An Adaptive Sliding Mode Control Method for Dissolved Oxygen Concentration Based on Event-Triggered Identification

Abstract

The present invention proposes an adaptive sliding mode control method for dissolved oxygen concentration based on event-triggered identification, which realizes the stable control of the dissolved oxygen concentration affected by delayed disturbance variables in the urban sewage treatment process. A dissolved oxygen concentration model for the urban sewage treatment process with a delay disturbance term is established, an event-triggered recursive least squares method is designed to identify the model parameters, and an adaptive sliding mode controller is designed to solve the problem that it is difficult to stably control the dissolved oxygen concentration affected by delayed disturbances in the urban sewage treatment process. The experimental results show that this method can realize the stable control of the dissolved oxygen concentration in the urban sewage treatment process and ensure the safe and stable operation of the urban sewage treatment process.

Description

Technical Field

[0001] Based on event-triggered identification, the present invention designs an adaptive sliding mode controller to achieve stable control of the dissolved oxygen concentration affected by time-delay disturbance variables in the urban sewage treatment process. The control of the dissolved oxygen concentration, as an important link in the urban sewage treatment process, is an important branch in the field of advanced manufacturing technology, belonging to both the field of intelligent control and the field of water treatment. Background Art

[0002] Sewage treatment refers to the process of purifying sewage to meet the water quality requirements for discharging into a certain water body or for reuse again, which is an important way to solve the water pollution problem. The activated sludge process is one of the most widely used sewage treatment processes, but this process involves a variety of complex physical, chemical and biological reaction processes. The size of the dissolved oxygen concentration in the aerobic zone of the activated sludge process directly affects the metabolism of microorganisms and the sewage treatment effect. If the dissolved oxygen concentration is too high, it will accelerate the consumption of organic matter in the sewage, resulting in the aging of activated sludge; if the dissolved oxygen concentration is too low, the activity of microorganisms will be inhibited, resulting in the decline, disintegration and deterioration of microorganisms. Therefore, the accurate control of the dissolved oxygen concentration is the key to ensuring the effluent water quality of the sewage treatment plant.

[0003] However, most actual sewage treatment plants adopt the plug-flow process. After the sewage flows into the biochemical reaction tank, it passes through each baffle in turn, thus forming a plug-flow time delay. The existence of the plug-flow time delay brings certain difficulties to the precise control of the dissolved oxygen concentration. Traditional PID control or nonlinear model predictive control cannot adapt to the above characteristics, which may reduce the system operation performance and sewage treatment efficiency or even damage the stability of the closed-loop system. How to design an effective controller for the control problems brought by the time-delay characteristics of urban sewage treatment process variables to achieve stable and efficient control of the urban sewage treatment process, and then ensure the effluent water quality is an urgent problem to be solved.

[0004] The present invention designs a method for adaptive sliding mode control of dissolved oxygen concentration based on event-triggered identification, establishes a dissolved oxygen concentration model for urban sewage treatment process with a delay disturbance term, designs a model parameter identification method based on event-triggered recursive least squares method, and designs an adaptive sliding mode controller to achieve stable control of the dissolved oxygen concentration in the urban sewage treatment process. Summary of the Invention

[0005] 1. A method for adaptive sliding mode control of dissolved oxygen concentration based on event-triggered identification, which establishes a dissolved oxygen concentration model for urban sewage treatment process with a delay disturbance term, constructs an event-triggered recursive least squares model parameter identification strategy, designs an adaptive sliding mode controller to achieve stable control of the dissolved oxygen concentration in the urban sewage treatment process; characterized in that it includes the following steps:

[0006] (1) Establish a dissolved oxygen concentration model for the urban sewage treatment process with a delayed disturbance term

[0007]

[0008] where represents the change in the dissolved oxygen concentration in the fifth zone of the biochemical reaction tank at time t; x(t) represents the dissolved oxygen concentration in the fifth zone of the biochemical reaction tank at time t; u(t) represents the oxygen transfer coefficient at time t; z(t - τ) represents the dissolved oxygen concentration in the fourth zone of the biochemical reaction tank at time t - τ; τ represents the time for sewage to flow from the fourth zone to the fifth zone of the biochemical reaction tank; f1(t) represents the unknown parameter of the state variable at time t; f2(t) represents the unknown parameter of the control variable at time t; g(t) is the unknown parameter of the lag disturbance variable at time t;

