A Non-uniform Sampling Model Predictive Control Method for Urban Sewage Treatment Process

Abstract

The present invention proposes a non-uniform sampling model predictive control method for the urban sewage treatment process, realizing the stable control of the dissolved oxygen concentration in the non-uniform sampling of the urban sewage treatment process. A linear polyhedron approximation kinetic equation for the dissolved oxygen concentration is constructed, the kinetic characteristics of the dissolved oxygen concentration change are extracted by using non-uniform sampling data, and a non-uniform sampling model predictive controller is designed, solving the problem that it is difficult to stably control the dissolved oxygen concentration in the non-uniform sampling of 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] The present invention designs a non-uniform sampling model predictive controller, realizing the stable control of the dissolved oxygen concentration in the non-uniform sampling process of urban sewage treatment. 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] Urban sewage treatment is a measure taken to change the nature of sewage so that it does not harm the environmental water area, and is an important way to solve the problem of urban water pollution. The activated sludge process is one of the most widely used sewage treatment processes. The size of the dissolved oxygen concentration in the aerobic zone of the activated sludge process can not only directly affect the metabolism of microorganisms, but also indirectly reflect the concentration of influent organic matter, having an important impact on the entire reaction process. Therefore, the accurate control of the dissolved oxygen concentration is the key to ensuring the effluent quality of the sewage treatment plant. The level of dissolved oxygen is mainly controlled by the amount of aeration, so the control of the amount of aeration can be realized according to the concentration and change of the dissolved oxygen.

[0003] Most traditional urban sewage treatment process control systems assume that the dissolved oxygen concentration is periodically sampled, that is, the sampling interval is a fixed constant, which greatly simplifies the analysis of the system. However, in the actual urban sewage treatment process system, objective reasons such as hardware device limitations or environmental factor impacts will lead to passive non-periodic sampling, which 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 non-uniform sampling in the urban sewage treatment process to achieve stable and efficient control of the urban sewage treatment process and then ensure the effluent quality is an urgent problem to be solved.

[0004] The present invention designs a non-uniform sampling model predictive control method for the urban sewage treatment process, constructs a local linear approximation kinetic equation of the dissolved oxygen concentration, extracts the kinetic characteristics of the dissolved oxygen concentration based on the polyhedron approximation method, and designs a non-uniform sampling model predictive controller, realizing the stable control of the dissolved oxygen concentration in the urban sewage treatment process. Summary of the Invention

[0005] A non-uniform sampling model predictive control method for the urban sewage treatment process, constructing a linear polyhedron approximation kinetic equation of the dissolved oxygen concentration in the urban sewage treatment process, designing a non-uniform sampling model predictive controller, and realizing the stable control of the dissolved oxygen concentration in the urban sewage treatment process; characterized by including the following steps:

[0006] (1)Construct the linear polyhedron approximation kinetic equation of the dissolved oxygen concentration in the urban sewage treatment process

[0007] The sampling interval of the dissolved oxygen concentration at the k-th sampling in the urban sewage treatment process is defined as ρ k , ρ k =t k -t k-1 , ρ k ∈[4.5, 10.5], with the unit of minutes; t k represents the k-th sampling time, t k-1 represents the (k - 1)-th sampling time; x k represents the dissolved oxygen concentration at time t k , with the unit of mg / L, x0 = 0 mg / L; u k represents the oxygen transfer coefficient at time t k , which is calculated by the non-uniform sampling model predictive controller, u0 = 84;

[0008] Construct the linearized kinetic equation of the dissolved oxygen concentration

[0009]

[0010] where x k is the dissolved oxygen concentration at time t k , x k-1 is the dissolved oxygen concentration at time t k-1 ; u k-1 is the oxygen transfer coefficient at time t k-1 ; A xk is the state coefficient of the linearized kinetic equation of the dissolved oxygen concentration at time t k , B xk is the input coefficient of the linearized kinetic equation of the dissolved oxygen concentration at time t k , c xk is the compensation term of the linearized kinetic equation of the dissolved oxygen concentration at time t k , which is used to compensate for the error caused by linearization

