A smooth running and non-interference switching PID control method for a sewage treatment system

Abstract

The present application is based on the tangent switching system modeling method, the non-disturbance switching technology and the PID control method, and data collection is carried out on the sewage discharge and effluent in the sewage treatment process, and a non-disturbance switching PID control method for a multi-modal system is disclosed. The method helps to improve the control accuracy, and also can improve the stability of the system operation. The method fully considers the non-negativity, multi-modal characteristics and controller switching oscillation problem of the control variable during modeling, and a non-disturbance switching PID controller is designed based on this. The non-disturbance switching strategy realizes the smooth switching of the controller and improves the stability of the system. At the same time, the application of linear programming method greatly improves the calculation efficiency, and has greater advantages for solving the calculation of complex systems.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of engineering technology and automatic control, and particularly relates to a disturbance-free switching PID control method for smooth operation of a sewage treatment system. BACKGROUND

[0002] At present, with the development of economy and the growth of population, people's demand for water resources gradually increases. Therefore, it is of key importance to put forward highly automated sewage treatment technology for improving the efficiency of sewage treatment. The existing urban sewage treatment is roughly divided into primary treatment, secondary treatment and tertiary treatment. The secondary treatment, also known as biological treatment system, mainly includes an aeration tank and a secondary sedimentation tank, and is the most important part in the sewage treatment process. The concentration of microorganisms and the concentration of dissolved oxygen in the sewage biochemical treatment process have an important influence on the water quality after sewage treatment, which requires the flow of discharged sewage to meet the sewage quantity required by the aeration tank and the sedimentation tank. Therefore, it is of great significance to control the discharge amount of sewage by automatic control technology for improving the water quality. Based on the above analysis, the present application proposes a new automatic control technology for sewage treatment system, so as to improve the water quality of sewage treatment and ensure the safe and smooth operation of the system.

[0003] Considering that the mode of the actual sewage treatment system is not fixed, taking urban sewage discharge as an example, sewage discharge has two peak values at 6:30-10:30 in the morning and 19:00-22:30 in the evening, and the sewage discharge is not high at other time periods. Therefore, using a single dynamic model to describe the actual sewage treatment system is not accurate, and it will cause problems such as increased difficulty in controller design, delayed control, etc. The present application intends to use a switching system with multiple modes to model the sewage treatment system. At the same time, the state of the sewage treatment system, i.e. sewage discharge, has non-negativity, and using existing sewage treatment models such as general switching system models, general state space models, etc. will cause modeling redundancy, which is not conducive to resource conservation and improvement of modeling accuracy. Therefore, the present application proposes a positive switching system that takes into account non-negativity and multi-mode to model the sewage treatment system, which improves the modeling accuracy and is more consistent with the actual system. When the sewage treatment system switches from one mode to another, the corresponding controller also switches to achieve the effect of "one-to-one" control. However, when the controller switches, switching chattering often occurs. When the controller vibration is severe, it will cause the effluent water quality to be substandard and the system to run unstably. In view of the controller switching vibration problem, the present application introduces certain limiting conditions to design a disturbance-free switching controller to achieve stable switching of the controller between multiple modes, realize smooth switching and improve system stability. Traditional control systems are mainly proportional control, but due to the large size of the sewage treatment system, the overall complexity, and the performance limitations of sensors, actuators and other devices, the real-time and accuracy of the sewage discharge of the actual sewage treatment system is not high, which increases the system error. Therefore, only proportional control cannot achieve accurate control of sewage discharge. In order to reduce the system error as much as possible, the present application proposes a control strategy based on a PID controller. The PID controller (proportional-integral-derivative controller) adjusts the deviation of the entire control system by setting the proportional unit P, the integral unit I, and the derivative unit D, so that the actual value of the controlled variable is consistent with the given value. The PID controller combines proportional (P) control, integral (I) control and derivative (D) control, and integrates the advantages of proportional control, integral control and derivative control, such as timely, accurate and smooth control process. From the calculation method, the linear programming method used in the present application has greater advantages in handling large-scale calculations compared to the general quadratic matrix inequality method.

