Nonlinear model predictive control method for chemical process based on mechanism model

Abstract

The present invention belongs to the field of industrial automation, and discloses a nonlinear model predictive control method for a chemical process based on a mechanism model. First, the time constant and lag time of the process model are identified according to the collected step response data of the nonlinear chemical process, and then the gain formula is derived in combination with the mechanism model formula of the nonlinear process, and then the model predictive controller of the nonlinear chemical process is designed, and finally the obtained precise optimal control law is implemented in the controlled nonlinear chemical process. The present invention combines the gain parameters of the nonlinear chemical process to accurately derive the model predictive control, avoiding the prediction error caused by the linearization model fitting in the traditional model predictive control, and finally realizing the precise control of the nonlinear chemical process, and further promoting the application and development of the nonlinear model predictive control based on the mechanism model in the chemical process.

Description

Technical Field

[0001] The invention belongs to the field of industrial automation, and in particular relates to a chemical process nonlinear model predictive control method based on a mechanism model. Background Art

[0002] For control loops in chemical processes, many of them are nonlinear processes. When dealing with such objects, traditional model predictive control algorithms usually perform linearization processing near the operating point to achieve the control effect. However, for processes with more serious nonlinearity near the operating point, such linearization processing cannot achieve the expected effect. This is due to the prediction error caused by linearization. For these chemical processes with serious nonlinearity, the model parameter with the most serious nonlinear time-varying is generally the gain. If accurate output prediction and derivation can be performed for the time-varying gain, this will avoid the prediction error caused by linearization fitting, thereby achieving precise control of nonlinear chemical processes and further paving the way for the application and development of nonlinear model predictive control in chemical processes. Summary of the invention

[0003] The present invention aims to provide a nonlinear model predictive control method for chemical processes based on a mechanism model, so as to solve the technical problem that when traditional model predictive control processes nonlinear chemical processes, there are prediction errors caused by linear fitting.

[0004] In order to solve the above technical problems, the specific technical scheme of the chemical process nonlinear model predictive control method based on the mechanism model of the present invention is as follows:

[0005] A chemical process nonlinear model predictive control method based on a mechanism model comprises the following steps:

[0006] Step 1: Collect the step response data of the nonlinear chemical process and fit the two model parameters of the chemical process: time constant and lag time;

[0007] Step 1.1: Add a step signal to the input of the nonlinear chemical process and record the step response data corresponding to the nonlinear chemical process;

[0008] Step 1.2: Collect the step response data y p (k) is converted into the corresponding dimensionless form y p * (k);

[0009] Step 1.3: First select the p * (k 1 )=0.39 and y p * (k 1)=0.63, and then calculate the time constant and lag time of the nonlinear chemical process model.

[0010] Step 1.4: Determine the mechanism model of the nonlinear chemical process and then calculate the real-time gain of the nonlinear chemical process;

[0011] Step 1.5: The final nonlinear chemical process transfer function model is obtained;

[0012] Step 2: Design a nonlinear model predictive controller for a nonlinear chemical process;

[0013] Step 2.1: In the zero-order hold and sampling time T s Under this, the transfer function model conversion of nonlinear chemical process is realized;

[0014] Step 2.2: For the discrete equation, introduce Smith estimation to compensate for the time delay;

[0015] Step 2.3: Based on the process model without time delay, obtain the predicted output of the nonlinear chemical process;

[0016] Step 2.4: Model predictive controller design for nonlinear chemical processes Select the objective function;

[0017] Step 2.5: Derivative the above objective function to obtain the optimal solution of nonlinear model predictive control;

[0018] Step 2.6: Apply the obtained optimal control law u(k) of the nonlinear model predictive control to the nonlinear chemical process, and in the next sampling period, repeat the steps in steps 2.2 to 2.5 to solve the new optimal control law.

