator and sensor failures.

[0011] Furthermore, in step 1, the dynamic model is as follows:

[0012]

[0013] Where x1 is the conversion rate of the reactants, x2 is the rate of change of the reaction temperature, u is the temperature of the unreacted coolant, and D... a It is the Damokhler number, Φ is the activation energy, and B is the activation energy. h β is the heat of reaction, β is the heat transfer coefficient, and y represents the output of the continuous reactor system.

[0014] Furthermore, in step 1, the state observer is configured as follows:

[0015]

[0016] in, denoted by , where b represents the estimated conversion rate of the system reaction components, and b represents the coefficients of the Hurwitz polynomial. This is an estimated value for the fault compensation coefficient. This is the actual measurement output after a sensor malfunction occurs, and u is the control input of the continuous reactor system.

[0017] Furthermore, in step 2, a nonlinear mapping method is introduced to perform coordinate transformation on the state of the continuous reactor, as follows:

[0018]

[0019] Where e1 is the tracking error, y d For the system's desired output trajectory, The error between the fault compensation coefficient and the estimated fault compensation coefficient is represented by l, where l is the fault compensation coefficient. z represents the error between the measured value after sensor fault compensation and the desired trajectory. i ζ represents the error between the nonlinear mapping function and the first-order filter. i (t) is a nonlinear mapping function. For a first-order filter, ε i1 (t), ε i2 (t) are all time-varying state constraint functions.

[0020] Furthermore, step 3 includes the following sub-steps:

[0021] Step 3.1, define the time-varying barrier Lyapunov function:

[0022]

[0023] in, θ i For the optimal parameter vector, For θ i The estimated value, Υ r is the lower bound of the effectiveness function Υ(t) of the actuator. i Design parameters; i = 2;

[0024] Step 3.2, differentiating equation (5) yields:

[0025]

[0026] in, Let P be the observation error, and λ be a positive matrix. max This represents the largest eigenvalue of matrix P. α1 is a virtual controller.

[0027] H,a * Let λ and k be positive constants, Ξ and η be the design gain parameters, and u be a positive design parameter. d For the controller when the actuator does not fail, τ(t) is the uncertain partitioned control function that is completely out of control. This is the time derivative of the first-order filter;

[0028] Step 3.3: Use a neural network to approximate the nonlinear function:

[0029]

[0030] in, Let S(χ) be the optimal weight vector, S(χ) be the Gaussian function vector, and θ(χ) be the approximation error.

[0031] for The upper bound;

[0032] Step 3.4, the adaptive controller for the continuous reactor is designed as follows:

[0033]

[0034] Where λ is a positive constant;

[0035] Adaptive law and The design is as follows:

[0036]

[0037] Where r1, k1, r2, and k2 are set positive constants.

[0038] Beneficial effects: By introducing a state observer, this invention enables accurate estimation of the internal states of a continuous stirred tank reactor (CSTR) system, such as the conversion rate of reaction components and the rate of change of reaction temperature, when the system state is unknown. This reduces the cost of the control system and improves efficiency.

[0039] This method is specifically applied to the control process of the CSTR system. By using a state observer to estimate unknown states in real time, the reactor can maintain good dynamic performance and stable operation even under the presence of modeling uncertainties and external disturbances, which significantly enhances the system's adaptability and robustness to complex operating conditions. Attached Figure Description

[0040] Figure 1 This is a flowchart of the control method of the present invention;

[0041] Figure 2 This is a state tracking diagram of a continuous stirred tank reactor (CSTR) system;

[0042] Figure 3 This is an observation error diagram of the CSTR (Continuous Stirred Tank Reactor) system;

[0043] Figure 4 This is a fault compensation coefficient trajectory diagram when a fault occurs in a continuous stirred tank reactor (CSTR) system.