[0004] Based on the above analysis, the present application establishes a positive switching system state space model of the sewage treatment system by using modern control theory technology, designs a non-perturbation switching PID controller for the sewage treatment system, realizes smooth switching of the controller, ensures efficient, safe and stable operation of the system, and improves the precision and stability of the system. Meanwhile, the linear programming method is used for solving, which reduces the calculation burden and saves the calculation resources, and has important reference value and practical significance for processing large-scale systems such as sewage systems. SUMMARY

[0005] The present application establishes a positive switching system model with positive and multi-modal characteristics for the sewage treatment process, and proposes a non-perturbation switching PID control method for smooth operation of the sewage treatment system.

[0006] A non-perturbation switching PID control method for smooth operation of a sewage treatment system, comprising the following steps:

[0007] Step 1, establishing a state space model of the sewage treatment process;

[0008] Step 2, constructing a non-perturbation switching PID controller for the sewage treatment system;

[0009] Step 3, introducing a reference controller;

[0010] Step 4, introducing a non-perturbation switching mechanism of the controller;

[0011] Step 5, constructing a non-perturbation switching PID control closed-loop system for the sewage treatment system;

[0012] Step 6, designing a linear programming form for ensuring smooth operation of the sewage treatment system;

[0013] Step 7, positive verification of the closed-loop control system of the sewage treatment system;

[0014] Step 8, stability verification of the closed-loop control system of the sewage treatment system;

[0015] Step 9, non-perturbation verification of the PID controller of the sewage treatment system.

[0016] Further, step 1 is specifically as follows:

[0017] 1.1 Collecting input and output data of the sewage treatment system to describe the actual system;

[0018] 1.2 Establishing a state space model of the sewage treatment process.

[0019] Further, step 2 is specifically as follows:

[0020] u(k)=K σ(k) y(k)+L σ(k)e(k) + M σ(k) (Δy(k)),

[0021] where e(k) = y(k-1) + e(k-1) - δe(k-1) represents the integral term of the controller, and the derivative term of the controller satisfies Δy(k) = y(k) - y(k-1) = C σ(k) x(k) - C σ(k) x(k-1), K σ(k) , L σ(k) , M σ(k) are the proportional, integral and derivative gain matrices of the controller, respectively, and σ(k m-1 ) = q, σ(k m ) = p, σ(k m+1 ) = r; the gain of the disturbance-free switching PID controller for the wastewater treatment process is designed, and its specific form is:

[0022]

[0023] where the symbol T represents the transpose of a vector or a matrix, 1 r represents an r-dimensional column vector with all elements being 1, represents an r-dimensional column vector with the ith element being 1 and the rest of the elements being 0, ξ p , η p and θ p are s-dimensional column vectors, is an n-dimensional column vector.

[0024] Further, the form of the reference controller in step 3 is as follows:

[0025] u * (k) = K * y(k) + L * e(k) + M * (Δy(k)),

[0026] where u * (k) represents the desired control input, K * , L * , M * are given matrices and satisfy

[0027]

[0028] Further, the specific constraint conditions of the controller disturbance-free switching mechanism in step 4 are as follows:

[0029]

[0030] where α ≥ 0, β ≥ 0, γ ≥ 0 are the disturbance-free performance indicators, u j (k) and respectively, the control input u(k) and the desired control input u * the jth element of the ith row of matrix A(k).

[0031] Further, step 5 is specified as follows:

[0032] Combining the state space model of step 1 and the disturbance-free PID control model of step 2, the PID closed-loop control system of the wastewater treatment control system is:

[0033]

[0034] where,

[0035]

[0036] I s denotes the sxs identity matrix.

[0037] Further, in step 6, the necessary and sufficient condition for designing a linear programming form to ensure the smooth operation of the wastewater treatment system is as follows:

[0038] Design constants 0 < δ ≤ 1, 0 < ρ < 1, λ > 1, i = 1, …, r, vector and vector such that

[0039]

[0040] For any p, q ∈ S, under the disturbance-free switching PID controller designed in step 2, the closed-loop system of the wastewater treatment system is positive and exponentially stable, and the average dwell time condition is designed as:

[0041]

[0042] Further, in step 7, the positive verification process of the closed-loop control system of the wastewater treatment system is as follows:

[0043] From the specific form of the disturbance-free switching PID controller designed in step 2 and condition (a) in step 6, we have

[0044]

[0045] That is, A p + B p K p C p + B p M p C p ≥ 0.

[0046] Combining the conditions in Step 2 and Step 6 Obtain

[0047]

[0048] i.e., B p L p ≥ 0, -B p M p Cp ≥ 0. Further, it is known that Therefore, the positivity of the closed-loop control system of the wastewater treatment system is guaranteed.

