Waste liquid circulation treatment control method and system based on negative pressure adaptive regulation

Abstract

The present application relates to the technical field of pump control, and more particularly, to a waste liquid circulation treatment control method and system based on negative pressure adaptive regulation and control, comprising: acquiring real-time state variables of pressure, flow and material concentration of a waste liquid treatment system, establishing a nonlinear state space model containing actuator delay and parameter uncertainty boundary, and converting the actuator delay into an augmented state variable through Pade approximation. The present application converts the actuator delay into an augmented state through Pade approximation, constructs a global augmented model containing error integral and control change rate, and solves the model mismatch and high-frequency jitter problems of traditional methods. At the same time, the sensitivity and cross correlation degree are used to adaptively configure a weighting matrix, and a disturbance observer is combined to realize feedforward compensation of lumped disturbance. In practical application, the present application effectively suppresses system oscillation and mechanical wear, and significantly improves the disturbance stability and negative pressure cooperative control precision of the waste liquid treatment process.

Description

Technical Field

[0001] This invention belongs to the field of pump control technology, and particularly relates to a waste liquid circulation treatment control method and system based on negative pressure adaptive regulation. Background Technology

[0002] In wastewater treatment processes, systems typically need to operate under a specific negative pressure to promote the removal of volatile harmful substances, prevent the escape of toxic gases, and improve the overall efficiency of physicochemical reactions. Therefore, negative pressure control is directly related to the operational safety and treatment quality of the wastewater recycling system. As wastewater continuously circulates within the system, material concentration, flow rate, and pipeline pressure are coupled and dynamically change, making the system susceptible to external factors such as upstream operating condition fluctuations and sudden changes in pipeline resistance. Simultaneously, large circulating pumps and fluid regulating valves, limited by their mechanical characteristics, often exhibit action delays and parameter uncertainties, easily leading to significant fluctuations in system negative pressure around the set value, reducing the stability and efficiency of wastewater treatment. Frequent and prolonged adjustments may also cause system fluid oscillations, accelerating the wear of critical actuators and increasing operational safety risks.

[0003] By establishing a multivariate mathematical model, constructing a state feedback control law, and conducting online observation and compensation for unknown external disturbances, coordinated regulation of key variables such as system pressure and flow can be achieved. However, when dealing with actuator delays in nonlinear systems, existing methods often employ simplified approximations or treat delays directly as external disturbances, lacking a mechanism to transform delay characteristics into augmented states and integrate them into the global optimization model, which easily leads to linearized model mismatch. Traditional LQR control, when constructing state weighting matrices and control weighting matrices, usually relies on trial and error based on human experience, failing to fully reflect the sensitivity of state variables to system performance indicators and the cross-correlation effects between multiple variables, making it difficult to obtain stable comprehensive control performance under complex operating conditions. Conventional optimal control laws often directly output absolute control quantities, lacking constraints and penalties on the rate of change of control inputs, which easily triggers abrupt large-scale movements of valves or pumps, exacerbating actuator saturation and mechanical fatigue. Existing disturbance observation compensation strategies, when facing lumped uncertainties formed by model mismatch and external disturbances, find it difficult to solve the feedforward compensation quantity by combining it with the algebraic characteristics of the system control input matrix, resulting in limited fusion effects of feedforward and feedback control. Under conditions of internal parameter changes or strong disturbances, the overall control stability and steady-state accuracy still cannot meet the requirements of high-stability waste liquid recycling treatment scenarios. Summary of the Invention

[0004] To address the shortcomings in waste liquid recycling systems, such as actuator delay model mismatch, subjective variable weight configuration, lack of constraints on control action rate, and limited feedforward compensation for lumped disturbances, which make it difficult for the system to achieve stable operation while balancing high-precision coordinated control and long-term equipment protection under complex dynamic conditions, this invention provides a waste liquid recycling control method and system based on negative pressure adaptive regulation.

[0005] According to a first aspect of the present invention, a waste liquid recycling treatment control method based on negative pressure adaptive regulation is provided, comprising: S1: acquiring real-time state variables of pressure, flow rate, and material concentration of the waste liquid treatment system, establishing a nonlinear state-space model including actuator delay and parameter uncertainty boundaries, and converting the actuator delay into augmented state variables through Pad approximation; S2: performing state augmentation on the linearized model input error integral term and the original control input quantity containing the augmented state variables, and defining the difference between the current control input and the control input at the previous moment as the control input change rate, and applying the control input change rate as a new... For the control input, in the linear quadratic regulator cost function constructed for the augmented system, the quadratic penalty term of the rate of change of the control input is used to limit the actuator action amplitude. The feedback gain matrix is ​​obtained by solving the algebraic Riccati equation corresponding to the cost function. S3: Construct a disturbance observer to estimate the lumped uncertainty composed of model mismatch and external disturbances online. Multiply the pseudo-inverse matrix of the global augmented input matrix reconstructed after state augmentation by the lumped uncertainty as a feedforward compensation term. Combine it with the feedback control quantity based on the feedback gain matrix to obtain the control law. Generate instructions based on the control law to adjust the speed of the circulating pump and the valve opening.

[0006] By transforming the actuator delay into an augmented state through the Pad approximation, the shortcomings of model mismatch in traditional methods are overcome, and the modeling accuracy is improved. At the same time, the rate of change of control input is used as a penalty term in the cost function, and feedforward compensation fusion feedback control is generated in combination with a disturbance observer. This effectively limits the mechanical fatigue caused by the step-like large-scale movement of valves or pumps, and significantly improves the system's anti-interference ability and steady-state negative pressure control accuracy when facing uncertain disturbances such as internal model mismatch and external pipeline fluctuations.

[0007] Furthermore, the actuator delay is transformed into an augmented state variable using the Pad approximation, including: constructing a nonlinear equation based on mechanistic modeling methods, with system pressure, flow rate, and waste liquid concentration as state variables and circulating pump speed and pipeline valve opening as control inputs; testing the actuator's step response and identifying the actuator's pure time delay constant as the actuator delay; determining the perturbation upper and lower bounds of each parameter in the nonlinear equation based on the measurement error range of system parameters to generate parameter uncertainty boundaries; and using the first-order Pad approximation to transform the transfer function of the delay element containing the pure time delay constant into a rational fraction form, and then transforming the rational fraction into a differential equation and inputting it into the nonlinear equation as an additional augmented state variable.

