Self-adaptive intelligent sliding mode control method and system for single-chamber microbial fuel cell

Abstract

The invention provides a self-adaptive intelligent sliding mode control method and system for a single-chamber microbial fuel cell, and belongs to the technical field of fuel cell control. The objective of the invention is to effectively process non-linear uncertainty in a microbial fuel cell through a self-adaptive intelligent algorithm, improve the anti-interference capability of a system to load change, and realize more efficient dynamic response and stable voltage output. The method comprises the following core steps: firstly, constructing a basic kinetic model of the microbial fuel cell; then designing a self-adaptive dynamic sliding mode surface, and approaching an approximation function of the uncertainty through a neural network; and finally, based on the Lyapunov stability theory, designing a control strategy to ensure stable operation of the system. The method combines the neural network and adaptive sliding mode control, significantly enhances the dynamic response and anti-interference performance of the system, optimizes the battery voltage output, and is widely applied to the fields of environmental monitoring, wastewater treatment and the like.

Description

Technical Field

[0001] The present invention belongs to the technical field of energy control. Background Art

[0002] Microbial fuel cells have become important biotechnological tools for clean energy in recent years. However, in practical applications, in systems such as environmental detection, wastewater treatment, and energy harvesting, the start-up time of single-chamber microbial fuel cells is relatively long and is susceptible to the influence of uncertain disturbances, such as changes in factors like temperature, pH, and load. Especially when the external load undergoes a sudden change, it causes instability in the output power and voltage of the system, making it difficult for the system to maintain stable operation and hard to ensure the steady-state application of microbial fuel cells in engineering practice. In addition, due to the time-varying, uncertain, and strongly coupled nature of single-chamber microbial fuel cell systems, there are great challenges in the steady-state voltage output. Although traditional control methods can improve the dynamic response of microbial fuel cells to a certain extent, when the external load suddenly changes in an uncertain environment, traditional controllers are difficult to effectively suppress the influence of load disturbances, resulting in a slow start-up of the output voltage and large fluctuations, seriously affecting the stability and power generation performance of the system. Therefore, a dynamic intelligent regulation control method is needed to enable the power generation process of microbial cells to resist external disturbances and quickly reach the expected steady-state value of the output voltage. Summary of the Invention

[0003] The present invention is an intelligent sliding mode control method and system for a single-chamber microbial fuel cell, aiming to improve the dynamic response of the system using adaptive sliding mode control, dynamically approximate the uncertain terms in the system through a neural network, intelligently adjust the sliding surface to eliminate jitter, effectively reduce the influence of output instability caused by changes in the external load, and improve the robustness of the system.

[0004] The steps of the present invention are as follows: S1. Construct a basic kinetic model of a single-chamber microbial fuel cell; Wherein 、 are state variables in the model, where represents the substrate concentration, represents the microbial concentration, is the basic substrate concentration of the anode, is the dilution rate, is the maximum growth rate of microorganisms, is the maximum substrate utilization rate, and are bounded disturbances with unknown upper bounds, is the decay coefficient, is the half-saturation constant; S2. Design an adaptive dynamic sliding surface using the error quantity to obtain the error derivative; Define the error quantity of the system as follows: where and are respectively and the equilibrium points to be achieved; The sliding surface is designed as: The error derivative is: S3. Use a neural network to dynamically approximate the uncertain terms in the error derivative; Derive the adaptive intelligent sliding mode control law according to the error derivative obtained in step 2 and , and adopt a neural network algorithm to dynamically approximate the uncertain terms. The neural network output is obtained by mapping with a Gaussian function. The adaptive sliding surface jitter is reduced by the saturation function reaching law to improve the dynamic response, and the design of the intelligent sliding mode control law improves the disturbance suppression effect of the system; Define the control quantity as: Set the uncertain function as follows: Substitute equations (1), (2), (9), (10), (11) into equations (7), (8) to obtain the system dynamic error derivative as: To achieve stable control, design the control laws and as respectively: where, and are the adaptive estimators of the disturbance, and are the boundary layer constants; and The approximate functions approximated by the neural network are used to estimate and values. The sliding mode control law reaches the sliding mode surface through the saturation functions and The approximate functions represented by the neural network 、 are respectively: where , are respectively the estimated values of the neural network weights, is the output obtained by mapping through the Gaussian function: In equations (16) and (17), 、 are respectively the approximation errors.. Assume: is bounded, that is, there exists a constant such that ; S4. Based on the Lyapunov stability theory, using the sliding mode surface , the weight estimation error and the disturbance error , construct a Lyapunov function to obtain the constraint conditions and parameters that satisfy stability, and the steady-state output voltage; Construct a Lyapunov function: where: , , , , , are respectively the neural network weight values is the constraint condition to satisfy the system stability Thus, we get: , , , ; where, 、 、 、 are design parameters; Combined with the output voltage equation of the microbial fuel cell as equation (20), the output voltage is: where: is the battery voltage; is the cathode potential, is the cathode voltage loss; is the anode potential, is the anode voltage loss; R is the ideal gas constant; T is the absolute temperature; F is the Faraday constant; and are the fixed parameters 8 and 4 respectively; 、 .