[0009] (2) Construct an event-triggered recursive least squares model parameter identification strategy to calculate the unknown parameters of the dissolved oxygen concentration model represents the estimated parameter matrix at time t, represents the estimated value of f1(t) at time t, represents the estimated value of f2(t) at time t, represents the estimated value of g(t) at time t, and T represents the transpose of the matrix;

[0010] Calculate the model fitness ε(t) at time t

[0011]

[0012] where || represents the absolute value operation, and x d (t) represents the set value of the dissolved oxygen concentration in the fifth zone of the biochemical reaction tank at time t, and x d (t) = 2 mg / L;

[0013] If ε(t) > ε0 holds, where ε0 is the triggering threshold and ε0 ∈ [0, 0.2], then parameter identification is triggered at time t. K sets of samples are used to identify the unknown parameters at time t, K ∈ [150, 300], k = 1, 2,..., K, and calculate the estimated parameter matrix of the k-th sample at time t

[0014]

[0015] where represents the estimated parameter matrix of the k-th sample at time t, represents the estimated value of f1(t) of the k-th sample at time t, represents the estimated value of f2(t) of the k-th sample at time t, represents the estimated value of g(t) of the k-th sample at time t; Denote the estimated parameter matrix of the (k - 1)-th sample at time t; Denote the estimated value of f1(t) of the (k - 1)-th sample at time t, Denote the estimated value of f2(t) of the (k - 1)-th sample at time t, Denote the estimated value of g(t) of the (k - 1)-th sample at time t; Denote the change in the dissolved oxygen concentration in the fifth partition of the k-th sample at time t, h k (t)=[x k (t), u k (t), z k-τ (t)] denote the observation data matrix of the k-th sample at time t, x k (t) denote the dissolved oxygen concentration value in the fifth partition of the k-th sample at time t, u k (t) denote the oxygen transfer coefficient value of the k-th sample at time t, z k (t - τ) denote the dissolved oxygen concentration value in the fourth partition of the biochemical reaction pool of the k-th sample at time t - τ, Q k (t) denote the gain vector of the k-th sample at time t:

[0016]

[0017] where P k-1 (t) denote the covariance matrix of the (k - 1)-th sample at time t, h k (t) denote the observation data matrix of the k-th sample at time t, -1 denote the inverse of the matrix, and the covariance matrix P of the k-th sample at time t k (t) is calculated as follows

[0018]

[0019] where I denote the 3×3 identity matrix; when k = K

[0020]

[0021] (3) Design an adaptive sliding mode controller based on event-triggered identification to stably control the dissolved oxygen concentration in the urban sewage treatment process, specifically

[0022] ① Let t = 1, ε0 = 0.025, K = 200;

[0023] ② Calculate the control error e(t) at time t

[0024] e(t)=x(t)-x d (t) (7)

[0025] where x d (t) denote the set value of the dissolved oxygen concentration in the fifth partition of the biochemical reaction pool at time t;

[0026] ③ Calculate the sliding mode surface S(t) at time t

[0027]

[0028] where e(t) represents the control error at time t;

[0029] ④ Calculate the model fitness ε(t) at time t

[0030]

[0031] ⑤ Judge whether ε(t)>ε0 holds. If it holds, take k = 1 and execute steps ⑥ - ⑦. If it does not hold, directly go to step ⑧;

[0032] ⑥ Calculate the estimated parameter matrix of the k - th sample at time t As shown in formulas (3) - (5);

[0033] ⑦ Judge whether k<K holds. If it holds, increase the value of k by 1 and go to step ⑥. If it does not hold, then let and go to step ⑧;

[0034] ⑧ Calculate the adaptive sliding mode control law u(t) at time t

[0035]

[0036] where sgn() represents the sign function, indicating the positive and negative sign of the sliding mode surface S(t); n(t) represents the adaptive gain coefficient at time t, and is calculated as follows

[0037]

[0038]

[0039] where n(t - 1) represents the adaptive gain coefficient at time t - 1, represents the change amount of the adaptive gain coefficient at time t, e(t) represents the control error at time t, u(t) represents the oxygen transfer coefficient at time t, and S(t) represents the sliding mode surface at time t;

[0040] ⑨ Judge whether t<200 holds. If it holds, increase the value of t by 1 and go to step ②. If it does not hold, end the loop;

[0041] (4) The input of the dissolved oxygen concentration adaptive sliding mode control system based on event - triggered identification is the oxygen transfer coefficient u(t), and the output is the dissolved oxygen concentration x(t) in the fifth partition of the biochemical reaction tank in the urban sewage treatment process. Use the obtained oxygen transfer coefficient u(t) to control the dissolved oxygen concentration x(t) in the fifth partition of the biochemical reaction tank in the urban sewage treatment process.