[0008] By identifying the pure time delay constant of the actuator and transforming it into an augmented state using the first-order Pad approximation, accurate time-delay dynamic characteristics are introduced into the control system, effectively solving the problem of control lag and fluid oscillation caused by treating the delay as an external disturbance in existing technologies.

[0009] Furthermore, it also includes: the linearized system matrix obtained by Taylor expansion of the nonlinear state-space model at the current operating point while retaining the first-order terms; the state weighting matrix and the control weighting matrix are constructed; the diagonal elements of the two matrices are proportional to the sensitivity of the state variables to the system performance index; and the off-diagonal elements are symmetrically processed according to the cross-correlation terms of the linearized system matrix and satisfy the positive semi-definite condition.

[0010] By utilizing the sensitivity of state variables to system performance indicators, a weighted matrix is ​​configured along the main diagonal, and cross-correlation terms are used to handle the off-diagonal parts. This overcomes the blindness in weight configuration caused by the reliance on trial and error based on human experience in traditional control strategies, and enables the optimization objective to be precisely focused on the key dynamic variables in waste liquid treatment.

[0011] Furthermore, satisfying the positive semi-definite condition includes: extracting the off-diagonal elements between state variables in the augmented linearized system matrix as cross-correlation terms, retaining the positive and negative signs of the cross-correlation terms and performing symmetry processing, and then mapping them proportionally to the corresponding off-diagonal positions of the state weighting matrix; the control weighting matrix is ​​taken as a diagonal matrix by default. If the actuator coupling test confirms that there is input coupling between the circulating pump speed and the valve opening, the off-diagonal terms are determined according to the correlation of the column vectors of the input matrix or the actuator coupling identification results, and the corresponding weighting matrix is ​​ensured to satisfy the positive semi-definite condition, so that strongly correlated variables are subject to collaborative penalty during the optimization process.

[0012] By identifying and processing the input coupling relationship between the circulating pump and the valve opening, the weighting matrix is ​​ensured to meet the positive semidefinite condition, and a collaborative penalty is applied to strongly correlated variables during the optimization process, which effectively suppresses system fluid oscillations caused by strong coupling of multiple actuators under complex waste liquid circulation conditions.

[0013] Furthermore, the diagonal elements of the two matrices are proportional to the sensitivity of the state variables to the system performance index, including: calculating the sensitivity coefficient of each state variable to the system pressure settling time, normalizing the sensitivity coefficient and using it as the diagonal element of the state weighting matrix, and using the reciprocal of the control input energy constraint or the reciprocal of the square of the maximum allowable change of the control input as the diagonal element of the control weighting matrix.

[0014] By establishing a sensitivity mapping between the system pressure stabilization time and state variables, and incorporating the energy and change limits of the control input into the diagonal elements of the matrix, the system can effectively constrain the energy consumption of system regulation and the limits of actuator action while ensuring rapid recovery of negative pressure, thus balancing control accuracy and hardware safety.

[0015] Furthermore, the global augmented input matrix reconstructed after state augmentation includes: calculating the Jacobian matrix of the nonlinear state-space model at the current steady-state operating point relative to the state variables and control input as the augmented linearized system matrix and augmented input matrix; calculating the deviation between the target negative pressure setpoint and the actual pressure measurement value of the waste liquid treatment system; discretizing and accumulating the deviation or integrating it over continuous time to generate an error integral term; using the error integral term and the original control input as new state variables, concatenating and combining them with the state vector of the linearized model containing the augmented state variables to construct a global state vector containing the original state, augmented state variables, original control input, and error integral term; and reconstructing the corresponding global augmented system matrix and global augmented input matrix based on the original augmented linearized system matrix, augmented input matrix, and integral mapping relationship to complete the construction of the augmented system.

[0016] By integrating the deviation between the actual negative pressure measurement and the target value to generate an error integral term, and splicing them together to construct a global augmented model, a zero steady-state error tracking mechanism is established at the bottom layer, fundamentally eliminating the steady-state control error that is easy to accumulate in the long-term continuous operation of the waste liquid circulation system.

[0017] Furthermore, a quadratic penalty term for the rate of change of control input is used to limit the actuator's action amplitude. This includes: constructing a comprehensive cost function that includes a quadratic form of state deviation, a quadratic form of control input, and a quadratic form of the rate of change of control input; calculating the absolute residual between the pressure output predicted by the nonlinear state-space model of the previous control cycle and the actual pressure output measured by the sensor in the current control cycle; and establishing an exponential mapping function between the weighting coefficients and the absolute residuals. When the absolute residuals increase, the weighting coefficients of the quadratic penalty term for the rate of change of control inputs are increased through the exponential mapping function to smooth the actuator's action and reduce energy consumption. When the absolute residuals decrease, the weighting coefficients are decreased to improve the system's response speed to errors.

[0018] An exponential mapping function based on the residuals of prediction and actual output is established to dynamically adjust the weight of the rate of change penalty term, which gives the system adaptive control capability. When the error is large, the system can smoothly execute actions to protect the pipeline network, and when the error is small, it can respond quickly, thus achieving an intelligent balance between system stability and dynamic adjustment rate.

[0019] Furthermore, the control law is obtained by combining the feedback control quantity based on the feedback gain matrix, including: constructing a state observer and calculating the difference between the actual value of the time derivative of the measurable state of the system and the predicted derivative of the linearized model; using a low-pass filter to filter the difference to eliminate high-frequency measurement noise and obtain lumped uncertainty; calculating the pseudo-inverse matrix of the global augmented input matrix and multiplying the pseudo-inverse matrix by the lumped uncertainty to generate a feedforward compensation term acting on the control input; and subtracting the feedforward compensation term from the feedback control quantity generated by the feedback gain matrix to obtain the control law.

[0020] By using a low-pass filter to eliminate high-frequency measurement noise and combining it with a pseudo-inverse matrix to map disturbances into feedforward compensation terms, external lumped uncertainty disturbances such as upstream operating condition fluctuations can be offset more accurately and quickly, significantly shortening the negative pressure recovery time under abnormal operating conditions and enhancing the robustness of the control strategy.