[0019] Furthermore, in step 1.2, the collected step response data y p (k) is converted into the corresponding dimensionless form y p * (k), the specific conversion formula is as follows:

[0020] y p * (k) = y p (k) / y f

[0021] Among them, y f is the step response data y of the nonlinear chemical process p (k) is the steady-state value.

[0022] Furthermore, the step 1.3 calculates the time constant and lag time of the nonlinear chemical process model according to the following formula:

[0023] T=2(k2 -k 1 )

[0024] τ=2k 1 -k 2

[0025] Among them, T and τ are the time constant and lag time of the nonlinear chemical process model, respectively.

[0026] Furthermore, the step 1.4 calculates the real-time gain of the nonlinear chemical process according to the following formula:

[0027] y m (k) = f(u(k))

[0028] K(k)=f′(u(k))

[0029] Among them, y m (k) is the model output of the nonlinear chemical process, u(k) is the input of the nonlinear chemical process, K(k) is the real-time gain of the nonlinear chemical process, f and f′ are the mechanism model of the nonlinear chemical process and the corresponding first-order derivative formula, respectively.

[0030] Furthermore, the nonlinear chemical process transfer function model obtained in step 1.5 is:

[0031]

[0032] Wherein, G(k) and s are the real-time transfer function and Laplace operator of the nonlinear chemical process respectively. Further, the step 2.1 is performed at the zero-order holder and the sampling time T s The transfer function model of the nonlinear chemical process is converted to:

[0033] y m (k) = αy m (k-1)+K(k-1)(1-α)u(k-1-d)

[0034] in, Furthermore, the time-delay-free model after compensation in step 2.2 is as follows:

[0035] y mc (k) = αy mc (k-1)+K(k-1)(1-α)u(k-1)

[0036] Among them, y mc (k) is the output of the nonlinear chemical process time-delay-free model after compensation;

[0037] Compensating the actual output of the nonlinear chemical process yields:

[0038] ypc (k) = y p (k)+y mc (k)-y mc (kd)

[0039] Among them, y pc (k) is the actual output of the nonlinear chemical process after compensation.

[0040] Furthermore, the predicted output of the nonlinear chemical process in step 2.3 is derived as follows:

[0041] Y mc (k) = Ay mc (k)+BU(k)

[0042] in,

[0043]

[0044]

[0045] P and M are the prediction time domain and control time domain of model predictive control, respectively, and their values ​​generally satisfy P>M;

[0046] The above prediction output derivation is simplified to

[0047] Y mc (k) = Ay mc (k)+Cφ(k)

[0048] in,

[0049]

[0050] Furthermore, the objective function of the model predictive controller design for the nonlinear chemical process in step 2.4 is selected as follows:

[0051]

[0052] Among them, Q is the weighted matrix of tracking error, e(k) is the compensated prediction error, and

[0053] e(k)=y pc (k)-y mc (k), Y r (k) is the corresponding reference trajectory, and its formula is

[0054]

[0055] y r (k+i)=β i y p (k)+(1-β i )c(k)

[0056] β is the reference trajectory softening coefficient, and c(k) is the set value corresponding to the nonlinear chemical process.

[0057] Furthermore, the step 2.5 derives the objective function of step 2.4 to obtain the optimal solution of the nonlinear model predictive control:

[0058] φ(k)=-(C Τ QC) -1 C Τ Q(Ay mc (k)+e(k)-Y r (k))

[0059] Take the first term of φ(k) 1 ), and then the optimal control law u(k) of nonlinear model predictive control can be obtained by solving the following one-variable multi-time equation:

[0060] f′(u(k))u(k)=φ(k 1 ).

[0061] The nonlinear model predictive control method for chemical processes based on mechanism models of the present invention has the following advantages: the present invention combines the gain parameters of the nonlinear chemical process to accurately derive the model predictive control, thereby avoiding the prediction error caused by linear model fitting in traditional model predictive control, and ultimately achieving precise control of nonlinear chemical processes, and further promoting the application and development of nonlinear model predictive control based on mechanism models in chemical processes. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] none. DETAILED DESCRIPTION

[0063] In order to better understand the purpose, structure and function of the present invention, a nonlinear model predictive control method for a chemical process based on a mechanism model of the present invention is further described in detail below.

