Large-time-delay process prediction control method of fixed-dimension state space model

Abstract

The invention provides a large-time-lag process prediction control method for a fixed-dimension state space model, and the method comprises the following steps: S1, carrying out the step response test of a controlled loop, collecting the corresponding process data, and calculating the parameters of a transfer function model of the controlled loop; s2, designing a compression state space model of the controlled process according to the transfer function model obtained through calculation; s3, designing a model prediction controller based on the obtained compression state space model; and S4, at each sampling moment, updating the state vector and applying the calculated control quantity to the controlled process. According to the method, an existing extended state space model is redesigned, and a state space model with fixed and extremely low dimensions is constructed, so that the dimension is greatly reduced while the model can effectively represent a controlled process, the subsequent model prediction control design is lighter, good control performance is still kept, and the method is suitable for large-scale popularization and application. And a foundation is laid for lightweight deployment of model prediction control.

Description

Technical Field

[0001] The present invention relates to a model predictive control method for large time-delay processes, specifically to a predictive control method for large time-delay processes with a fixed-dimensional state space model, and belongs to the technical field of automatic control. Background Art

[0002] Model predictive control has been widely applied in the fields of process industry, energy systems, and industrial automation because it can effectively handle complex control problems such as multi-variables, time-delay, and constraints. Traditional model predictive control is usually designed based on a state space model. For a controlled process with large time-delay characteristics, an extended state space model is generally used for characterization.

[0003] In the extended state space model, the state vector is usually constructed as x(k) = [Δy_p(k), Δu(k), …, Δu(k - d), e(k)] T , where e(k) is the tracking error. A significant problem with this model is that the dimension of the state vector is directly related to the system time-delay d. When the system has large time-delay characteristics, the dimension of the state vector will increase sharply, resulting in an overly high dimension of the system matrix, which will significantly increase the computational complexity of the model predictive controller.

[0004] The computational burden brought by the high-dimensional state space model is particularly prominent in resource-constrained control systems, such as embedded controllers and low-cost programmable controllers. The high-dimensional model not only increases the computational resources and time required to solve the optimal control problem, but may also lead to numerical calculation problems, reducing control performance or stability. In addition, parameter identification and online update of the high-dimensional model also face greater challenges.

[0005] Currently, the computational complexity problem of model predictive control for large time-delay processes is mainly solved by the following methods: one is to adopt a more computationally efficient optimization algorithm; the second is to reduce the computational amount by reducing the prediction horizon and control horizon; the third is to use an approximate model to simplify the calculation. However, these methods either require complex algorithm implementation or will sacrifice control performance, and it is difficult to achieve lightweight deployment while maintaining control performance.

[0006] Therefore, there is an urgent need for a new model characterization method that can significantly reduce the model dimension while accurately describing the dynamic characteristics of large time-delay processes, providing a basis for the lightweight implementation of model predictive control. Summary of the Invention

[0007] Based on the above background, the object of the present invention is to provide a predictive control method for large time-delay processes with a fixed-dimensional state space model, which redesigned the existing extended state space model to construct a state space model with a fixed and extremely low dimension, enabling the model to effectively represent the controlled process while greatly reducing the dimension, thereby making the subsequent model predictive control design more lightweight, while still maintaining good control performance, laying a foundation for the lightweight deployment of model predictive control.

[0008] To achieve the above object of the invention, the present invention provides the following technical solutions:

[0009] A predictive control method for large time-delay processes with a fixed-dimensional state space model, the method comprising the following steps:

[0010] S1. Conduct a step response test on the controlled loop and collect the corresponding process data, and calculate the transfer function model parameters of the controlled loop;

[0011] S2. Design a compressed state space model of the controlled process according to the calculated transfer function model;

[0012] S3. Design a model predictive controller based on the obtained compressed state space model;

[0013] S4. At each sampling moment, update the state vector and apply the calculated control quantity to the controlled process.

[0014] Preferably, the step S1 specifically includes:

[0015] S1.1. By adjusting the manipulated variable of the controlled loop, generate a step signal and record the process data between the output of the controlled loop and the new steady state;

[0016] S1.2. Perform dimensionless conversion on the collected step test data, calculate the gain K of the controlled process model, and then introduce the two-point method to calculate the time constant T and the lag time τ of the controlled process model.