[0011]

[0012] Construct the linear polyhedron approximation kinetic equation of the dissolved oxygen concentration

[0013]

[0014] where x k ′ is the output of the linear polyhedron approximation kinetic equation of the dissolved oxygen concentration at time t k , x′ k-1 is the output of the linear polyhedron approximation kinetic equation of the dissolved oxygen concentration at time t k-1 , with the unit of mg / L, x0′ = 0 mg / L; [Axk,d (ρ k ), B xk,d (ρ k )] ∈ Ω, where Ω is a polyhedral constraint set defined as follows

[0015]

[0016] where v is an intermediate variable;

[0017] (2) Design a non-uniform sampling model predictive controller

[0018] ① Let k = 1, x0 = 0 mg / L, u0 = 84;

[0019] ② Judge whether k < 120 holds. If it holds, go to step ③; if not, go to step ④;

[0020] ③ If k = 1, then u k = u k-1 + 11.1e k-1 , go to step ⑦; if k = 2, then u k = u k-1 + 11.1e k-1 - 11.2e k-2 , go to step ⑦; if k > 2, then u k = u k-1 + 11.1e k-1 - 11.2e k-2 + 0.6e k-3 , and go to step ⑦; where e k-1 = x k-1 - r k-1 is the error between the actual dissolved oxygen concentration and the set value of the dissolved oxygen concentration at time t k-1 , e k-2 = x k-2 - r k-2 is the error between the actual dissolved oxygen concentration and the set value of the dissolved oxygen concentration at time t k-2 , e k-3 = x k-3 - r k-3 is the error between the actual dissolved oxygen concentration and the set value of the dissolved oxygen concentration at time t k-3 ;

[0021] ④ Construct an optimal steady-state problem to make the output of the linear polyhedral approximation kinetic equation of the dissolved oxygen concentration track the set value of the dissolved oxygen concentration, form a quadratic programming (5), and solve for the optimal parameter vector β k at time t k , the oxygen transfer coefficient at the optimal steady-state equilibrium point and the dissolved oxygen concentration at the optimal steady-state equilibrium point

[0022]

[0023] Constraint conditions

[0024] where min represents the function for solving the minimum value; r k is the set value of the dissolved oxygen concentration at time t, with the unit of milligram per liter; 1 k is an 81-dimensional column vector with all elements being 1; β 81 is the 81-dimensional parameter vector at time t k is the 40-dimensional column vector with all elements being k ; u s is the 40-dimensional column vector with all elements being ; x s is the 40-dimensional column vector with all elements being ; is the oxygen transfer coefficient at the equilibrium point of the linear polyhedron approximation kinetic equation (3) of the dissolved oxygen concentration at time t k , is the dissolved oxygen concentration at the equilibrium point of the linear polyhedron approximation kinetic equation (3) of the dissolved oxygen concentration at time t k , 0 ≤ u s ≤ 240; T represents the transpose of a matrix; H 40 (u k-120 ,..., u k-1 ) and H 40 (x′ k-120 ,..., x′ k-1 ) are

[0025]

[0026]

[0027] where u k-q is the oxygen transfer coefficient at time t k-q , x′ k-q is the output of the linear polyhedron approximation kinetic equation of the dissolved oxygen concentration at time t k-q , q = 1,..., 120;

[0028] ⑤ Construct an optimal control problem to make the actual dissolved oxygen concentration track the set value of the dissolved oxygen concentration, form a quadratic programming (8), and solve for the optimal parameter vector α k at time t k , the optimal control law and the optimal predicted output

[0029]

[0030] Constraint conditions

[0031] where min represents the function for solving the minimum value; r k is the set value of the dissolved oxygen concentration at time t k ; is the predicted control input vector at time t k ; is the predicted control output vector at time t k ; α k is the 81-dimensional parameter vector at time t k ; H 40 (x k-120 ,..., x k-1 ) is