[0005] The beneficial effects of the present invention are as follows: 1. Stable robustness: Considering the sudden change of the external load in the applications such as environmental monitoring and wastewater treatment of the single-chamber microbial fuel cell, the present invention proposes a control method that uses neural network technology to dynamically approximate the uncertain function of the system. When the controller faces the changes in the external environment and load disturbances, it can update the weights of the neural network in real time, ensuring that the control system still maintains strong robustness and stability when the external load changes violently; 2. Improving the system response speed: Aiming at the problem of long dynamic response time in the power generation startup stage of the single-chamber microbial fuel cell, the present invention proposes an intelligent sliding mode control method for the single-chamber microbial fuel cell. This method combines neural network intelligent control and adaptive sliding mode control. The adaptive sliding mode control solves the problem of slow system dynamic response speed caused by environmental changes, ensures that the voltage quickly converges to the steady state value, and maintains the stable operation state of the system. Description of the Drawings

[0006] Figure 1 is the schematic diagram of the framework process of the present invention; Figure 2 is the comparison diagram of the output voltages of the single-chamber microbial fuel cell under the traditional sliding mode control and the adaptive intelligent sliding mode control method of the single-chamber microbial fuel cell in an uncertain environment; Figure 3 is the comparison diagram of the output voltages of the single-chamber microbial fuel cell under the traditional sliding mode control and the adaptive intelligent sliding mode control method of the single-chamber microbial fuel cell under the load mutation interference in an uncertain environment. Detailed Embodiments

[0007] The present invention proposes an adaptive intelligent sliding mode control method for a single-chamber microbial fuel cell. Aiming at the long start-up time and susceptibility to sudden changes in external load during the power generation process of a nonlinear single-chamber microbial system, an intelligent sliding mode control strategy for a single-chamber microbial fuel cell is designed by utilizing the nonlinear approximation ability of a neural network. Through the analysis of the microbial kinetic model, the sliding mode surface of the control system is designed, and a neural network algorithm is introduced to dynamically approximate the uncertain function in the system. Especially in the start-up stage of the microbial fuel cell, the adaptive control significantly improves the start-up response speed by quickly adjusting the system parameters; in the steady-state operation stage, the sliding mode control and the neural network work together to dynamically approximate the uncertain function in real time, effectively weakening the influence of external load disturbances and ensuring the stability of the power generation performance of the system in an environment of uncertain factors and load mutations. This method significantly improves the dynamic response and anti-interference ability of the microbial fuel cell system under load disturbance conditions, while ensuring the stability and robustness of the system output voltage.