[0021] Furthermore, an exponential mapping function between the weighting coefficients and the absolute residuals is established, including: setting the weighting coefficients, amplification coefficients, and adjustment factors of the basic penalty term; multiplying the absolute residuals by the adjustment factor and using it as the independent variable of the exponential function, calculating its exponential power value and multiplying it by the amplification coefficient, and then adding it to the weighting coefficients of the basic penalty term to obtain the weighting coefficients of the second penalty term of the control input change rate in the current control cycle.

[0022] By setting specific adjustment factors and amplification coefficients to quantify the exponential mapping function, a calibrable engineering implementation means is provided for the adaptive adjustment of the penalty weight, ensuring the operability and control effectiveness of the adaptive control strategy in various on-site wastewater treatment environments.

[0023] According to a second aspect of the present invention, a waste liquid recycling treatment control system based on negative pressure adaptive regulation is also provided, including a processor and a memory, the memory storing a computer program, and the processor executing the computer program to implement the waste liquid recycling treatment control method based on negative pressure adaptive regulation as described in any of the above claims.

[0024] Beneficial Effects: A nonlinear model incorporating actuator delay and parameter uncertainty boundaries is established. The Pad approximation is used to equivalently treat the delay element, and a weighted matrix is ​​constructed by combining variable sensitivity and cross-correlation terms, improving the accuracy of system modeling and the targeted nature of performance optimization. In the control solution stage, an error integral term is introduced to reduce steady-state error, and a penalty term for the rate of change of control input is added to the cost function to limit the actuator's action amplitude and reduce equipment wear. This penalty weight is updated in real time based on the actual output residual of the system, helping to improve the smoothness and accuracy of the adjustment process. By constructing a disturbance observer to estimate model mismatch and external disturbances online, and combining feedforward compensation and feedback gain to generate a control law, stable regulation of the circulating pump speed and valve opening is achieved, thereby enhancing the operational stability and control reliability of the waste liquid treatment negative pressure control system. Attached Figure Description

[0025] Figure 1 A flowchart of a waste liquid recycling treatment control method based on negative pressure adaptive regulation;

[0026] Figure 2 A schematic diagram of decoupling and fitting the step response and time delay characteristics of the actuator; Figure 3 A schematic diagram of comparative tests at the controller level to suppress the effects of high-frequency vibration in the system; Figure 4 This diagram illustrates the comparative experiment of composite ablation and the full analysis, summary, and verification of step recovery efficacy. Detailed Implementation

[0027] like Figure 1 As shown, a waste liquid recycling treatment control method based on negative pressure adaptive regulation is provided, including the following steps: S1. Establish and linearize a model containing delay augmentation and uncertainty, and determine the state weighting matrix and control weighting matrix according to sensitivity and cross-correlation terms.

[0028] Specifically, the real-time state variables of pressure, flow rate, and material concentration of the waste liquid treatment system are obtained, and a nonlinear state-space model including actuator delay and parameter uncertainty boundary is established. The actuator delay is transformed into an augmented state variable through Pad approximation. The nonlinear state-space model is Taylor expanded at the current operating point, retaining the first-order terms to obtain a linearized system matrix. A state weighting matrix and a control weighting matrix are constructed. The diagonal elements of the two matrices are proportional to the sensitivity of the state variables to the system performance index. The off-diagonal elements are symmetric according to the cross-correlation terms of the linearized system matrix and satisfy the positive semidefinite condition.

[0029] Real-time state variables of pressure, flow rate, and material concentration in the waste liquid treatment system are obtained by acquiring analog signals through pressure sensors, electromagnetic flow meters, and online concentration meters installed in the waste liquid circulation pipeline. These analog signals are then converted to digital signals by an analog-to-digital converter. The serial port read function in the programmable logic controller (PLC), such as the FB module in the Siemens S7 series, is called to read the real-time data and store it in a data block as the current state variables. A nonlinear state-space model incorporating actuator delays and parameter uncertainty boundaries is established. This model derives the system equations based on Bernoulli's equation and the law of conservation of mass. The circulating pump speed and valve opening are used as control inputs. A time delay term between the control command and the actual action of the actuators is introduced. Fluctuation ranges are set for fluid density and pipe resistance coefficient as parameter uncertainty boundaries, establishing a continuous-time nonlinear ordinary differential equation system. Transforming actuator delay into augmented state variables using the Pade approximation involves applying a first-order Pade approximation algorithm to the time delay term, calling the Pade function in the control system toolbox to calculate the polynomial coefficients, representing the time delay term as a rational transfer function, and then using a state-space implementation method to transform this rational transfer function into a state-space differential equation. The internal states of the rational transfer function are then set as augmented state variables and added to the original state vector. Here, "actuator" refers to the collective term for the terminal actuators in a waste liquid recycling system that receive control commands and drive the controlled object to perform physical actions. In a specific embodiment of this invention, the actuator includes a circulating pump and an electric regulating valve.

[0030] It should be noted that the diagonal elements of the two matrices are proportional to the sensitivity of the system performance index. This means that the diagonal elements of the state-weighted matrix are directly determined based on the sensitivity of the corresponding state variables to the system performance index, while the diagonal elements of the control-weighted matrix are determined based on the constraint sensitivity of the control input to the system performance index. In specific implementations, the constraint sensitivity of the control input to the system performance index can be equivalently characterized by the reciprocal of the control input energy constraint or the reciprocal of the square of the maximum allowable change in the control input. Therefore, using the reciprocals of the squares of the maximum allowable change in the actuator speed and valve opening as the diagonal elements of the control-weighted matrix does not change the overall principle of determining the weighting matrix based on the sensitivity of the system performance index. For off-diagonal elements, the state-weighted matrix undergoes signed symmetry processing based on the state cross-correlation terms in the augmented linearized system matrix; the control-weighted matrix is ​​taken as a diagonal matrix when there is no input coupling identification result. If the actuator coupling test confirms that there is input coupling between the circulating pump speed and the valve opening, then its off-diagonal terms are determined based on the correlation of the column vectors of the input matrix or the actuator coupling identification result.