[0032]

[0033] where u k-q is the actual oxygen transfer coefficient at time t k-q , x k-q is the actual dissolved oxygen concentration at time t k-q , q = 1,..., 120;

[0034] ⑥ Let u k be equal to the first element of

[0035] ⑦ Calculate the output x k ' of the linear polyhedron approximation kinetic equation of the dissolved oxygen concentration according to formula (3);

[0036] ⑧ Judge whether k < 1000 holds. If it holds, increase the value of k by 1 and go to step ②. If it does not hold, end the loop;

[0037] (3) Stable control of the dissolved oxygen concentration in the urban sewage treatment process

[0038] The input of the non-uniform sampling model predictive control system for the urban sewage treatment process is the oxygen transfer coefficient u k , and the output is the dissolved oxygen concentration x k in the fifth partition of the biochemical reaction tank in the urban sewage treatment process. The oxygen transfer coefficient u k obtained by solving with the non-uniform sampling model predictive controller is used to control the dissolved oxygen concentration x k in the fifth partition of the biochemical reaction tank in the urban sewage treatment process.

[0039] The creativity of the present invention is mainly reflected in:

[0040] (1) The present invention addresses the problem of difficulty in constructing a model caused by non-uniform sampling of the dissolved oxygen concentration during the urban sewage treatment process. It constructs a linear polyhedron approximation kinetic equation for the dissolved oxygen concentration, extracts the kinetic characteristics of the dissolved oxygen concentration change using non-uniform sampling data, and lays a foundation for the design of the controller;

[0041] (2) The present invention addresses the problem of difficulty in stable control caused by non-uniform sampling of the dissolved oxygen concentration during the urban sewage treatment process. It designs a non-uniform sampling model predictive controller and realizes the stable control of the dissolved oxygen concentration during the urban sewage treatment process;

[0042] It should be noted particularly 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 during the sewage treatment process, etc. As long as the control principle of the present invention is adopted, it should fall within the scope of the present invention. Description of the Drawings

[0043] Figure 1 is the control result diagram of the dissolved oxygen concentration of the present invention

[0044] Figure 2 is the control result error diagram of the dissolved oxygen concentration of the present invention

[0045] Figure 3 is the result diagram of the oxygen transfer coefficient of the present invention Detailed Embodiments

[0046] A non-uniform sampling model predictive control method for the urban sewage treatment process constructs a linear polyhedron approximation kinetic equation for the dissolved oxygen concentration in the urban sewage treatment process, designs a non-uniform sampling model predictive controller, and realizes the stable control of the dissolved oxygen concentration in the urban sewage treatment process; characterized by including the following steps:

[0047] (1) Construct a linear polyhedron approximation kinetic equation for the dissolved oxygen concentration in the urban sewage treatment process

[0048] The sampling interval of the dissolved oxygen concentration at the k-th sampling in the urban sewage treatment process is defined as ρ k , ρ k =t k -t k-1 , ρ k ∈[4.5, 10.5], with the unit of minute; t k represents the k-th sampling moment, t k-1 represents the (k - 1)-th sampling moment; x k represents the dissolved oxygen concentration at the moment of t k , with the unit of mg / L, x0 = 0 mg / L; u k represents the oxygen transfer coefficient at the moment of t k , which is calculated by the non-uniform sampling model predictive controller, u0 = 84;

[0049] Construct a linearized kinetic equation for dissolved oxygen concentration

[0050]

[0051] where x k is the dissolved oxygen concentration at time t k x k-1 is the dissolved oxygen concentration at time t k-1 ; u k-1 is the oxygen transfer coefficient at time t k-1 ; A xk is the state coefficient of the linearized kinetic equation for dissolved oxygen concentration at time t k , B xk is the input coefficient of the linearized kinetic equation for dissolved oxygen concentration at time t k , c xk is the compensation term of the linearized kinetic equation for dissolved oxygen concentration at time t k , used to compensate for the error generated by linearization