[0044] Figure 5 It is a trajectory diagram of the adaptive rate of the CSTR (Continuous Stirred Tank Reactor) system;

[0045] Figure 6 This is a trajectory diagram of the controller of a continuous stirred tank reactor (CSTR) system. Detailed Implementation

[0046] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0047] Traditional CSTR (Continuous Stirred Tank Reactor) control systems struggle to handle unknown disturbances or nonlinear changes in real time. For example, fluctuations in feed flow rate can lead to unstable reactant concentrations, and changes in ambient temperature can disrupt the reactor's thermal equilibrium. These external uncertainties significantly affect system stability. Nonlinear changes in reaction rate with temperature can complicate the system's dynamic characteristics, and dynamic fluctuations in the heat transfer coefficient can make temperature control unstable. These internal uncertainties further increase the design difficulty of the control system.

[0048] like Figure 1 As shown, the present invention provides an observer-based adaptive neural network continuous reactor control method, comprising the following steps:

[0049] Step 1: Construct a kinetic model to estimate the conversion rate of the reaction components and the rate of change of the reaction temperature inside the continuous reactor, and use a state observer to estimate the unmeasurable state in the continuous reactor;

[0050] The kinetic model is fundamental to describing the internal reaction process of the CSTR, but its nonlinearity and uncertainty limit the performance of traditional control methods. The kinetic model is as follows:

[0051]

[0052] Where x1 is the conversion rate of the reactants, x2 is the rate of change of the reaction temperature, u is the temperature of the unreacted coolant, and D... a It is the Damokhler number, Φ is the activation energy, and B is the activation energy. h β is the heat of reaction, β is the heat transfer coefficient, and y represents the output of the continuous reactor system.

[0053] The state observer is set as follows:

[0054]

[0055] in, denoted by , where b represents the estimated conversion rate of the system reaction components, and b represents the coefficients of the Hurwitz polynomial. This is an estimated value for the fault compensation coefficient. This is the actual measurement output after a sensor malfunction occurs, and u is the control input of the continuous reactor system.

[0056] Step 2: Introduce a nonlinear mapping method to ensure that all states satisfy the time-varying constraints of the design;

[0057] A nonlinear mapping method is introduced to perform coordinate transformation on the state of the continuous reactor, as follows:

[0058]

[0059] Where e1 is the tracking error, y d For the system's desired output trajectory, The error between the fault compensation coefficient and the estimated fault compensation coefficient is represented by l, where l is the fault compensation coefficient. z represents the error between the measured value after sensor fault compensation and the desired trajectory. i ζ represents the error between the nonlinear mapping function and the first-order filter. i (t) is a nonlinear mapping function. For a first-order filter, ε i1 (t), ε i2 (t) are all time-varying state constraint functions.

[0060] Step 3 involves using a neural network to approximate the unknown nonlinear dynamic function in the continuous reactor and designing an adaptive controller based on Lyapunov stability theory to estimate the conversion rate of unmeasurable reaction components and address actuator and sensor failures. This includes the following sub-steps:

[0061] Step 3.1, define the time-varying barrier Lyapunov function:

[0062]

[0063] in, and θ i For the optimal parameter vector, For θ i The estimated value, Υ r is the lower bound of the effectiveness function Υ(t) of the actuator. i Design parameters; i = 2;

[0064] Step 3.2, differentiating equation (5) yields:

[0065]

[0066] in, Let P be the observation error, and λ be a positive matrix. max This represents the largest eigenvalue of matrix P. α1 is a virtual controller.

[0067]

[0068] H,a * Let λ and k be positive constants, Ξ and η be the design gain parameters, and u be a positive design parameter. d For the controller when the actuator does not fail, τ(t) is the uncertain partitioned control function that is completely out of control. This is the time derivative of the first-order filter;

[0069] Step 3.3: Use a neural network to approximate the nonlinear function:

[0070]

[0071] in, Let S(χ) be the optimal weight vector, S(χ) be the Gaussian function vector, and θ(χ) be the approximation error.