[0008] The present invention adopts the following technical solutions. The present invention proposes an adaptive sliding mode control method for a single-chamber microbial fuel cell based on intelligent approximation by a neural network, specifically including the following steps; Step 1: Construct a kinetic model of a single-chamber microbial fuel cell. Taking the dilution rate as the control variable, and the microbial concentration and substrate concentration as state variables, and considering unknown bounded disturbances in the state equation and ; Step 2: Design an adaptive dynamic sliding mode surface using the error quantity to improve the dynamic response speed and optimize the performance of the system; Step 3: To ensure that the system can quickly and stably reach the expected control target under the conditions of the existence of uncertain factors and sudden changes in the external load, the sliding mode surface is adjusted in real time through adaptive control to improve the dynamic response speed, and a neural network is used to dynamically approximate the uncertain terms in the system to eliminate jitter and effectively weaken the influence of sudden changes in the external load on the system; Step 4: Based on the Lyapunov stability theory, using the sliding mode surface , the weight estimation error quantity and the disturbance error quantity , construct a Lyapunov function to obtain the constraint conditions for ensuring the stability of the system: .

[0009] To explain the technical content, structural characteristics, implementation objectives, etc. of the present invention in detail, the present invention will be comprehensively explained below with reference to the accompanying drawings; The present invention relates to an intelligent sliding mode control method for a single-chamber microbial fuel cell, including the following steps; Step 1. Construct a kinetic model of a single-chamber microbial fuel cell; Step 2: Design an adaptive dynamic sliding surface using the error quantity to improve the dynamic response speed and optimize the system performance; Step 3: In traditional sliding mode control, only the sliding surface is designed. To improve the system's ability to resist sudden load changes, the uncertain quantities with nonlinear and strong coupling characteristics in the system are uniformly defined, and the neural network intelligent control technology is used to dynamically approximate the uncertain terms of the adaptive sliding mode control; Step 4: According to the Lyapunov stability law, use the sliding surface , the weight estimation error quantity and the interference error quantity to construct a Lyapunov function, deduce the stable conditions to ensure the system, and solve the constraint parameters of the stable conditions.

[0010] The method is specifically implemented according to the following steps: Step 1: Construct a kinetic model of the microbial fuel cell; Specifically, the microbial fuel cell model is constructed based on the parameters of the microbial fuel cell and the microbial and electrochemical kinetic equations. The mathematical models of the microbial fuel cell are (1) and (2), as follows: where , are the state variables in the model, where represents the substrate concentration, represents the microbial concentration, is the basic substrate concentration of the anode, is the dilution rate, is the maximum growth rate of microorganisms, is the maximum utilization rate of the substrate, and are bounded disturbances with unknown upper bounds, is the decay coefficient, is the half-saturation constant; Step 2: Design an adaptive dynamic sliding surface using the error quantity to obtain the error derivative; Define the error quantity of the system as follows: where , are respectively , the equilibrium points to be achieved; The specific sliding surface design is as follows: Obtain the error derivative: Step 3: Use a neural network to dynamically approximate the uncertainties in the error derivative; Derive the adaptive intelligent sliding mode control law based on the error derivative obtained in Step 2 and , and adopt a neural network algorithm to dynamically approximate the uncertain terms. The neural network output is obtained by mapping with a Gaussian function. The adaptive sliding mode surface jitter is reduced through a saturation function reaching law to improve the dynamic response, and the intelligent sliding mode control law design improves the disturbance suppression effect of the system; Since the system will be affected by non - linear disturbances during elimination, define the control quantity : Set the uncertainty function as follows: Substitute equations (1), (2), (9), (10), (11) into equations (7), (8) to obtain the system dynamic error derivative as: To achieve stable control, design the control laws and respectively as: where and are the adaptively estimated disturbance terms, and are the boundary layer constants; and are the approximate functions approximated by the neural network, used to estimate the values of and . The sliding mode control law reaches the sliding mode surface through the saturation functions and . The approximate functions represented by the neural network , are respectively: where , They are the estimated values of the neural network weights, is the output obtained by mapping through the Gaussian function: In equations (16) and (17), and are the approximation errors respectively. Assume that: is bounded, that is, there exists a constant such that Step 4: Based on the Lyapunov stability theory, using the sliding mode surface , the weight estimation error and the disturbance error , construct a Lyapunov function to obtain the constraint conditions and parameters that satisfy stability, and the steady-state output voltage; Construct the Lyapunov function: where: , , , , , are the neural network weight values respectively is the constraint condition to satisfy the system stability Thus, we get: , , , , where , , , are design parameters; Combined with the output voltage equation of the microbial fuel cell as equation (20), the output voltage is: where: is the battery voltage; is the cathode potential, is the cathode voltage loss; is the anode potential, is the anode voltage loss; R is the ideal gas constant; T is the absolute temperature; F is the Faraday constant; and are the fixed parameters 8 and 4 respectively; , .