[0052]

[0053] Construct a linear polyhedron approximation kinetic equation for dissolved oxygen concentration

[0054]

[0055] where x k ′ is the output of the linear polyhedron approximation kinetic equation for dissolved oxygen concentration at time t k , x′ k-1 is the output of the linear polyhedron approximation kinetic equation for dissolved oxygen concentration at time t k-1 , with the unit of mg / L, x0′ = 0 mg / L; [A xk,d (ρ k ), B xk,d (ρ k )] ∈ Ω, where Ω is defined as the polyhedron constraint set as follows

[0056]

[0057] where v is an intermediate variable

[0058] (2) Design a non-uniform sampling model predictive controller

[0059] ① Let k = 1, x0 = 0 mg / L, u0 = 84

[0060] ② Judge whether k < 120 holds. If it holds, go to step ③; if not, go to step ④

[0061] ③ If k = 1, then u k = uk-1 +11.1e k-1 , go to step ⑦; if k = 2, then u k = u k-1 +11.1e k-1 -11.2e k-2 , go to step ⑦; if k > 2, then u k = u k-1 +11.1e k-1 -11.2e k-2 +0.6e k-3 , and go to step ⑦; where e k-1 = x k-1 - r k-1 is the error between the actual dissolved oxygen concentration and the set value of the dissolved oxygen concentration at time t, e k-1 = x k-2 = x k-2 - r k-2 is the error between the actual dissolved oxygen concentration and the set value of the dissolved oxygen concentration at time t, e k-2 = x k-3 = x k-3 - r k-3 is the error between the actual dissolved oxygen concentration and the set value of the dissolved oxygen concentration at time t k-3 ;

[0062] ④ Construct the optimal steady-state problem to make the linear polyhedron approximation kinetic equation of the dissolved oxygen concentration track the set value of the dissolved oxygen concentration, form the quadratic programming (5), and solve the optimal parameter vector β k at time t k , the oxygen transfer coefficient at the optimal steady-state equilibrium point and the dissolved oxygen concentration at the optimal steady-state equilibrium point

[0063]

[0064] Constraint conditions

[0065] where min represents the function to solve the minimum value; r k is the set value of the dissolved oxygen concentration at time t k , in milligrams per liter; 1 81 is an 81-dimensional column vector with all elements being 1; β k is an 81-dimensional parameter vector at time t k ; u s is a 40-dimensional column vector with all elements being ; x s is a 40-dimensional column vector with all elements being ; is at time t kOxygen transfer coefficient at the equilibrium point of the linear polyhedron approximation kinetic equation (3) of the dissolved oxygen concentration at a certain moment is t k Dissolved oxygen concentration at the equilibrium point of the linear polyhedron approximation kinetic equation (3) of the dissolved oxygen concentration at a certain moment, 0 ≤ u s ≤ 240; T represents the transpose of a matrix; H 40 (u k-120 ,..., u k-1 ) and H 40 (x′ k-120 ,..., x′ k-1 ) are

[0066]

[0067]

[0068] where u k-q is the oxygen transfer coefficient at time t k-q , x′ k-q is the output of the linear polyhedron approximation kinetic equation of the dissolved oxygen concentration at time t k-q , q = 1,..., 120;

[0069] ⑤ Construct an optimal control problem to make the actual dissolved oxygen concentration track the set value of the dissolved oxygen concentration, form a quadratic programming (8), and solve for the optimal parameter vector α k at time t k , the optimal control law and the optimal prediction output

[0070]

[0071] Constraint conditions

[0072] where min represents the function to solve the minimum value; r k is the set value of the dissolved oxygen concentration at time t k ; is the predicted control input vector at time t k , is the predicted control output vector at time t k ; α k is the 81-dimensional parameter vector at time t k ; H 40 (x k-120 ,..., x k-1 ) are