[0049] Further, the stability verification process of the closed-loop control system of the wastewater treatment system in Step 8 is as follows:

[0050] Construct Lyapunov function

[0051]

[0052] where, Take the difference of V p , we get

[0053]

[0054] According to the conditions (b)-(e) in Step 6, it is derived that

[0055]

[0056] It is known that each subsystem is stable. Further, combining the condition (f) in Step 6 and the designed average residence time, we get

[0057]

[0058] Finally, after rearrangement, we get

[0059]

[0060] where,

[0061] Therefore, the stability of the closed-loop control system of the wastewater treatment system is guaranteed.

[0062] Further, the non-perturbation verification process of the PID controller of the wastewater treatment system in Step 9 is as follows:

[0063] First, according to Steps 3 and 4, we get the following equations:

[0064]

[0065] where, and denote the jth row element of K p and K *

[0066] Then, according to the gain matrix form in step 2, we get

[0067]

[0068] Combined with conditions (g) and (h) in step 6 and y(k)≥0, the following inequalities are obtained

[0069]

[0070] According to conditions (i) and (j) in step 6 and y(k-1)≥0, we get

[0071]

[0072] Similarly, according to conditions (k) and (l) in step 6 and e(k-1)≥0 and 1-δ>0, we can get

[0073]

[0074] Combined with the above three inequalities, the following inequalities are derived

[0075]

[0076] Further, we can get

[0077]

[0078] Therefore, the disturbance-free switching PID controller of the sewage treatment system is effective.

[0079] Based on the tangent switching system model, disturbance-free switching technology and PID control method, the present application collects data of sewage flow in the sewage treatment process, and proposes a PID controller design method which can be switched without disturbance, so as to ensure efficient, safe and stable operation of the control system. At the same time, the linear programming method is used to reduce the calculation burden and save the calculation resources. Data privacy is safe. The model established by the present application fully considers the characteristics of the actual system such as positivity, multimodality, switching oscillation, etc., and has higher application value. BRIEF DESCRIPTION OF DRAWINGS

[0080] Figure 1 is a sewage treatment process flow chart;

[0081] Figure 2 is a disturbance-free switching PID control structure schematic diagram of the stable operation of the sewage treatment system of the present application. DETAILED DESCRIPTION ​

[0082] The application is further described below with reference to the accompanying drawings.

[0083] As Figure 1 shown, a dynamic model of the sewage treatment process is established with the sewage treatment process as the research object, the urban flow into the sewage treatment system as the control input, and the domestic water outflow after the three-stage treatment as the output.

[0084] The smooth running and undisturbed switching PID control method of the sewage treatment system of the application comprises the following steps:

[0085] Step 1, a state space model of the sewage treatment process is established by combining the data transmission dynamic process data packet quantity data.

[0086] 1.1 Collect the input and output data of the sewage treatment system to describe the actual system:

[0087] As Figure 1 shown, the sewage to be treated first enters the grid and the primary sedimentation tank, mainly to remove the solid pollutants in the sewage in the suspended state, which is also called the pretreatment process. The sewage after the pretreatment enters the aeration tank and the secondary sedimentation tank containing microorganisms for biochemical treatment, mainly to remove the organic pollutants in the sewage in the colloidal and dissolved state. Then, the sewage after the secondary treatment continues to be treated in the third stage to obtain the domestic water that can be used, and a part of the water that is not completely treated flows into the river. The whole sewage treatment process ends. In the biochemical treatment process, the backflow microorganism concentration, the dissolved oxygen concentration and the like have a significant influence on the water quality, so the sewage flow into the aeration tank and the secondary sedimentation tank should be strictly controlled. Considering the huge and complex sewage treatment system and the limitation of the equipment, errors are inevitable in the process of the control system, therefore, a superior controller is applied in the sewage treatment system to improve the control precision. Considering the non-negativity and multi-modal characteristics of the sewage discharge, the actual sewage treatment system is modeled as a positive switching system model. Since the corresponding controller will also be switched when the switching system is switched, the switching oscillation phenomenon is prone to occur, therefore, a smooth switching undisturbed switching PID controller design method is proposed. In addition, in order to reduce the system calculation burden and improve the calculation efficiency, a linear programming method is adopted. Figure 2 is the undisturbed switching PID control structure diagram.