[0064] The chemical process nonlinear model predictive control method based on the mechanism model of the present invention comprises the following steps:

[0065] Step 1: Collect the step response data of the nonlinear chemical process and fit the two model parameters of the time constant and lag time of the chemical process, as follows:

[0066] a. Add a step signal to the input of the nonlinear chemical process and record the step response data corresponding to the nonlinear chemical process.

[0067] b. Collect the step response data y p (k) is converted into the corresponding dimensionless form y p* (k), the specific conversion formula is as follows:

[0068] y p * (k) = y p (k) / y f

[0069] Among them, y f is the step response data y of the nonlinear chemical process p (k) is the steady-state value.

[0070] c. First select the one that satisfies y p * (k 1 )=0.39 and y p * (k 1 )=0.63, and then calculate the time constant and lag time of the nonlinear chemical process model according to the following formula.

[0071] T=2(k 2 -k 1 )

[0072] τ=2k 1 -k 2

[0073] Among them, T and τ are the time constant and lag time of the nonlinear chemical process model, respectively.

[0074] d. Determine the mechanism model of the nonlinear chemical process, and then calculate the real-time gain of the nonlinear chemical process according to the following formula. The specific calculation formula is as follows:

[0075] y m (k) = f(u(k))

[0076] K(k)=f′(u(k))

[0077] Among them, y m (k) is the model output of the nonlinear chemical process, u(k) is the input of the nonlinear chemical process, K(k) is the real-time gain of the nonlinear chemical process, f and f′ are the mechanism model of the nonlinear chemical process and the corresponding first-order derivative formula, respectively.

[0078] e. The final nonlinear chemical process transfer function model is:

[0079]

[0080] Among them, G(k) and s are the real-time transfer function and Laplace operator of the nonlinear chemical process respectively. Step 2: Design a nonlinear model predictive controller for the nonlinear chemical process. The specific steps are as follows:

[0081] a. In the zero-order holder and sampling time T s Under this condition, the transfer function model of nonlinear chemical process can be transformed into:

[0082] y m (k) = αy m (k-1)+K(k-1)(1-α)u(k-1-d)

[0083] in,

[0084] b. For the above discrete equation, Smith estimation is introduced to compensate for the time lag. The compensated time-lag-free model is as follows:

[0085] y mc (k) = αy mc (k-1)+K(k-1)(1-α)u(k-1)

[0086] Among them, y mc (k) is the output of the nonlinear chemical process time-delay-free model after compensation.

[0087] Furthermore, compensating the actual output of the nonlinear chemical process yields

[0088] y pc (k) = y p (k)+y mc (k)-y mc (kd)

[0089] Among them, y pc (k) is the actual output of the nonlinear chemical process after compensation.

[0090] c. Based on the process model without time lag, the prediction output of the nonlinear chemical process can be derived as follows:

[0091] Y mc (k) = Ay mc (k)+BU(k)

[0092] in,

[0093]

[0094]

[0095] P and M are the prediction domain and control domain of model predictive control respectively, and their values ​​generally satisfy P>M.

[0096] Furthermore, the above prediction output derivation can be simplified to

[0097] Y mc (k) = Ay mc (k)+Cφ(k)

[0098] in,

[0099]

[0100] d. Model predictive controller design for nonlinear chemical processes selects the following objective function

[0101]

[0102] Where Q is the weighted matrix of the tracking error, e(k) is the compensated prediction error, and here we can take e(k)=y pc (k)-y mc (k) Y r (k) is the corresponding reference trajectory, and its formula is

[0103]

[0104] y r (k+i)=β i y p (k)+(1-β i )c(k)

[0105] β is the reference trajectory softening coefficient, and c(k) is the set value corresponding to the nonlinear chemical process.