[0073]

[0074] where uk-q For t k-q Actual oxygen transfer coefficient at time t, x k-q For t k-q Actual dissolved oxygen concentration at time t, q = 1, ..., 120;

[0075] ⑥ Let u k be equal to the first element of

[0076] ⑦ Calculate the output x' of the linear polyhedron approximation kinetic equation of dissolved oxygen concentration according to formula (3) k ;

[0077] ⑧ Judge whether k < 1000 holds. If it holds, increase the value of k by 1 and go to step ②. If it does not hold, end the loop;

[0078] (3) Stable control of dissolved oxygen concentration in urban sewage treatment process

[0079] The input of the non-uniform sampling model predictive control system for the urban sewage treatment process is the oxygen transfer coefficient u k , and the output is the dissolved oxygen concentration x in the fifth partition of the biochemical reaction tank in the urban sewage treatment process k . Use the oxygen transfer coefficient u obtained by solving the non-uniform sampling model predictive controller k to control the dissolved oxygen concentration x in the fifth partition of the biochemical reaction tank in the urban sewage treatment process k . Figure 1 Display the dissolved oxygen concentration value of the system. X-axis: time, unit is minute. 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 2 , X-axis: time, unit is minute. Y-axis: dissolved oxygen concentration error value, unit is mg / L; Figure 3 Display the oxygen transfer coefficient value. X-axis: time, unit is minute. Y-axis: oxygen transfer coefficient value. The results prove the effectiveness of this method.