[0017] Preferably, the calculation formula for the dimensionless conversion is:

[0018] y * (k) = y p (k) / y s ;

[0019] where y * (k) is the dimensionless form of the actual output y p (k) of the controlled process, and y s is the steady state value of y p (k);

[0020] The calculation formula for the gain K is:

[0021] K = y s / t;

[0022] where t is the step change amplitude of the input of the controlled process;

[0023] The calculation formulas for the time constant T and the lag time τ are as follows:

[0024] T = 2(k2 - k1);

[0025] τ = 2k1 - k2;

[0026] When calculating the time constant T and the lag time τ of the controlled process model using the two-point method, the two points are selected as y * (k1) = 0.39 and y * (k2) = 0.63.

[0027] Preferably, step S2 specifically includes:

[0028] S2.1. Discretize the transfer function model under the sampling period T s to obtain the corresponding discrete equation model:

[0029] y m (k) = ay m (k - 1) + bu(k - 1 - d);

[0030] where y m (k) and u(k) are the output and input of the discrete equation model at time k, respectively, b = K(1 - α), d = τ / T s , T s is the sampling interval;

[0031] S2.2. Introduce a Smith predictor to correct the discrete equation model to obtain a discrete equation model without time delay:

[0032] y mc (k) = ay mc (k - 1) + bu(k - 1);

[0033] where y mc (k) is the output of the model without time delay, and a and b are the coefficients in the discrete equation model;

[0034] At the same time, correct the actual output of the process, and the corrected process output is:

[0035] y pc (k) = y p (k) + y mc (k) - y mc (k - d)

[0036] where y pc (k) is the corrected process output, y p (k) is the original process output, and d is the time delay of the process model;

[0037] S2.3. Convert the model without time delay into an incremental form:

[0038] Δy mc (k) = aΔy mc (k - 1) + bΔu(k - 1);

[0039] S2.4. Construct the state vector of the compressed state - space model:

[0040] x(k) = [Δy mc (k), e c (k)] T ;

[0041] where e c (k) is the tracking error calculated based on the corrected process output, and the calculation formula is e c (k) = y pc (k) - s(k); s(k) is the set value of the process output at time k;

[0042] S2.5. Establish a state - space model based on the compressed state vector:

[0043] x(k + 1) = Ax(k) + BΔu(k);

[0044] where,

[0045]

[0046] Preferably, the dimension of the system matrix A of the compressed state - space model is fixed at 2×2, and the dimension of the input matrix B is fixed at 2×1.

[0047] Preferably, the step S3 specifically includes:

[0048] S3.1. Based on the compressed state - space model, construct the output prediction equation of the process:

[0049] X(k) = θx(k) + γΔu(k);

[0050] where,

[0051]

[0052] P is the prediction horizon of the model predictive control;

[0053] S3.2. Introduce the objective function:

[0054]

[0055] Among them, Q and R are the weighting parameters for the predicted state and the process input increment respectively;

[0056] By minimizing the above objective function, the optimal control increment of the model predictive control based on the compressed state space model is solved:

[0057] Δu(k) = -(γ T Qγ + R) -1 γ T Qθx(k);

[0058] S3.3. Calculate the optimal control quantity u(k) required by the controlled process according to the obtained optimal control increment and apply it to the actual process:

[0059] u(k) = u(k - 1) + Δu(k).

[0060] Preferably, the prediction horizon P of the model predictive control takes the value of 1.

[0061] Preferably, the step S4 specifically includes:

[0062] At each sampling time k, obtain the actual process output y p (k), calculate the corrected process output y pc (k), update the state vector x(k), and use the calculation formula Δu(k) = -(γ T Qγ + R) -1 γ T Qθx(k) to calculate the optimal control increment, and apply the control quantity u(k) = u(k - 1) + Δu(k) to the controlled process.

[0063] Compared with the prior art, the present invention has the following advantages:

[0064] The present invention discloses a method for predicting and controlling a large time-delay process using a fixed-dimensional state space model. The compressed state space model proposed by the present invention has a system matrix and an input matrix that always maintain a fixed low dimension for a first-order process, regardless of the time delay, and is independent of the time delay parameter, thereby avoiding the problem that the dimension of the traditional extended state space model increases linearly with the increase of the time delay. The model predictive controller based on the compressed state space model of the present invention has a calculation amount that is independent of the size of the time delay, significantly reduces the calculation burden of the controller, and enables the control algorithm to be efficiently implemented on a resource-constrained hardware platform. The present invention modifies the discrete equation model by introducing a Smith predictor and constructs a special state vector, so that the compressed model can accurately characterize the dynamic characteristics of the large time-delay process, ensuring that the controller maintains good control performance. Since the model dimension is fixed and low, the controller solution process is simplified, and the present invention is particularly suitable for deployment on resource-constrained control platforms such as embedded systems and programmable logic controllers, providing an effective way to achieve lightweight model predictive control. BRIEF DESCRIPTION OF THE DRAWINGS

[0065] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying creative work.