[0088] 1.2 Collect the sewage discharge data in the sewage treatment process, establish the state space model of the sewage treatment process, and the form is as follows:

[0089] x(k+1)=A σ(k) x(k)+B σ(k) u(k),k∈N,

[0090] y(k) = C σ(k) x(k), k ∈ N,

[0091] where, denotes the wastewater flow rate in the aeration tank or secondary sedimentation tank of the wastewater treatment system, denotes the control input, i.e., the wastewater flow rate into the aeration tank or secondary sedimentation tank, denotes the wastewater flow rate out of the aeration tank or secondary sedimentation tank after treatment. σ(k) denotes the rule that the wastewater treatment system mode change obeys, and takes values in a finite set S = {1, 2, …, N}, N ∈ N + A σ(k) , B σ(k) , C σ(k) denote system matrices, and it is assumed that A σ(k) ≥ 0, B σ(k) ≥ 0, C σ(k) ≥ 0. N + denote n-dimensional, r-dimensional, s-dimensional Euclidean matrix spaces and the set of positive integers, respectively.

[0092] Step 2, construct a disturbance-free switching PID controller for the wastewater treatment system, the specific method is:

[0093] u(k) = K σ(k) y(k) + L σ(k) e(k) + M σ(k) (Δy(k)),

[0094] where e(k) = y(k-1) + e(k-1) - δe(k-1) denotes the integral term of the controller, and the differential term of the controller satisfies Δy(k) = y(k) - y(k-1) = C σ(k) x(k) - C σ(k) x(k-1), K σ(k) , L σ(k) , M σ(k) are the proportional, integral, and differential gain matrices of the controller, respectively, and σ(k m-1 ) = q, σ(k m ) = p, σ(k m+1 ) = r. The disturbance-free switching PID controller gain for the wastewater treatment process is designed, and its specific form is:

[0095]

[0096] where the symbol T denotes the transpose of a vector or matrix, 1 r denotes an r-dimensional column vector with all elements being 1, denotes an r-dimensional column vector with the ith element being 1 and the rest being 0, ξ p , η p , and θp is an s-dimensional column vector, is an n-dimensional column vector.

[0097] Step 3, introduce a reference controller in the form of

[0098] u * (k) = K * y(k) + L * e(k) + M * (Δy(k)),

[0099] where u * (k) denotes the desired control input, K * , L * , M * are given matrices and satisfy

[0100]

[0101] Step 4, introduce a controller bumpless switching mechanism with the specific constraints of

[0102]

[0103] where α ≥ 0, β ≥ 0, γ ≥ 0 are bumpless performance indicators, u j (k) and are the jth row elements of the control input u(k) and the desired control input u * (k), respectively.

[0104] Step 5, construct the bumpless switching PID control closed-loop system for the wastewater treatment system:

[0105] Combining the state space model of Step 1 and the bumpless PID control model in Step 2, the closed-loop control system of the wastewater treatment control system is:

[0106]

[0107] where

[0108]

[0109] I s denotes the s × s-dimensional identity matrix.

[0110] Step 6, design the necessary and sufficient conditions for the linear programming form that guarantees the smooth operation of the wastewater treatment system as follows:

[0111] Design constants 0 < δ ≤ 10 < ρ < 1 λ > 1, i = 1, ···, r, vector φ p > 0, φ p> 0 and vector such that

[0112]

[0113] For any p,q∈S, the closed-loop system of the wastewater treatment system is positive and exponentially stable under the bumpless transfer PID controller designed in Step 2, and the average residence time condition is designed as:

[0114]

[0115] Step 7, the positive verification process of the closed-loop control system of the wastewater treatment system is as follows:

[0116] The specific form of the bumpless transfer PID controller designed in Step 2 and condition (a) in Step 6 give

[0117]

[0118] That is, A p + B p K p C p + B p M p C p ≥ 0.

[0119] Combining the conditions in Step 2 and Step 6 we get

[0120]

[0121] That is, B p L p ≥ 0, -B p M p C p ≥ 0. Further, we know Therefore, the positivity of the closed-loop control system of the wastewater treatment system is guaranteed.