[0031] The linearized system matrix is ​​obtained by Taylor expansion of the nonlinear state-space model at the current operating point, retaining the first-order terms. This involves calculating the Jacobian matrix of the nonlinear ordinary differential equations at the current sampling period's state and input operating points, and then using finite difference algorithms from the numerical computation library, such as the central difference method, to obtain the partial derivatives of the nonlinear function with respect to the state vector and input vector, respectively. Higher-order terms of the second order and above are truncated to obtain the discrete-time state transition matrix and control input matrix. Construct state weighting matrices and control weighting matrices. The diagonal elements of the state weighting matrix are proportional to the sensitivity of the corresponding state variables to the system performance index. The diagonal elements of the control weighting matrix are determined based on the control input energy constraints or the maximum allowable change in control input. The off-diagonal elements of the state weighting matrix are treated with signed symmetry based on the state cross-correlation terms in the augmented linearized system matrix and satisfy the positive semi-definite condition. The control weighting matrix is ​​a diagonal matrix when there are no input coupling identification results. The process is as follows: set the system performance index as a weighted sum of state error and control energy consumption, calculate the partial derivative of the set system performance index with respect to each state variable as the state sensitivity, and assign the normalized state sensitivity value to the main diagonal of the state weighting matrix. The main diagonal of the control weighting matrix is ​​determined based on the reciprocal of the square of the energy constraints or the maximum allowable change in each control input. For the off-diagonal elements of the state weighting matrix, extract the cross terms between corresponding states from the augmented linearized system matrix, retain their signs, and sum these elements, divide by two, and assign the sum to the corresponding positions in the state weighting matrix to ensure symmetry. Control the weighting matrix to be a diagonal matrix when there is no input coupling identification result. Call eigenvalue decomposition functions from the linear algebra library, such as the `eig` function, to solve for all eigenvalues ​​of the matrix. If negative eigenvalues ​​exist, add a positive bias constant to the main diagonal until all eigenvalues ​​are non-negative, ensuring that both matrices satisfy the positive semi-definite condition.

[0032] In one possible embodiment, establishing a nonlinear state-space model that includes the boundary conditions of actuator delay and parameter uncertainty, and transforming the actuator delay into an augmented state variable through the Pad approximation, includes: Based on the mechanism modeling method, a nonlinear equation is constructed with system pressure, flow rate, and waste liquid concentration as state variables and circulating pump speed and pipeline valve opening as control inputs. The step response of the actuator is tested, and the pure time delay constant of the actuator is identified as the actuator delay. The first-order Pad approximation is used to convert the transfer function of the delay element containing the pure time delay constant into a rational fraction form, and the rational fraction is transformed into a differential equation and input into the nonlinear equation as an additional augmented state variable. According to the measurement error range of the system parameters, the perturbation upper and lower bounds of each parameter in the nonlinear equation are determined to generate parameter uncertainty boundaries.

[0033] The pressure (e.g., -80 kPa to -10 kPa), flow rate (e.g., 10-50 L / min), and material concentration (e.g., 5%-30%) of the waste liquid treatment system are selected as state variables. The circulation pump speed (e.g., 1000-3000 rpm) and valve opening (e.g., 0-100%) are used as control inputs to construct the system state differential equation. Step signals with an amplitude of 10% are applied to the valve opening channel and the circulation pump speed channel, respectively (e.g., valve opening abruptly changes from 50% to 60%, and circulation pump speed abruptly changes from 2000 rpm to 2200 rpm). The pressure and flow response curves are recorded to identify the pure time lag constants of the valve actuator and the circulation pump actuator; for example, the measured time lag constant for the valve channel is 1.2 s, and the measured time lag constant for the circulation pump channel is 0.8 s. A first-order Pad approximation is applied to both input channels, for example, using... Transform it into a rational fraction (1-0.6s) / (1+0.6s), and then... The equation is transformed into a rational fraction (1-0.4s) / (1+0.4s), which is then mapped to first-order ordinary differential equations and input into the original system. This constructs two-dimensional augmented state variables corresponding one-to-one with the two control inputs, achieving algebraic-loop-free decoupling of the time-delay element. For parameters such as the pipeline fluid resistance coefficient, perturbation upper and lower bounds of ±10% are determined based on the nominal error of the measuring sensor and the viscosity drift of the medium. Boundary parameters are superimposed on the nominal nonlinear equation to generate an uncertainty boundary model suitable for comprehensive evaluation. The decoupling and fitting of the actuator's step response and time-delay characteristics is illustrated below. Figure 2 As shown.

[0034] In one possible embodiment, the step of performing a Taylor expansion of the nonlinear state-space model at the current operating point, retaining first-order terms to obtain a linearized system matrix, constructing a state-weighted matrix and a control-weighted matrix, wherein the diagonal elements of both matrices are proportional to the sensitivity of the state variables to the system performance index, and the off-diagonal elements are symmetricized according to the cross-correlation terms of the linearized system matrix and satisfy the positive semi-definite condition, including: The Jacobian matrix of the nonlinear state-space model at the current steady-state operating point relative to the state variables and control input is calculated as the linearized system matrix and input matrix. The sensitivity coefficients of each state variable to the system pressure settling time are calculated, normalized, and used as the diagonal elements of the state-weighted matrix. The reciprocal of the control input energy constraint or the reciprocal of the square of the maximum allowable change in control input is also used as the diagonal elements of the control-weighted matrix. Off-diagonal elements between state variables in the augmented linearized system matrix are extracted as cross-correlation terms. The positive and negative signs of these cross-correlation terms are retained, and after symmetry processing, they are mapped proportionally to the corresponding off-diagonal positions in the state-weighted matrix. The control-weighted matrix is ​​assumed to be a diagonal matrix. If actuator coupling tests confirm input coupling between the circulating pump speed and valve opening, the off-diagonal terms are determined based on the correlation of the input matrix column vectors or the actuator coupling identification results. The corresponding weighted matrix is ​​ensured to satisfy the positive semi-definite condition, so that strongly correlated variables are subject to collaborative penalties during the optimization process.