[0066] Figure 1 It is a flow chart of a large time-delay process predictive control method of a fixed-dimensional state space model of the present invention. DETAILED DESCRIPTION

[0067] The technical solution of the present invention is further described in detail below through specific embodiments and in conjunction with the accompanying drawings. It should be understood that the implementation of the present invention is not limited to the following embodiments, and any form of modification and / or change made to the present invention will fall within the protection scope of the present invention.

[0068] In the present invention, unless otherwise specified, all parts and percentages are weight units, and the equipment and raw materials used can be purchased from the market or are commonly used in the art. The methods in the following embodiments, unless otherwise specified, are conventional methods in the art. The components or equipment in the following embodiments, unless otherwise specified, are universal standard parts or components known to those skilled in the art, and their structures and principles are known to those skilled in the art through technical manuals or conventional experimental methods.

[0069] The embodiment of the present invention discloses a method for predictive control of a large time-delay process in a fixed-dimensional state space model. Figure 1 As shown, the method comprises the following steps:

[0070] S1. Make a step response test for the controlled loop and collect the corresponding process data, and calculate the transfer function model parameters of the controlled loop;

[0071] S2. Design a compressed state space model of the controlled process according to the calculated transfer function model;

[0072] S3. Design a model predictive controller based on the obtained compressed state space model;

[0073] S4. At each sampling moment, update the state vector and apply the calculated control quantity to the controlled process.

[0074] The following takes the control loop of the furnace temperature of the waste plastic refining pyrolysis furnace as an example to illustrate the steps of this method in detail.

[0075] Among them, the furnace pyrolysis temperature is the controlled target, and the opening of the burner is the adjustment means. This method includes the following steps:

[0076] S1. Make a step response test for the control loop of the furnace temperature of the pyrolysis furnace and collect the corresponding furnace temperature data, and calculate the transfer function model parameters of the furnace temperature control loop;

[0077] S2. Design a compressed state space model of the controlled process according to the calculated transfer function model of the temperature control loop;

[0078] S3. Design a model predictive controller based on the obtained compressed state space model of the pyrolysis temperature loop;

[0079] S4. At each sampling moment, update the state vector and apply the calculated control quantity to the controlled process.

[0080] Step S1 specifically includes:

[0081] S1.1. Adjust the PID controller of the furnace temperature control loop to the manual state, adjust the dial to generate a step change, and record the data between the furnace pyrolysis temperature and the new steady-state temperature;

[0082] S1.2. Perform a dimensionless conversion on the collected furnace pyrolysis temperature data, calculate the gain K of the process model of the furnace temperature control loop, and then introduce the two-point method to calculate the time constant T and the lag time τ of the process model of the pyrolysis temperature control loop.

[0083] Among them, the calculation formula for dimensionless conversion is:

[0084] y * (k) = y p (k) / y s ;

[0085] where y * (k) is the dimensionless form of the actual output y p (k) of the controlled process, and y s is the steady-state value of y p (k);

[0086] The calculation formula for the gain K is:

[0087] K = y s / t;

[0088] where t is the step change amplitude of the input of the controlled process;

[0089] The calculation formulas for the time constant T and the lag time τ are:

[0090] T = 2(k2 - k1);

[0091] τ = 2k1 - k2;

[0092] In the calculation of the time constant T and the lag time τ of the controlled process model using the two-point method, the two points are selected as y * (k1) = 0.39 and y * (k2) = 0.63.