[0072] for The upper bound;

[0073] Step 3.4, the adaptive controller for the continuous reactor is designed as follows:

[0074]

[0075] Where λ is a positive constant;

[0076] Adaptive law and The design is as follows:

[0077]

[0078] Where r1, k1, r2, and k2 are set positive constants.

[0079] like Figure 2 The figure shows the state tracking diagram of the continuous stirred tank reactor (CSTR) system; it can be seen from the figure that the observed system state... It achieved good tracking results for the actual system state x1. For example... Figure 3 The figure shows the observation error diagram of the CSTR (Continuous Stirred Tank Reactor) system. The diagram illustrates the observed system state. Compared to the actual system state x1, the error is smaller. For example... Figure 4 The figure shows the trajectory of the fault compensation coefficient when a fault occurs in the CSTR (Continuous Stirred Tank Reactor) system. It can be seen from the figure that the fault compensation coefficient can respond promptly when a sensor fault occurs. Figure 5 The figure shows the trajectory of the adaptive law of the CSTR system. It can be seen from the figure that the adaptive law of the CSTR system tends to stabilize. Figure 6 The figure shows the trajectory of the controller of the CSTR system. As can be seen from the figure, the controller of the CSTR system is progressively stable and the control effect is good.

[0080] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. An observer-based adaptive neural network continuous reactor control method, characterized in that: The method comprises the following steps: Step 1, constructing a kinetic model for estimating the conversion rate of the reaction components and the rate of change of the reaction temperature in the continuous reactor, and using a state observer to estimate the unmeasurable state in the continuous reactor; The kinetic model is: （1） wherein, is the conversion of the reaction components, is the rate of change of the reaction temperature, is the temperature of the unreacted coolant, is the Damokhler number, is the activation energy, is the heat of reaction, is the heat transfer coefficient, denotes the output of the continuous reactor system; The state observer is configured to: （2） wherein, represents an estimate of the conversion of the system reaction components, represents a coefficient of the Hurwitz polynomial, is an estimate of the fault compensation coefficient, is the actual measured output after the occurrence of a sensor fault, is the control input of the continuous stirred tank system; Step 2, introducing a nonlinear mapping method to perform coordinate transformation on the state of the continuous reactor to ensure that all states satisfy the designed time-varying constraints; Step 3, using a neural network to approximate the unknown nonlinear dynamic function in the continuous reactor, and designing an adaptive controller based on Lyapunov stability theory to achieve estimation of the unmeasurable reaction component conversion rate and cope with actuator and sensor failures.

2. The control method according to claim 1, characterized by: In step 2, the nonlinear mapping method is introduced to perform coordinate transformation on the state of the continuous reactor, specifically as follows: （3） （4） wherein is a tracking error, is a system desired output trajectory, , is an error of the fault compensation coefficient and the fault compensation coefficient estimate, is a fault compensation coefficient, , denotes an error between the sensor fault compensated measurement and the desired trajectory, denotes an error of the nonlinear mapping function and the first order filter, is a nonlinear mapping function, is a first order filter, , are both time-varying state constraint functions.

3. The control method according to claim 1, characterized by: Step 3 comprises the following sub-steps: Step 3.1, define a time-varying barrier Lyapunov function: （5） in, and , For the optimal parameter vector, for The estimated value, Validity function for the actuator The lower bound, For design parameters; ; Step 3.2, derive equation (5) to obtain: （6） wherein = is the observation error, is a positive matrix, denotes the largest eigenvalue of the matrix P, , is a virtual controller, , , , , , is a positive constant, , is a designed gain parameter, , is a positive designed parameter, is the controller when no fault occurs in the actuator, is the completely off control zone control function, is the derivative of the first order filter with respect to time; Step 3.3, use a neural network to approximate the nonlinear function: （7） wherein is the optimal weight vector, is the Gaussian function vector, is the approximation error, , , is an upper bound on Step 3.4, the adaptive controller of the continuous reactor is designed as: （8） wherein is a normal number; Adaptive law and The design is as follows: （9） wherein , , and are set normal numbers.

Images