[0106] e. Taking the derivative of the above objective function, we can get the optimal solution of nonlinear model predictive control:

[0107] φ(k)=-(C Τ QC) -1 C Τ Q(Ay mc (k)+e(k)-Y r (k))

[0108] Take the first term of φ(k) 1 ), and then the optimal control law u(k) of nonlinear model predictive control can be obtained by solving the following univariate multi-time equation.

[0109] f′(u(k))u(k)=φ(k 1 )

[0110] f. Apply the optimal control law u(k) of the nonlinear model predictive control to the nonlinear chemical process, and in the next sampling period, repeat the steps (b) to (e) to solve the new optimal control law.

[0111] Example:

[0112] Take the melt index control in the polyolefin production process as an example, where the controlled variable is the melt index and the adjustment means is the hydrogen concentration.

[0113] Step 1: Collect the step response data of the polyolefin production process and fit the two model parameters of the time constant and lag time of the polyolefin production process, as follows:

[0114] A step signal is added to the hydrogen concentration of the polyolefin production process, and the melt index step response data corresponding to the polyolefin production process is recorded.

[0115] The collected melt index step response data y p (k) is converted into the corresponding dimensionless form y p * (k), the specific conversion formula is as follows:

[0116] y p * (k) = y p (k) / y f

[0117] Among them, y f is the step response data of melt index in polyolefin production process p (k) is the steady-state value.

[0118] First, choose the one that satisfies y p * (k 1 )=0.39 and y p * (k 1 )=0.63, and then calculate the time constant and lag time of the polyolefin production process model according to the following formula.

[0119] T=2(k 2 -k 1 )

[0120] τ=2k 1 -k 2

[0121] Where T and τ are the time constant and lag time of the polyolefin production process model, respectively.

[0122] The mechanism model of the polyolefin production process is determined, and then the real-time gain of the polyolefin production process is calculated according to the following formula. The specific calculation formula is as follows:

[0123] y m (k) = f(u(k))

[0124] K(k)=f′(u(k))

[0125] Among them, y m (k) is the melt index model output of the polyolefin production process, u(k) is the hydrogen concentration input of the polyolefin production process, K(k) is the real-time gain of the polyolefin production process, and f, f′ are the mechanism model of the polyolefin production process and the corresponding first-order derivative equations, respectively.

[0126] The final transfer function model of the polyolefin production process is:

[0127]

[0128] Wherein, G(k) and s are the real-time transfer function and Laplace operator of the polyolefin production process, respectively. Step (2). Design a nonlinear model predictive controller for the polyolefin production process. The specific steps are as follows:

[0129] a. In the zero-order holder and sampling time T s Under this condition, the transfer function model of the polyolefin production process can be converted into:

[0130] y m (k) = αy m (k-1)+K(k-1)(1-α)u(k-1-d)

[0131] in,

[0132] b. For the above discrete equation of polyolefin production process, Smith estimation is introduced to compensate for the time lag. The time lag-free model of polyolefin production process after compensation is as follows:

[0133] y mc (k) = αy mc (k-1)+K(k-1)(1-α)u(k-1)

[0134] Among them, y mc (k) is the output of the compensated melt index time-delay-free model of the polyolefin production process.

[0135] Further, compensating the actual melt index output of the polyolefin production process yields

[0136] y pc (k) = y p(k)+y mc (k)-y mc (kd)

[0137] Among them, y pc (k) is the actual melt index output of the polyolefin production process after compensation.

[0138] c. Based on the process model without time lag of polyolefin production process, the melt index prediction output of polyolefin production process can be derived as follows:

[0139] Y mc (k) = Ay mc (k)+BU(k)

[0140] in,

[0141]

[0142]

[0143] P and M are the prediction domain and control domain of model predictive control respectively, and their values ​​generally satisfy P>M.