[0042] The creativity of the present invention is mainly reflected in:

[0043] (1) Aiming at the problem that it is difficult to accurately establish a dissolved oxygen concentration model in the urban sewage treatment process due to the plug flow time delay, the present invention establishes a dissolved oxygen concentration model for the urban sewage treatment process with a delay disturbance term, and designs an event-triggered recursive least squares method to identify the model parameters, laying a foundation for the controller design;

[0044] (2) Aiming at the problem that it is difficult to stably control the dissolved oxygen concentration affected by the time delay disturbance in the urban sewage treatment process, the present invention designs an adaptive sliding mode controller to achieve the stable control of the dissolved oxygen concentration in the urban sewage treatment process;

[0045] It should be particularly noted that for the convenience of description, the present invention adopts the control of the dissolved oxygen concentration. Similarly, the present invention can also be applied to the control of ammonia nitrogen in the sewage treatment process, etc. As long as the principle of the present invention is adopted for control, it should fall within the scope of the present invention. Description of the Drawings

[0046] Figure 1 is the control structure diagram of the present invention

[0047] Figure 2 is the event trigger result diagram of the present invention

[0048] Figure 3 is the dissolved oxygen concentration control result diagram of the present invention

[0049] Figure 4 is the dissolved oxygen concentration control result error diagram of the present invention Detailed Embodiments

[0050] 1. A method for adaptive sliding mode control of dissolved oxygen concentration based on event-triggered identification, which establishes a dissolved oxygen concentration model for the urban sewage treatment process with a delay disturbance term, constructs an event-triggered recursive least squares model parameter identification strategy, designs an adaptive sliding mode controller, and realizes the stable control of the dissolved oxygen concentration in the urban sewage treatment process; it is characterized by including the following steps:

[0051] (1) Establish a dissolved oxygen concentration model for the urban sewage treatment process with a delay disturbance term

[0052]

[0053] Wherein Denote the change in the dissolved oxygen concentration in the fifth zone of the biochemical reaction tank at time t; x(t) represents the dissolved oxygen concentration in the fifth zone of the biochemical reaction tank at time t; u(t) represents the oxygen transfer coefficient at time t; z(t - τ) represents the dissolved oxygen concentration in the fourth zone of the biochemical reaction tank at time t - τ; τ represents the time for sewage to flow from the fourth zone to the fifth zone of the biochemical reaction tank; f1(t) represents the unknown parameter of the state variable at time t; f2(t) represents the unknown parameter of the control variable at time t; g(t) is the unknown parameter of the lag disturbance variable at time t;

[0054] (2) Construct an event-triggered recursive least squares model parameter identification strategy to calculate the unknown parameters of the dissolved oxygen concentration model Denote the estimated parameter matrix at time t, Denote the estimated value of f1(t) at time t, Denote the estimated value of f2(t) at time t, Denote the estimated value of g(t) at time t, T represents the transpose of the matrix;

[0055] Calculate the model fitness ε(t) at time t

[0056]

[0057] where || represents the absolute value operation, x d (t) represents the set value of the dissolved oxygen concentration in the fifth zone of the biochemical reaction tank at time t, x d (t) = 2 mg / L;

[0058] If ε(t) > ε0 holds, where ε0 is the trigger threshold and ε0 ∈ [0, 0.2], then parameter identification is triggered at time t, and K sets of samples are used to identify the unknown parameters at time t, K ∈ [150, 300], k = 1, 2,..., K, and calculate the estimated parameter matrix of the k-th sample at time t

[0059]

[0060] where Denote the estimated parameter matrix of the k-th sample at time t, Denote the estimated value of f1(t) of the k-th sample at time t, Denote the estimated value of f2(t) of the k-th sample at time t, Denote the estimated value of g(t) of the k-th sample at time t; Denote the estimated parameter matrix of the (k - 1)-th sample at time t; Denote the estimated value of f1(t) of the (k - 1)-th sample at time t, Denote the estimated value of f2(t) of the (k - 1)-th sample at time t, Denotes the estimated value of the (k - 1)-th sample g(t) at time t; Denotes the change in the dissolved oxygen concentration in the fifth partition of the k-th sample at time t, h k (t)=[x k (t), u k (t), z k-τ (t)] Denotes the observation data matrix of the k-th sample at time t, x k (t) Denotes the dissolved oxygen concentration value in the fifth partition of the k-th sample at time t, u k (t) Denotes the oxygen transfer coefficient value of the k-th sample at time t, z k (t - τ) Denotes the dissolved oxygen concentration value in the fourth partition of the biochemical reaction tank of the k-th sample at time t - τ, Q k (t) Denotes the gain vector of the k-th sample at time t:

[0061]

[0062] Where P k-1 (t) Denotes the covariance matrix of the (k - 1)-th sample at time t, h k (t) Denotes the observation data matrix of the k-th sample at time t, -1 denotes the inverse of the matrix, and the covariance matrix P of the k-th sample at time t k (t) is calculated as follows

[0063]

[0064] Where I denotes the 3×3 identity matrix; when k = K

[0065]

[0066] (3) Design an adaptive sliding mode controller based on event-triggered identification to stably control the dissolved oxygen concentration in the urban sewage treatment process, specifically

[0067] ① Let t = 1, ε0 = 0.025, K = 200;

[0068] ② Calculate the control error e(t) at time t

[0069] e(t)=x(t)-x d (t) (19)

[0070] Where x d (t) Denotes the set value of the dissolved oxygen concentration in the fifth partition of the biochemical reaction tank at time t;

[0071] ③ Calculate the sliding mode surface S(t) at time t

[0072]

[0073] where \(e(t)\) represents the control error at time \(t\);

[0074] ④ Calculate the model fitness \(\varepsilon(t)\) at time \(t\)

[0075]

[0076] ⑤ Determine whether \(\varepsilon(t)>\varepsilon_0\) holds. If it holds, then set \(k = 1\) and execute steps ⑥ - ⑦. If it does not hold, then directly go to step ⑧;

[0077] ⑥ Calculate the estimated parameter matrix of the \(k\)-th sample at time \(t\) as shown in formulas (3) - (5);

[0078] ⑦ Determine whether \(k < K\) holds. If it holds, then increment the value of \(k\) by 1 and go to step ⑥. If it does not hold, then set and go to step ⑧;

[0079] ⑧ Calculate the adaptive sliding mode control law \(u(t)\) at time \(t\)

[0080]

[0081] where \(\text{sgn}()\) represents the sign function, indicating the positive and negative signs of the sliding mode surface \(S(t)\); \(n(t)\) represents the adaptive gain coefficient at time \(t\), and is calculated as follows

[0082]

[0083]

[0084] where \(n(t - 1)\) represents the adaptive gain coefficient at time \(t - 1\), represents the change in the adaptive gain coefficient at time \(t\), \(e(t)\) represents the control error at time \(t\), \(u(t)\) represents the oxygen transfer coefficient at time \(t\), and \(S(t)\) represents the sliding mode surface at time \(t\);

[0085] ⑨ Determine whether \(t < 200\) holds. If it holds, then increment the value of \(t\) by 1 and go to step ②. If it does not hold, then end the loop;

[0086] (4) The input of the dissolved oxygen concentration adaptive sliding mode control system based on event - triggered identification is the oxygen transfer coefficient \(u(t)\), and the output is the dissolved oxygen concentration \(x(t)\) in the fifth partition of the biochemical reaction pool in the urban sewage treatment process. The dissolved oxygen concentration \(x(t)\) in the fifth partition of the biochemical reaction pool in the urban sewage treatment process is controlled by using the obtained oxygen transfer coefficient \(u(t)\). Figure 2 Show the triggering situation of the system. X - axis: time, unit is days, Y - axis: event triggering situation; Figure 3Display the dissolved oxygen concentration value of the system. X-axis: time, unit is day; Y-axis: dissolved oxygen concentration value, unit is mg / L. The solid line is the expected dissolved oxygen concentration value, and the dashed line is the actual dissolved oxygen concentration value. The error between the actual output dissolved oxygen concentration and the expected dissolved oxygen concentration is as Figure 4 , X-axis: time, unit is day; Y-axis: dissolved oxygen concentration error value, unit is mg / L. The result proves the effectiveness of this method.