[0035] At the current steady-state operating point, the Jacobian partial derivative matrix of the nonlinear system state equation is calculated, retaining the first derivative. This yields a 3×3 linearized state submatrix and a 3×2 input submatrix corresponding to the original physical state. The 2-dimensional augmented state variables are then incorporated into the linearized model, forming at least a 5×5 augmented linearized system matrix and a 5×2 augmented input matrix, ensuring the augmented state variables substantially participate in subsequent weighting and control solutions. A unit disturbance is applied at the current steady-state operating point, and the settling time for the system pressure to recover to within the ±2 kPa stability bandwidth is recorded. The partial derivatives of the settling time with respect to each state variable are calculated as sensitivity coefficients. These sensitivity coefficients are normalized and multiplied by the basic penalty coefficient, then configured as the main diagonal elements of the state weighting matrix. The reciprocals of the squares of the maximum changes in actuator speed and valve opening are used as the diagonal elements of the control weighting matrix. The diagonal rule of this control weighting matrix is ​​used to constrain the intensity of input actions and is no longer expressed as being proportional to the sensitivity of the state variables. Extract the off-diagonal elements representing the degree of influence between state variables from the augmented linearized system matrix as cross-correlation terms. Let the normalized cross-correlation terms in the augmented linearized system matrix be... and Then the off-diagonal elements of the state weighting matrix are arranged according to... The scaling factor ρ is determined, preferably 0.5. The weighting matrix is ​​a diagonal matrix by default; if off-diagonal terms are required, they are determined based on the correlation of the input matrix column vectors or the actuator coupling identification results. Negative eigenvalues ​​are eliminated by adjusting the values ​​of the main diagonal elements or by performing eigenvalue decomposition to ensure that the reconstructed state weighting matrix satisfies the positive semi-definite condition. Cross-penalties are applied to variables that generate strongly correlated oscillations in the solution of the quadratic objective function.

[0036] S2, the model is state augmented, a penalty term for the rate of change of control input adjusted with residuals is added to the cost function, and the feedback gain matrix is ​​obtained by solving the algebraic Riccati equation.

[0037] Specifically, state augmentation is performed on the linearized model input error integral term and the original control input, which include augmented state variables. The rate of change of the control input is used as the new control input. In the linear quadratic regulator cost function constructed for the augmented system, the quadratic penalty term of the rate of change of the control input is used to limit the actuator action amplitude. The weight coefficient of the penalty term is adjusted according to the residual between the model output and the actual output of the previous cycle. The feedback gain matrix is ​​obtained by solving the algebraic Riccati equation corresponding to the cost function.

[0038] State augmentation is performed on the linearized model containing augmented state variables, including the input error integral term and the original control input. The rate of change of the control input is used as the new control input. The process involves calculating the difference between the set reference value and the current state variable as the tracking error, and applying a numerical integration algorithm, such as the trapezoidal integral method, to accumulate the tracking error to obtain the error integral term. The original state vector, the augmented state variables of the Pad approximation input, the error integral term, and the original control input from the previous time step are concatenated into a new global augmented state vector. The difference between the current control input and the control input from the previous time step, i.e., the rate of change of the control input, is set as the new control input vector. Based on the original state space equations, the global augmented state transition matrix and the augmented control input matrix under the new control input are derived, and then the global augmented discrete state space equations are established.

[0039] In the cost function of the linear quadratic regulator constructed for the augmented system, a quadratic penalty term for the rate of change of control input is introduced to limit the actuator's action amplitude. The weight coefficient of this penalty term is adjusted based on the residual between the model output and the actual output of the previous cycle. This process involves constructing a cost function that includes a quadratic term for the augmented state deviation and a quadratic term for the rate of change of control input. In each sampling cycle, the L2 norm of the residual between the currently acquired system output and the output predicted based on the model in the previous cycle is calculated. An exponential smoothing algorithm is then used to calculate the weight coefficient of the penalty term based on this residual. The weight coefficient of the penalty term increases exponentially as the residual increases, and decreases as the residual decreases. The feedback gain matrix is ​​obtained by solving the algebraic Riccati equation corresponding to the cost function. This is achieved using the constructed global augmented state transition matrix, the augmented control input matrix, and the state weighting matrix and control weighting matrix containing the weight coefficients of the penalty term. A discrete-time algebraic Riccati equation is constructed. A discrete Riccati equation solver, such as the `dare` function, from a scientific computing library is used to obtain the positive semi-definite solution matrix of the Riccati equation using the Schur vector method or Newton's iteration method. This positive semi-definite solution matrix is ​​then multiplied and inverted with the global augmented state transition matrix and the control input matrix to calculate the optimal feedback gain matrix. This algebraic Riccati equation is used to solve for the optimal feedback gain matrix in a linear quadratic regulator (LQR).

[0040] In one possible embodiment, the state augmentation of the linearized model input error integral term and the original control input, which includes augmented state variables, includes: Calculate the deviation between the target negative pressure setpoint and the actual pressure measurement value of the waste liquid treatment system; discretize and accumulate the deviation or integrate it over continuous time to generate an error integral term; use the error integral term and the original control input as new state variables, and concatenate them with the state vector of the linearized model containing augmented state variables to construct a global state vector containing the original state, augmented state variables, original control input, and error integral term; based on the original augmented linearized system matrix, augmented input matrix, and integral mapping relationship, reconstruct the corresponding global augmented system matrix and global augmented input matrix to complete the construction of the augmented system.

[0041] The difference between the target negative pressure setpoint of the waste liquid treatment system and the real-time value collected by the pressure sensor is obtained. This difference is then discretized and accumulated over the system's digital control sampling period. Anti-integral saturation upper and lower limits are set for the accumulated result to generate an error integral term. This single-dimensional error integral term, the 2-dimensional original control input for the current period, and the original 3-dimensional state variables and 2-dimensional augmented state variables are sequentially concatenated as column vectors to form a total of 8-dimensional global augmented state vector. Correspondingly, the 5×5 state weighting matrix obtained in step S1 is embedded into the global augmented state weighting matrix, and integral error weights and control amplitude weights are assigned to the error integral term and the original control input, respectively, forming an 8×8-dimensional global augmented state weighting matrix. The error integral term weight is used to suppress long-term steady-state deviations, and the original control input weight is used to constrain the absolute amplitudes of the circulating pump speed and valve opening. By algebraically rearranging the original state equations in a difference scheme, the next-time state of the augmented state vector is expressed in block matrix form. The global augmented system matrix, which includes the original linearized system matrix, input matrix, and pressure output selection matrix, is extracted. The control input in the original equations is rewritten as the control input change rate between two adjacent sampling periods. Combined with the corresponding global augmented input matrix, a global augmented model with integral zero steady-state error tracking and rate of change suppression characteristics is constructed.