[0011] Simulation content and results: To verify the effectiveness of the control method described in the present invention, a constant voltage output experiment of a microbial fuel cell was carried out in the MATLAB simulation environment and compared with the traditional sliding mode.

[0012] From Figure 2 From the output voltage comparison diagram of a single-chamber microbial fuel cell under traditional sliding mode control and intelligent sliding mode control methods in an uncertain environment, it can be seen that the control algorithm proposed in the present invention can improve the response speed of the system faster, enable the voltage to reach the expected value faster, and has a better control effect. Secondly, from Figure 3 It can be seen that in the case of external disturbances in the system, the control algorithm proposed in the present invention can still maintain a fast response and quickly complete convergence. The simulation results show that the adaptive intelligent sliding mode control method proposed in the present invention has significant advantages in the constant voltage output control of a single-chamber microbial fuel cell. Compared with the traditional sliding mode control, it can more effectively suppress the influence of external disturbances, achieve fast tracking of the state and stable output of the voltage, and improve the robustness of the system.

Claims

1. An adaptive intelligent sliding mode control method and system for a single-chamber microbial fuel cell, characterized in that: The steps are as follows: S1: Construct a basic kinetic model of a single-chamber microbial fuel cell; Specifically, the single-chamber microbial fuel cell model is constructed based on the parameters of the microbial fuel cell and the microbial and electrochemical kinetic equations. The mathematical model of the microbial fuel cell is represented by the following equations (1) and (2): Among them , are state variables in the model, where represents the substrate concentration, represents the microorganism concentration, is the basic substrate concentration of the anode, is the dilution rate, is the maximum growth rate of microorganisms, is the maximum utilization rate of the substrate, and are bounded disturbances with unknown upper bounds, is the decay coefficient, is the half-saturation constant; S2: Design an adaptive dynamic sliding surface using the error quantity to obtain the error derivative; Define the error quantity of the system as follows: wherein and are respectively and the balance points to be achieved Design the sliding surface as follows: The error derivative is: S3: Use a neural network to dynamically approximate the uncertainties in the error derivative; Derive the adaptive intelligent sliding mode control law according to the error derivative obtained in Step 2 and , adopt the neural network algorithm to dynamically approximate the uncertain terms, and the output of the neural network is obtained by the Gaussian function mapping. The saturation function reaching law is used to reduce the jitter of the adaptive sliding mode surface and improve the dynamic response, and the design of the intelligent sliding mode control law improves the disturbance rejection effect of the system; Define the control quantity : Set the uncertainty function as follows: Substitute equations (1), (2), (9), (10), (11) into equations (7), (8) to obtain the system dynamic error derivative as: To achieve stable control, a control law is designed and are respectively as follows: Among them, and are adaptive estimators of interference, and are boundary layer constants; and are approximate functions approximated by neural networks respectively, used to estimate and values. The sliding mode control law reaches the sliding mode surface through the saturation functions and The approximate functions represented by neural networks 、 are respectively:​ Among them , are the estimated values of the neural network weights respectively, is the output obtained by mapping through the Gaussian function: In equations (16) and (17), , are the approximation errors respectively. Assume that: is bounded, that is, there exists a constant such that ; S4. Based on the Lyapunov stability theory, using the sliding mode surface , the weight estimation error quantity and the interference error quantity , construct a Lyapunov function to obtain the constraint conditions and parameters for stability and the steady-state output voltage; Construct a Lyapunov function: Where: ， , , , , are neural network weight values respectively To satisfy the constraint conditions for system stability Thus, we obtain: , , , , where , , , are design parameters; Combined with the output voltage equation of the microbial fuel cell as equation (20), the output voltage is: Wherein: is the battery voltage; is the cathode potential, is the cathode voltage loss; is the anode potential, is the anode voltage loss; R is the ideal gas constant; T is the absolute temperature; F is the Faraday constant; and are fixed parameters 8 and 4 respectively; 、 .

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