[0144] Furthermore, the above polyolefin production process melt index prediction output derivation can be simplified as follows:

[0145] Y mc (k) = Ay mc (k)+Cφ(k)

[0146] in,

[0147]

[0148] d. Model predictive controller design for polyolefin production process Select the following objective function

[0149]

[0150] Where Q is the weighted matrix of the melt index tracking error, e(k) is the compensated melt index prediction error, and here we can take e(k) = y pc (k)-y mc (k) Y r (k) is the corresponding melt index reference trajectory, and its formula is:

[0151]

[0152] y r (k+i)=β i y p (k)+(1-β i )c(k)

[0153] β is the softening coefficient of the melt index reference trajectory, and c(k) is the melt index setting value corresponding to the polyolefin production process.

[0154] e. By taking the derivative of the above objective function, the optimal solution of the nonlinear model predictive control of the melt index of the polyolefin production process can be obtained as follows:

[0155] φ(k)=-(C Τ QC) -1 C Τ Q(Ay mc (k)+e(k)-Y r (k))

[0156] Take the first term of φ(k) 1 ), and then the optimal hydrogen concentration input u(k) for the predictive control of the melt index nonlinear model of the polyolefin production process can be obtained by solving the following one-variable multi-time equation.

[0157] f′(u(k))u(k)=φ(k 1 )

[0158] f. The optimal hydrogen concentration input u(k) obtained by the nonlinear model predictive control is implemented in the polyolefin production process, and in the next sampling period, the steps in (b) to (e) are cyclically solved to obtain a new optimal hydrogen concentration input.

[0159] The present invention combines the gain parameters in the nonlinear mechanism model to perform accurate output prediction and derivation, and ultimately obtains the precise control quantity of the nonlinear chemical process, thereby achieving more precise control of the nonlinear chemical process and promoting the application and development of nonlinear model predictive control based on the mechanism model in chemical processes.

[0160] The method of the present invention first identifies the time constant and lag time of the process model according to the collected step response data of the nonlinear chemical process, then derives the gain formula in combination with the mechanism model formula of the nonlinear process, then designs the model predictive controller of the nonlinear chemical process, and finally implements the obtained precise optimal control law on the controlled nonlinear chemical process.

[0161] The technical solution of the present invention is to establish a nonlinear model predictive control method for chemical processes based on a mechanism model by means of nonlinear chemical process step response data collection, partial model parameter identification, gain formula derivation, nonlinear model predictive controller design, etc., so as to avoid the prediction error caused by model linearization in traditional model predictive control, and ultimately achieve precise control of nonlinear chemical processes, and further improve the stability of nonlinear chemical process production.

[0162] It is to be understood that the present invention is described by some embodiments, and it is known to those skilled in the art that various changes or equivalent substitutions may be made to these features and embodiments without departing from the spirit and scope of the present invention. In addition, under the teachings of the present invention, these features and embodiments may be modified to adapt to specific circumstances and materials without departing from the spirit and scope of the present invention. Therefore, the present invention is not limited by the specific embodiments disclosed herein, and all embodiments falling within the scope of the claims of this application are within the scope of protection of the present invention.