[0042] In one possible embodiment, the linear quadratic regulator cost function constructed for the augmented system utilizes a quadratic penalty term of the rate of change of the control input to limit the actuator's action amplitude. The weight coefficients of the penalty term are adjusted based on the residual between the model output and the actual output of the previous cycle, including: A comprehensive cost function is constructed, comprising a quadratic form of state deviation, a quadratic form of control input, and a quadratic form of control input rate of change. In the current control cycle, the absolute residual between the pressure output predicted by the nonlinear state-space model of the previous control cycle and the actual pressure output measured by the sensor is calculated. An exponential mapping function is established between the weighting coefficients and the absolute residual. When the absolute residual increases, the weighting coefficient of the quadratic penalty term for the control input rate of change is increased through the exponential mapping function to smooth actuator action and reduce energy consumption. When the absolute residual decreases, the weighting coefficient of the penalty term is decreased to improve the system's response speed to errors.

[0043] A comprehensive cost function based on a linear quadratic regulator architecture is constructed. This comprehensive cost function is the sum of the quadratic weighted integrals of the global state deviation vector, the control input amplitude vector, and the control input rate of change vector. The quadratic form of the control input rate of change is used as a penalty term to prevent high-frequency jitter of the actuator. In each control cycle, the predicted pressure output calculated based on the nonlinear state-space model of the previous cycle and the actual measured pressure output of the pressure sensor are obtained, and the absolute value of the difference between the two is taken as the absolute residual of the current cycle. An exponential mapping relationship is established between the weighting coefficient of the second-order penalty term for the control input change rate and the absolute residual. For example, the weighting coefficient of the basic penalty term is set to 0.5, the amplification factor to 10, and the adjustment factor to 0.2. The specific calculation process is as follows: the absolute residual is multiplied by the adjustment factor and used as the independent variable of the exponential function. Its exponential value is calculated and multiplied by the amplification factor, and then added to the weighting coefficient of the basic penalty term to obtain the weighting coefficient of the second-order penalty term for the control input change rate in the current control cycle. When the absolute residual increases, the weighting coefficient of the penalty term increases exponentially through this exponential mapping function to limit the control input change rate, thereby smoothing the actuator action and reducing energy consumption. Conversely, when the absolute residual decreases, the weighting coefficient of the penalty term decreases to near the basic weight, reducing the constraint on the control input change rate and improving the system's response speed to errors. The system's suppression of high-frequency vibration influence is illustrated in the controller-level comparative test diagram. Figure 3 As shown.

[0044] It should be noted that, on the semi-physical simulation platform of the waste liquid treatment system, with other parameters fixed, a step response test was conducted using the weighting coefficient of the basic penalty term as the variable. When the weighting coefficient of the basic penalty term was 0.5, the actuator action curve was smooth without sharp fluctuations; therefore, 0.5 was determined as the value of the weighting coefficient of the basic penalty term. On the simulation platform, the amplification factor was used... Perform robustness testing on the variables when At this time, the weights saturate to their upper limit under moderate perturbations, causing the system response to be overly conservative; when At that time, under large disturbances, the weight increase was insufficient, and the actuator still exhibited significant jitter. The optimal compromise was achieved across the entire operating range. The residual sequence of the on-site wastewater treatment system under typical disturbance conditions was collected. With the goal of minimizing the variance of the control variable fluctuation, the adjustment factor was optimized offline using the gradient descent method. The optimization convergence value was between 0.18 and 0.22. Considering the convenience of engineering tuning, the adjustment factor was set to 0.2.

[0045] S3 constructs a disturbance observer to estimate lumped uncertainty, converts it into feedforward compensation quantity and merges it with the feedback quantity to form a control law, and issues commands to adjust the speed of the circulating pump and the valve opening.

[0046] Specifically, a disturbance observer is constructed to estimate the lumped uncertainty caused by model mismatch and external disturbances online. The pseudo-inverse matrix of the global augmented input matrix is ​​multiplied by the lumped uncertainty as a feedforward compensation term, which is combined with the feedback control quantity based on the feedback gain matrix to obtain the control law. The control law is used to generate instructions to adjust the speed of the circulating pump and the valve opening.

[0047] A disturbance observer is constructed to estimate the lumped uncertainty caused by model mismatch and external disturbances online. The process involves constructing the state observer equation using the nominal linearized system matrix. The difference between the actual measured differential values ​​of the state variables and the differential values ​​calculated based on the nominal model is used as the residual signal. This residual signal is filtered by a compensation network consisting of a low-pass filter algorithm, such as a Butterworth low-pass filter, to remove high-frequency measurement noise. The output result is then used as the lumped uncertainty at the current moment. The pseudo-inverse of the globally augmented input matrix is ​​multiplied by the lumped uncertainty as a feedforward compensation term. This term is combined with the feedback control quantity based on the feedback gain matrix to obtain the control law. This process involves calling a singular value decomposition algorithm, such as the svd function, from the matrix operation library to obtain the Moore-Penrose generalized inverse matrix of the globally augmented input matrix. The Moore-Penrose generalized inverse matrix is ​​a generalized inverse form used for non-square or non-invertible matrices.