[0093] Step S2 specifically includes:

[0094] S2.1. Discretize the transfer function model of the furnace cracking temperature control loop under the sampling period T s to obtain the corresponding discrete equation model:

[0095] y m (k) = ay m (k - 1) + bu(k - 1 - d);

[0096] where y m (k) and u(k) are the output of the discrete equation model and the burner opening at time k, respectively, b = K(1 - α), d = τ / T s , and T s is the sampling interval;

[0097] S2.2. Introduce a Smith predictor to correct the discrete equation model of the furnace cracking temperature loop to obtain the discrete equation model of the time-delay-free temperature control loop:

[0098] y mc (k) = ay mc (k - 1) + bu(k - 1);

[0099] where y mc(k) is the output of the model without time delay, and a and b are the coefficients in the discrete equation model of the furnace pyrolysis temperature loop;

[0100] At the same time, the actual output of the process is corrected, and the corrected process output is:

[0101] y pc (k) = y p (k) + y mc (k) - y mc (k - d)

[0102] Among them, y pc (k) is the corrected pyrolysis temperature, y p (k) is the original pyrolysis temperature, and d is the time delay of the process model of the furnace pyrolysis temperature loop;

[0103] S2.3. Convert the discrete model of the furnace pyrolysis temperature loop without time delay into an incremental form, and add a difference operator to both ends of the corresponding discrete equation model:

[0104] Δy mc (k) = aΔy mc (k - 1) + bΔu(k - 1);

[0105] S2.4. Construct the state vector of the compressed state space model of the furnace pyrolysis temperature loop:

[0106] x(k) = [Δy mc (k), e c (k)] T ;

[0107] Among them, e c (k) is the tracking error based on the corrected pyrolysis temperature, and the calculation formula is e c (k) = y pc (k) - s(k); s(k) is the set value of the pyrolysis temperature at the corresponding moment k;

[0108] It should be noted that if the traditional extended state space model is used to design the model predictive controller of the furnace pyrolysis temperature loop, the dimension of the state vector of the constructed furnace pyrolysis temperature loop will be relatively large, which will include multiple past values of the burner opening. The specific corresponding traditional extended state vector will be constructed as x(k) = [Δy p (k), Δu(k), …, Δu(k - d), e(k)] T , where e(k) is the actual tracking error of the pyrolysis temperature e(k) = y p(k) - s(k). Here, the larger the time delay in the pyrolysis temperature loop, the more elements in the traditional extended state vector, and thus the larger the dimension of the corresponding system matrix. In the compressed state vector of the designed pyrolysis temperature loop, regardless of the time delay, there are only two elements here, so the dimension of its corresponding system matrix is a fixed 2*2, which will bring great time and resource advantages to the subsequent optimization and solution of the model predictive controller for the pyrolysis temperature loop.

[0109] S2.5. Establish the state space model of the pyrolysis temperature loop based on the compressed state vector:

[0110] x(k + 1) = Ax(k) + BΔu(k);

[0111] Where,

[0112]

[0113] It can be clearly seen that for the first-order pyrolysis temperature loop, regardless of the time delay, the dimensions of the system matrix and the input matrix of the designed compressed state space model are fixed 2*2 and 2*1.

[0114] Step S3 specifically includes:

[0115] S3.1. Based on the above state space model of the compressed pyrolysis temperature loop, the output prediction equation of the pyrolysis temperature is:

[0116] X(k) = θx(k) + γΔu(k);

[0117] Where,

[0118]

[0119] P is the prediction time domain of the model predictive controller for the pyrolysis temperature loop, and the value is selected as 1.

[0120] S3.2. Introduce the objective function to the model predictive controller of the pyrolysis temperature loop:

[0121]

[0122] Where, Q and R are the weighting parameters for the predicted state and the process input increment of the pyrolysis temperature loop respectively.

[0123] By minimizing the above objective function, the optimal burner opening increment for the pyrolysis temperature loop based on the compressed state space model is obtained:

[0124] Δu(k) = -(γTQγ + R) -1 γ T Qθx(k);

[0125] S3.3. Calculate the optimal burner opening u(k) required for the pyrolysis temperature loop based on the obtained optimal burner opening increment, and then implement and apply it:

[0126] u(k) = u(k - 1) + Δu(k).

[0127] Step S4 specifically includes:

[0128] At each sampling time k, obtain the actual process output y p (k), calculate the corrected process output y pc (k), update the state vector x(k), and use the calculation formula Δu(k) = -(γ T Qγ + R) -1 γ T Qθx(k) to calculate the optimal control increment, and apply the control quantity u(k) = u(k - 1) + Δu(k) to the controlled process. Specifically, after obtaining the latest state vector of the pyrolysis temperature loop, perform cyclic update implementation of the optimal burner opening according to the calculation formula of the optimal burner opening increment.