[0122] Step 8, the stability verification process of the closed-loop control system of the wastewater treatment system is as follows:

[0123] Construct the Lyapunov function

[0124]

[0125] where, Taking the difference of V p we get

[0126]

[0127] According to condition (b)-(e) in Step 6, we have

[0128]

[0129] It is known that each subsystem is stable. Further, combining condition (f) in Step 6 and the designed average residence time, we have

[0130]

[0131] Finally, we have

[0132]

[0133] where

[0134] Therefore, the stability of the closed-loop control system of the wastewater treatment system is guaranteed.

[0135] Step 9, the non-perturbation verification process of the PID controller of the wastewater treatment system is as follows:

[0136] First, according to Steps 3 and 4, we have the following equations:

[0137]

[0138] where and represent the jth row elements of K p and K * , respectively.

[0139] Then, according to the gain matrix form in Step 2, we have

[0140]

[0141] Combining conditions (g) and (h) in Step 6 and y(k) ≥ 0, we have the following inequalities

[0142]

[0143] According to conditions (i) and (j) in Step 6 and y(k-1) ≥ 0, we have

[0144]

[0145] Similarly, according to conditions (k) and (l) in Step 6 and e(k-1) ≥ 0 and 1-δ > 0, we have

[0146]

[0147] Combining the above three inequalities, the following inequality is derived

[0148]

[0149] Further, we can get

[0150]

[0151] Therefore, the non-perturbative switching PID controller of the sewage treatment system is effective.

Claims

1. A smooth running and disturbance-free switching PID control method for a sewage treatment system, characterized in that The following steps are: Step 1, establishing a state space model of the wastewater treatment process; Step 2, constructing a disturbance-free switching PID controller for the wastewater treatment system; Step 3, introducing a reference controller; Step 4, introducing a disturbance-free switching mechanism for the controller; Step 5, constructing a disturbance-free switching PID control closed-loop system for the wastewater treatment system; Step 6, designing a linear programming form to ensure smooth operation of the wastewater treatment system; Step 7, positive verification of the closed-loop control system of the wastewater treatment system; Step 8, stability verification of the closed-loop control system of the wastewater treatment system; Step 9, disturbance-free verification of the PID controller of the wastewater treatment system; Step 2 is as follows: u(k) = K σ(k) y(k) + L σ(k) e(k) + M σ(k) (Δy(k)), where e(k) = y(k - 1) + e(k - 1) - δe(k - 1) represents the integral term of the controller, and the differential term of the controller satisfies Δy(k) = y(k) - y(k - 1) = C σ(k) x(k) - C σ(k) x(k - 1), K σ(k) , L σ(k) , M σ(k) are the proportional, integral and differential gain matrices of the controller, respectively, and σ(k m-1 ) = q, σ(k m ) = p, σ(k m+1 ) = r; the gain of the disturbance-free switching PID controller designed for the sewage treatment process is specifically as follows: where the notation represents the transpose of a vector or matrix, 1 r represents an r-dimensional column vector with all elements equal to 1, represents an r-dimensional column vector with the i-th element equal to 1 and all other elements equal to 0, ξ p , η p and θ p are s-dimensional column vectors, p is an n-dimensional column vector; The specific constraint conditions of the controller disturbance-free switching mechanism in Step 4 are: Where α≥0, β≥0, and γ≥0 are the non-disruption performance indicators. and The control input u(k) and the desired control input u are respectively. * (k) of the row element; Step 5 is as follows: Combining the state space model of Step 1 and the disturbance-free PID control model in Step 2, the PID closed-loop control system of the wastewater treatment control system is: wherein, I s denotes the s x s identity matrix; In Step 6, the necessary and sufficient conditions for designing a linear programming form to ensure smooth operation of the wastewater treatment system are as follows: Design constants 0 < δ ≤ 1, 0 < p < 1, λ > 1, i = 1,..., r, vector and vector such that For any p, q ∈ S, the closed-loop system of the wastewater treatment system is positive and exponentially stable under the designed disturbance-free switching PID controller in Step 2, and the average residence time condition is designed as:

2. A smooth transition PID control method for the steady operation of a sewage treatment system according to claim 1, characterized in that, Step 1 is as follows: 1.1 Collect input and output data of the wastewater treatment system to describe the actual system; 1.2 Establish a state space model of the wastewater treatment process.

3. The smooth transition PID control method for the operation of a wastewater treatment system according to claim 1, characterized in that, The form of the reference controller in Step 3 is as follows: u * (k) = K * y(k) + L * e(k) + M * (Δy(k)), where u * (k) denotes the desired control input, K * , L * , M * are given matrices and satisfy respectively

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