[0048] The obtained pseudo-inverse matrix is ​​multiplied by the lumped uncertainty output by the perturbation observer to obtain the feedforward compensation term used to offset the uncertainty. The feedback gain matrix K is then multiplied by the global augmented state vector. Multiply and take the negative to obtain the feedback control quantity. The pseudo-inverse of the globally augmented input matrix. With aggregate uncertainty Multiplying them together yields the feedforward compensation term. ;and in accordance with The control law that produces the current control cycle output as the rate of change of the control input is obtained. Then by To obtain the actual control input command for the current cycle. ,in, The actual control input value of the previous control cycle is used; then, the actual control input command is converted into an analog current signal of 4 to 20 mA by a digital-to-analog converter. The current signal is transmitted to the inverter drive terminal through the electrical control cabinet to change the output frequency to adjust the speed of the circulating pump, and transmitted to the electric regulating valve positioner to drive the micro motor to adjust the valve opening, so as to realize the closed-loop control of the negative pressure of the waste liquid treatment system.

[0049] In one possible embodiment, the construction of the disturbance observer estimates the lumped uncertainty constituted by model mismatch and external disturbances online. The pseudo-inverse of the globally augmented input matrix is ​​multiplied by the lumped uncertainty as a feedforward compensation term, which is then combined with a feedback control quantity based on the feedback gain matrix to obtain the control law, including: A state observer is constructed, and the difference between the actual value of the time derivative of the measurable state of the system and the predicted derivative of the linearized model is calculated. A low-pass filter is used to filter the difference to eliminate high-frequency measurement noise and obtain the lumped uncertainty. The pseudo-inverse matrix of the global augmented input matrix is ​​calculated, and the pseudo-inverse matrix is ​​multiplied by the estimated value of the lumped uncertainty to generate a feedforward compensation term acting on the control input. The feedforward compensation term is subtracted from the feedback control quantity generated by the feedback gain matrix to obtain the control law.

[0050] The backward Euler difference formula is used to calculate the actual time derivative of the measured state variable in the current sampling period. The difference between this time derivative and the predicted state derivative of the linearized model substituted with the state and input of the previous period is calculated, and this multidimensional derivative difference is set as the lumped uncertainty. To prevent noise amplification caused by numerical differentiation, the sampling period within the sensor used for state derivative estimation is set to 0.01s, and the controller command update period is set to 0.1s. A first-order infinite impulse response low-pass filter with a filtering coefficient of 0.85 is used to process the internal sampling sequence. Its equivalent cutoff frequency is determined by the filtering coefficient and the sampling period. This filter is used to attenuate high-frequency measurement noise above 10Hz before outputting the lumped uncertainty within the control period. The Moore-Penrose pseudo-inverse matrix of the global augmented input matrix is ​​calculated using singular value decomposition. This pseudo-inverse matrix is ​​then multiplied by the filtered lumped uncertainty to map the spatial disturbance to the control input space, generating a feedforward compensation term. The control law is obtained by subtracting the feedforward compensation term from the feedback control quantity generated by the feedback gain matrix obtained from the algebraic Riccati equation. This law is used to perform feedforward compensation for disturbances and shorten the disturbance recovery time to within 3 seconds.

[0051] The experiment was conducted using a semi-simulation platform for a waste liquid treatment system. The initial pressure was set to -10 kPa, the target pressure to -60 kPa, the rated flow rate to 30 L / min, and the waste liquid concentration to 15%. The controller command update cycle was set to 0.1 s, the sensor sampling cycle for state derivative estimation and low-pass filtering was set to 0.01 s, the circulating pump speed range was limited to 1000 to 3000 rpm, and the valve opening range was 0 to 100%. Four control groups were set up: a basic linear quadratic regulator control group, a fixed-weight reconfiguration group with the control input rate-of-change penalty removed, an uncompensated group with the disturbance observer feedforward compensation removed, and the proposed scheme group including full delay augmentation, cross-penalty, weights, and a disturbance observer.

[0052] At the 30th second of system operation, a step disturbance simulating pipe filter blockage was manually input, and the response data of each group was recorded. The pressure overshoot of the basic linear quadratic regulator control group was 18.5%, the settling time was 12.5s, the disturbance recovery time was 14.2s, and the steady-state error was 3.2kPa. The overshoot of the fixed-weight group decreased to 7.1%, but the peak rate of change of the circulating pump speed reached 450rpm / s, and the actuator exhibited high-frequency jitter. The uncompensated group experienced a maximum pressure drop of 11.4kPa during the disturbance, with a disturbance recovery time of 9.8s. The proposed scheme group has a pressure overshoot of 2.5%, a settling time shortened to 4.2s, a steady-state error less than 0.5kPa, a maximum pressure drop limited to 3.1kPa during the disturbance, a disturbance recovery time of 2.7s, and a pump speed change rate constrained to within 50rpm / s. Figure 4 As shown.

[0053] Compared to the basic control group, the complete scheme reduces the settling time by 66.4% and the steady-state error by 84.3%. This is attributed to the synergistic effect of Pad's approximate delay decoupling and error integral term augmentation, which eliminates oscillations caused by time delay and achieves zero steady-state error tracking. Compared to the fixed-weight group, the weighting mechanism reduces the high-frequency jitter amplitude of the actuator by 88.8%, reducing system energy consumption and extending hardware lifespan. Compared to the uncompensated group, the introduction of the disturbance observer reduces the disturbance recovery time by 72.4%, indicating that the feedforward compensation term based on the pseudo-inverse of the globally augmented input matrix can approximate the state-space disturbance to the control end, which helps to feedforward compensate for external lumped uncertainties.

[0054] This invention also provides a waste liquid recycling treatment control system based on negative pressure adaptive regulation. The system includes a processor and a memory. The memory stores computer program instructions. When the computer program instructions are executed by the processor, they implement the waste liquid recycling treatment control method based on negative pressure adaptive regulation according to the first aspect of this invention. The system also includes other components well known to those skilled in the art, such as a communication bus and a communication interface. Their settings and functions are known in the art and will not be described in detail here.