Claims

1. A non-uniform sampling model predictive control method for urban sewage treatment process, characterized in that, Including the following steps: (1) Construct a linear polyhedron approximation kinetic equation for the dissolved oxygen concentration in the urban sewage treatment process The sampling interval for the k-th sampling of the dissolved oxygen concentration in the urban sewage treatment process is defined as ρ k , ρ k = t k - t k-1 , ρ k ∈ [4.5, 10.5], in minutes; t k represents the k-th sampling time, t k-1 represents the (k - 1)-th sampling time; x k represents the dissolved oxygen concentration at time t k , in mg / L, x0 = 0 mg / L; u k represents the oxygen transfer coefficient at time t k , calculated by the non-uniform sampling model predictive controller, u0 = 84; Construct a linearized kinetic equation for the dissolved oxygen concentration where x k is the dissolved oxygen concentration at time t k ; x k-1 is the dissolved oxygen concentration at time t k-1 ; u k-1 is the oxygen transfer coefficient at time t k-1 ; A xk is the state coefficient of the linearized kinetic equation of the dissolved oxygen concentration at time t k ; B xk is the input coefficient of the linearized kinetic equation of the dissolved oxygen concentration at time t k ; c xk is the compensation term of the linearized kinetic equation of the dissolved oxygen concentration at time t k , which is used to compensate for the error caused by linearization Construct a linear polyhedron approximation kinetic equation for the dissolved oxygen concentration where x k ′ is the output of the linear polyhedron approximation kinetic equation of the dissolved oxygen concentration at time t, x′ k is the output of the linear polyhedron approximation kinetic equation of the dissolved oxygen concentration at time t, with the unit of milligram per liter, x0′ = 0 mg / L; [A k-1 is t k-1 is the output of the linear polyhedron approximation kinetic equation of the dissolved oxygen concentration at time t, with the unit of milligram per liter, x0′ = 0 mg / L; [A xk,d (ρ k ), B xk,d (ρ k )] ∈ Ω, where Ω is the polyhedron constraint set defined as follows where v is an intermediate variable; (2) Design a non-uniform sampling model predictive controller ① Let k = 1, x0 = 0 mg / L, u0 = 84; ② Judge whether k < 120 holds. If it holds, go to step ③; if it does not hold, go to step ④; ③ If k = 1, then u k = u k-1 + 11.1e k-1 , go to step ⑦; if k = 2, then u k = u k-1 + 11.1e k-1 - 11.2e k-2 , go to step ⑦; if k > 2, then u k = u k-1 + 11.1e k-1 - 11.2e k-2 + 0.6e k-3 , and go to step ⑦; where e k-1 = x k-1 - r k-1 is the error between the actual dissolved oxygen concentration and the set value of the dissolved oxygen concentration at time t k-1 , e k-2 = x k-2 - r k-2 is the error between the actual dissolved oxygen concentration and the set value of the dissolved oxygen concentration at time t k-2 , e k-3 = x k-3 - r k-3 is the error between the actual dissolved oxygen concentration and the set value of the dissolved oxygen concentration at time t k-3 ; ④Construct the optimal steady-state problem to make the dissolved oxygen concentration linearly approximate the kinetic equation output to track the set value of the dissolved oxygen concentration, form formula (5), and solve for t k The optimal parameter vector β at the moment k , the oxygen transfer coefficient at the optimal steady-state equilibrium point and the dissolved oxygen concentration at the optimal steady-state equilibrium point Constraints where min represents the function for solving the minimum value; r k is the set value of the dissolved oxygen concentration at time t, with the unit of milligram per liter; 1 k is an 81-dimensional column vector with all elements being 1; β 81 is the 81-dimensional parameter vector at time t; u k is an k is the 40-dimensional column vector with all elements being s ; x is the 40-dimensional column vector with all elements being s ; ; is the oxygen transfer coefficient at the optimal steady-state equilibrium point of the linear polyhedron approximation kinetic equation (3) of the dissolved oxygen concentration at time t, k is the dissolved oxygen concentration at the optimal steady-state equilibrium point of the linear polyhedron approximation kinetic equation (3) of the dissolved oxygen concentration at time t, 0 ≤ u is the dissolved oxygen concentration at the optimal steady-state equilibrium point of the linear polyhedron approximation kinetic equation (3) of the dissolved oxygen concentration at time t, 0 ≤ u k ≤ 240; T represents the transpose of a matrix; H s ≤ 240; T represents the transpose of a matrix; H 40 (u k-120 ,..., u k-1 ) and H 40 (x′ k-120 ,..., x′ k-1 ) are where u k-q is the oxygen transfer coefficient at time t k-q , x' k-q is the output of the linear polyhedron approximation kinetic equation of the dissolved oxygen concentration at time t k-q , q = 1, ..., 120; ⑤Construct an optimal control problem to make the actual dissolved oxygen concentration track the set value of the dissolved oxygen concentration, form formula (8), and solve for the optimal parameter vector α at time t k at time t k , the optimal control law and the optimal predicted output Constraints where min represents the function for solving the minimum value; r k is the k set value of the dissolved oxygen concentration at time t; is the k predicted control input vector at time t, p = 1, 2,..., 40; is the k predicted control output vector at time t; α k is the k 81 - dimensional parameter vector at time t; H 40 (x k-120 ,..., x k-1 ) is where u k-q is the actual oxygen transfer coefficient at time t k-q , x k-q is the actual dissolved oxygen concentration at time t k-q , q = 1, ..., 120; ⑥ Let u k be equal to the first element of ⑦ Calculate the output x of the linear polyhedron approximation kinetic equation of the dissolved oxygen concentration according to formula (3). k '; ⑧ Judge whether k < 1000 holds. If it holds, increase the value of k by 1 and go to step ②. If it does not hold, end the loop; (3) Stable control of the dissolved oxygen concentration in the urban sewage treatment process The input of the non-uniform sampling model predictive control system for the urban sewage treatment process is the oxygen transfer coefficient u k , and the output is the dissolved oxygen concentration x in the fifth partition of the biochemical reaction tank in the urban sewage treatment process k . The oxygen transfer coefficient u obtained by solving with the non-uniform sampling model predictive controller k controls the dissolved oxygen concentration x in the fifth partition of the biochemical reaction tank in the urban sewage treatment process k .

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