Claims

1. A chemical process nonlinear model predictive control method based on a mechanism model, characterized in that: The steps include: Step 1: Collect the step response data of the nonlinear chemical process and fit the two model parameters of the chemical process: time constant and lag time; Step 1.1: Add a step signal to the input of the nonlinear chemical process and record the step response data corresponding to the nonlinear chemical process; Step 1.2: Collect the step response data y p (k) is converted into the corresponding dimensionless form y p * (k); Step 1.3: First select the p * (k1) = 0.39 and y p * (k2) = 0.63, and then calculate the time constant and lag time of the nonlinear chemical process model; Step 1.4: Determine the mechanism model of the nonlinear chemical process and then calculate the real-time gain of the nonlinear chemical process; The step 1.4 calculates the real-time gain of the nonlinear chemical process according to the following formula: y m (k)=f(u(k)) K(k)=f′(u(k)) Among them, y m (k) is the model output of the nonlinear chemical process, u(k) is the input of the nonlinear chemical process, K(k) is the real-time gain of the nonlinear chemical process, f, f′ are the mechanism model of the nonlinear chemical process and the corresponding first-order derivative equation respectively; Step 1.5: The final nonlinear chemical process transfer function model is obtained; Step 2: Design a nonlinear model predictive controller for a nonlinear chemical process; Step 2.1: In the zero-order hold and sampling time T s Under this, the transfer function model conversion of nonlinear chemical process is realized; In step 2.1, the zero-order holder and the sampling time T s The transfer function model of the nonlinear chemical process is converted to: y m (k)=αy m (k-1)+K(k-1)(1-α)u(k-1-d) in, Step 2.2: For the discrete equation, introduce Smith estimation to compensate for the time delay; The time-delay-free model after compensation in step 2.2 is as follows: y mc (k)=αy mc (k-1)+K(k-1)(1-α)u(k-1) Among them, y mc (k) is the output of the nonlinear chemical process time-delay-free model after compensation; Compensating the actual output of the nonlinear chemical process yields: and pc (k)=y p (k)+y mc (k)-y mc (kd) Among them, y pc (k) is the actual output of the nonlinear chemical process after compensation; Step 2.3: Based on the process model without time delay, obtain the predicted output of the nonlinear chemical process; The predicted output of the nonlinear chemical process in step 2.3 is derived as follows: Y mc (k)=Month mc (k)+THIS(k) in, P and M are the prediction time domain and control time domain of model predictive control respectively, and the value satisfies P>M; The above prediction output derivation is simplified to Y mc (k)=Yes mc (k)+Cφ(k) in, Step 2.4: Select objective function for model predictive controller design of nonlinear chemical process; Step 2.4 selects the following objective function for model predictive controller design of nonlinear chemical process Where Q is the weighted matrix of the tracking error, e(k) is the compensated prediction error, and e(k)=y pc (k)-y mc (k), Y r (k) is the corresponding reference trajectory, and its formula is and r (k+i)=β i and p (k)+(1-β i )c(k) β is the reference trajectory softening coefficient, c(k) is the set value corresponding to the nonlinear chemical process; Step 2.5: Derivative the above objective function to obtain the optimal solution of nonlinear model predictive control; Step 2.5 derivates the objective function of step 2.4 to obtain the optimal solution of nonlinear model predictive control: φ(k)=-(C Τ (QC) -1 C Τ Q(Is mc (k)+e(k)-Y r (k)) Take out the first term φ(k1) of φ(k), and then solve the following one-variable multi-time equation to obtain the optimal control law u(k) of nonlinear model predictive control: f′(u(k))u(k)=φ(k1); Step 2.6: Apply the obtained optimal control law u(k) of the nonlinear model predictive control to the nonlinear chemical process, and in the next sampling period, repeat the steps in steps 2.2 to 2.5 to solve the new optimal control law.

2. The chemical process nonlinear model predictive control method based on the mechanism model according to claim 1 is characterized in that: In step 1.2, the acquired step response data y p (k) is converted into the corresponding dimensionless form y p * (k), the specific conversion formula is as follows: and p * (k)=y p (k) / y f Among them, y f is the nonlinear chemical process step response data y p (k) is the steady-state value.

3. The chemical process nonlinear model predictive control method based on mechanism model according to claim 1, characterized in that: The step 1.3 calculates the time constant and lag time of the nonlinear chemical process model according to the following formula: T=2(k2-k1) τ=2k1-k2 Among them, T and τ are the time constant and lag time of the nonlinear chemical process model, respectively.

4. The chemical process nonlinear model predictive control method based on mechanism model according to claim 1, characterized in that: The nonlinear chemical process transfer function model obtained in step 1.5 is: Among them, G(k) and s are the real-time transfer function and Laplace operator of the nonlinear chemical process respectively.

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