Claims

1. An adaptive sliding mode control method for dissolved oxygen concentration based on event-triggered identification, characterized in that, It includes the following steps: (1) Establish a dissolved oxygen concentration model for the urban sewage treatment process with a delay disturbance term Among them represents the change in the dissolved oxygen concentration in the fifth zone of the biochemical reaction tank at time t; x(t) represents the dissolved oxygen concentration in the fifth zone of the biochemical reaction tank at time t; u(t) represents the oxygen transfer coefficient at time t; z(t - τ) represents the dissolved oxygen concentration in the fourth zone of the biochemical reaction tank at time t - τ; τ represents the time for sewage to flow from the fourth zone to the fifth zone of the biochemical reaction tank; f1(t) represents the unknown parameter of the state variable at time t; f2(t) represents the unknown parameter of the control variable at time t; g(t) is the unknown parameter of the lag disturbance variable at time t; (2) Construct a recursive least squares model parameter identification strategy based on event triggering to calculate the unknown parameters of the dissolved oxygen concentration model Denote the estimated parameter matrix at time t, Denote the estimated value of f1(t) at time t, Denote the estimated value of f2(t) at time t, Denote the estimated value of g(t) at time t, where T represents the transpose of the matrix; Calculate the model fitness ε(t) at time t where || represents the absolute value operation, and x d (t) represents the set value of the dissolved oxygen concentration in the fifth partition of the biochemical reaction tank at time t, and x d (t) = 2 mg / L; If ε(t)>ε0 holds, where ε0 is the triggering threshold and ε0∈[0, 0.2], then parameter identification is triggered at time t. K sets of samples are used to identify the unknown parameters at time t, K∈[150, 300], k = 1, 2, …, K, and the estimated parameter matrix of the k-th sample at time t is calculated Among them represents the estimated parameter matrix of the k-th sample at time t, represents the estimated value of f1(t) of the k-th sample at time t, represents the estimated value of f2(t) of the k-th sample at time t, represents the estimated value of g(t) of the k-th sample at time t; represents the estimated parameter matrix of the (k - 1)-th sample at time t; represents the estimated value of f1(t) of the (k - 1)-th sample at time t, represents the estimated value of f2(t) of the (k - 1)-th sample at time t, represents the estimated value of g(t) of the (k - 1)-th sample at time t; represents the change in the dissolved oxygen concentration in the fifth partition of the k-th sample at time t, h k (t) = [x k (t), u k (t), z k-τ (t)] represents the observation data matrix of the k-th sample at time t, x k (t) represents the dissolved oxygen concentration value in the fifth partition of the k-th sample at time t, u k (t) represents the oxygen transfer coefficient value of the k-th sample at time t, z k (t - τ) represents the dissolved oxygen concentration value in the fourth partition of the biochemical reaction tank of the k-th sample at time t - τ, Q k (t) represents the gain vector of the k-th sample at time t: where P k-1 (t) represents the covariance matrix of the (k - 1)-th sample at time t, and h k (t) represents the observation data matrix of the k-th sample at time t, -1 represents the inverse of the matrix, and the covariance matrix P k (t) is calculated as follows where I represents the 3×3 identity matrix; when k = K (3) Design an adaptive sliding mode controller based on event-triggered identification to stably control the dissolved oxygen concentration in the urban sewage treatment process, specifically ① Let t = 1, ε0 = 0.025, K = 200; ② Calculate the control error e(t) at time t e(t) = x(t) - x d (t) (7) where x d (t) represents the set value of the dissolved oxygen concentration in the fifth zone of the biochemical reaction tank at time t; ③ Calculate the sliding mode surface S(t) at time t where e(t) represents the control error at time t; ④ Calculate the model fitness ε(t) at time t ⑤ Judge whether ε(t)>ε0 holds. If it holds, let k = 1 and execute steps ⑥-⑦. If it does not hold, directly go to step ⑧; ⑥ Calculate the estimated parameter matrix of the k-th sample at time t As shown in formulas (3)-(5); ⑦ Determine whether k < K holds. If it holds, increment the value of k by 1 and go to step ⑥. If it does not hold, then go to step ⑧; ⑧ Calculate the adaptive sliding mode control law u(t) at time t where sgn() represents the sign function, indicating the positive and negative sign of the sliding mode surface S(t); n(t) represents the adaptive gain coefficient at time t, and is calculated as follows where n(t - 1) represents the adaptive gain coefficient at time t - 1, represents the change in the adaptive gain coefficient at time t, e(t) represents the control error at time t, u(t) represents the oxygen transfer coefficient at time t, and S(t) represents the sliding mode surface at time t; ⑨ Judge whether t<200 holds. If it holds, let the value of t increase by 1 and go to step ②. If it does not hold, end the loop; (4) The input of the adaptive sliding mode control system for dissolved oxygen concentration based on event-triggered identification is the oxygen transfer coefficient u(t), and the output is the dissolved oxygen concentration x(t) in the fifth partition of the biochemical reaction tank in the urban sewage treatment process. Use the obtained oxygen transfer coefficient u(t) to control the dissolved oxygen concentration x(t) in the fifth partition of the biochemical reaction tank in the urban sewage treatment process.

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