Claims

1. A waste liquid recycling treatment control method based on negative pressure adaptive regulation, characterized in that, include: S1: Obtain the real-time state variables of pressure, flow rate and material concentration of the waste liquid treatment system, establish a nonlinear state space model including actuator delay and parameter uncertainty boundary, transform the actuator delay into an augmented state variable through Pad approximation, and obtain the linearized system matrix by Taylor expansion of the nonlinear state space model at the current operating point while retaining the first-order terms. Construct the state weighting matrix and the control weighting matrix. The diagonal elements of the two matrices are proportional to the sensitivity of the state variables to the system performance index, and the off-diagonal elements are symmetric according to the cross-correlation terms of the linearized system matrix and satisfy the semi-positive definite condition. Satisfying the positive semi-definite condition includes: extracting off-diagonal elements between state variables in the augmented linearized system matrix as cross-correlation terms, retaining the positive and negative signs of the cross-correlation terms and performing symmetry processing, and then mapping them proportionally to the corresponding off-diagonal positions of the state weighting matrix; the control weighting matrix is ​​taken as a diagonal matrix by default. If the actuator coupling test confirms that there is input coupling between the circulating pump speed and the valve opening, the off-diagonal terms are determined according to the correlation of the column vectors of the input matrix or the actuator coupling identification results, and the corresponding weighting matrix is ​​ensured to satisfy the positive semi-definite condition, so that strongly correlated variables are subject to cooperative penalty during the optimization process; S2: The linearized model, including augmented state variables, is used to perform state augmentation on the input error integral term and the original control input. The difference between the current control input and the control input at the previous moment is defined as the control input change rate. This change rate is used as the new control input. In the linear quadratic regulator cost function constructed for the augmented system, a quadratic penalty term of the control input change rate is used to limit the actuator's action amplitude. This includes: constructing a comprehensive cost function containing quadratic state deviation, quadratic control input, and quadratic control input change rate; calculating the absolute residual between the pressure output predicted by the nonlinear state-space model of the previous control cycle and the actual pressure output measured by the sensor in the current control cycle; establishing an exponential mapping function between the weighting coefficients and the absolute residuals. When the absolute residuals increase, the weighting coefficients of the quadratic penalty term of the control input change rate are increased through the exponential mapping function to smooth actuator action and reduce energy consumption; when the absolute residuals decrease, the weighting coefficients are decreased to improve the system's response speed to errors; and solving the algebraic Riccati equation corresponding to the cost function to obtain the feedback gain matrix. S3: Construct a disturbance observer to estimate the lumped uncertainty caused by model mismatch and external disturbances online. Multiply the pseudo-inverse matrix of the reconstructed global augmented input matrix after state augmentation by the lumped uncertainty as a feedforward compensation term. Combine this with the feedback control quantity based on the feedback gain matrix to obtain the control law. Generate instructions based on the control law to adjust the speed of the circulating pump and the valve opening.

2. The waste liquid recycling treatment control method based on negative pressure adaptive regulation according to claim 1, characterized in that, The actuator delay is transformed into an augmented state variable using the Pad approximation, including: Based on the mechanism modeling method, a nonlinear equation is constructed with system pressure, flow rate, and waste liquid concentration as state variables and circulating pump speed and pipeline valve opening as control inputs; the step response of the actuator is tested, and the pure time delay constant of the actuator is identified as the actuator delay; according to the measurement error range of the system parameters, the perturbation upper and lower bounds of each parameter in the nonlinear equation are determined to generate parameter uncertainty boundaries. The first-order Pad approximation is used to convert the transfer function of the delay element, which contains a pure time delay constant, into a rational fractional form. The rational fraction is then converted into a differential equation and input into the nonlinear equation as an additional augmented state variable.

3. The waste liquid recycling treatment control method based on negative pressure adaptive regulation according to claim 1, characterized in that, The diagonal elements of the two matrices are proportional to the sensitivity of the state variables to system performance indicators, including: Calculate the sensitivity coefficients of each state variable to the system pressure settling time, normalize the sensitivity coefficients and use them as the diagonal elements of the state weighting matrix, and use the reciprocal of the control input energy constraint or the reciprocal of the square of the maximum allowable change in control input as the diagonal elements of the control weighting matrix.

4. The waste liquid recycling treatment control method based on negative pressure adaptive regulation according to claim 1, characterized in that, The reconstructed global augmented input matrix after state augmentation includes: Calculate the Jacobian matrix of the nonlinear state-space model at the current steady-state operating point relative to the state variables and control inputs as the augmented linearized system matrix and the augmented input matrix; Calculate the deviation between the target negative pressure setpoint and the actual pressure measurement value of the waste liquid treatment system; discretize and accumulate the deviation or integrate it over continuous time to generate an error integral term; use the error integral term and the original control input as new state variables, and concatenate them with the state vector of the linearized model containing augmented state variables to construct a global state vector containing the original state, augmented state variables, original control input, and error integral term; based on the original augmented linearized system matrix, augmented input matrix, and integral mapping relationship, reconstruct the corresponding global augmented system matrix and global augmented input matrix to complete the construction of the augmented system.

5. The waste liquid recycling treatment control method based on negative pressure adaptive regulation according to claim 1, characterized in that, The control law is obtained by combining the feedback control quantity based on the feedback gain matrix, including: A state observer is constructed to calculate the difference between the actual value of the time derivative of the measurable state of the system and the predicted derivative of the linearized model; a low-pass filter is used to filter the difference to eliminate high-frequency measurement noise and obtain the lumped uncertainty. Calculate the pseudo-inverse of the global augmented input matrix, multiply the pseudo-inverse by the lumped uncertainty to generate a feedforward compensation term acting on the control input, and subtract the feedforward compensation term from the feedback control quantity generated by the feedback gain matrix to obtain the control law.

6. The waste liquid recycling treatment control method based on negative pressure adaptive regulation according to claim 1, characterized in that, Establish an exponential mapping function between the weighting coefficients and the absolute residuals, including: Set the weight coefficient, amplification coefficient, and adjustment factor for the basic penalty term; multiply the absolute residual by the adjustment factor and use it as the independent variable of the exponential function, calculate its exponential value and multiply it by the amplification coefficient, and then add it to the weight coefficient of the basic penalty term to obtain the weight coefficient of the second penalty term for the control input change rate in the current control cycle.

7. A waste liquid recycling treatment control system based on negative pressure adaptive regulation, comprising a processor and a memory, characterized in that, The memory stores a computer program, and the processor executes the computer program to implement the waste liquid recycling treatment control method based on negative pressure adaptive regulation as described in any one of claims 1-6.

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