[0129] In this article, specific examples are used to elaborate on the principle and implementation manner of the present invention. The description of the above embodiments is only used to help understand the method and its core idea of the present invention. It should be noted that for those of ordinary skill in the art of this technology, without departing from the principle of the present invention, several improvements and modifications can still be made to the present invention, and these improvements and modifications also fall within the protection scope of the claims of the present invention.

Claims

1. A predictive control method for a large time-delay process in a fixed-dimensional state space model, characterized in that: The method comprises the following steps: S1. Perform a step response test on the controlled loop and collect corresponding process data to calculate the transfer function model parameters of the controlled loop; S2. designing a compressed state space model of the controlled process according to the calculated transfer function model; S3. designing a model predictive controller based on the obtained compressed state space model; S4. At each sampling moment, the state vector is updated and the calculated control quantity is applied to the controlled process.

2. The method for predictive control of a large time-delay process based on a fixed-dimensional state space model according to claim 1, characterized in that: The step S1 specifically includes: S1.

1. Adjust the manipulated variable of the controlled loop to generate a step signal, and record the process data between the output of the controlled loop and the new steady state; S1.

2. Perform dimensionless quantization conversion on the collected step test data, and calculate the gain K of the controlled process model. Then, introduce the two-point method to calculate the time constant T and lag time τ of the controlled process model.

3. The method for predictive control of a large time-delay process based on a fixed-dimensional state space model according to claim 2, characterized in that: The calculation formula for the dimensionless conversion is: and * (k)=y p (k) / y s ; Among them, y * (k) is the actual output y of the controlled process p (k) in dimensionless form, y s for y p (k) steady-state value; The calculation formula of the gain K is: K=y s / t; Where t is the step change amplitude of the controlled process input; The calculation formula of the time constant T and the lag time τ is: T = 2(k2-k1); τ = 2k1-k2; The two-point method is used to calculate the time constant T and lag time τ of the controlled process model. The two points are selected as y * (k1) = 0.39 and y * (k2)=0.

63.

4. The method for predictive control of a large time-delay process based on a fixed-dimensional state space model according to claim 1, characterized in that: The step S2 specifically includes: S2.

1. The transfer function model is set at sampling period T s Perform discretization operation under the following conditions to obtain the corresponding discrete equation model: y m (k)=month m (f-1)+this(f-1-d); Among them, y m u(k) and u(k) are the output and input of the discrete equation model at time k, respectively. b=K(1-α), d=τ / T s , T s is the sampling interval; S2.

2. Introduce the Smith predictor to modify the discrete equation model and obtain a discrete equation model without time lag: y mc (k)=month mc (k-1)+this(k-1); Among them, y mc (k) is the output of the model without time lag, a and b are the coefficients in the discrete equation model; At the same time, the actual output of the process is corrected, and the corrected process output is: and pc (k)=y p (k)+y mc (k)-y mc (kd) Among them, y pc (k) is the corrected process output, y p (k) is the original process output, and d is the time lag of the process model; S2.

3. Convert the time-delay-free model into incremental form: Δy mc (k)=aΔy mc (k-1)+bΔu(k-1); S2.

4. Construct the state vector of the compressed state space model: x(k)=[Δy mc (k),e c (k)] T ; Among them, e c (k) is the tracking error calculated based on the corrected process output, and the calculation formula is e c (k) = y pc (k)-s(k); s(k) is the process output setting value corresponding to time k; S2.

5. Establish a state space model based on the compressed state vector: x(k+1)=Ax(k)+BΔu(k); in, 5. The method for predictive control of a large time-delay process based on a fixed-dimensional state space model according to claim 4, characterized in that: The dimension of the system matrix A of the compressed state space model is fixed at 2×2, and the dimension of the input matrix B is fixed at 2×1.

6. The method for predictive control of a large time-delay process based on a fixed-dimensional state space model according to claim 1, characterized in that: The step S3 specifically includes: S3.

1. Based on the compressed state space model, the output prediction equation of the construction process is: X(k)=θx(k)+γΔu(k); in, P is the prediction time domain of model predictive control; S3.2, introduce the objective function: Among them, Q and R are weighted parameters for the predicted state and process input increment respectively; By minimizing the above objective function, the optimal control increment of the model predictive control based on the compressed state space model is solved: Δu(k)=-(γ T Qγ+R) -1 c T Qθx(k); S3.

3. Calculate the optimal control quantity u(k) required by the controlled process based on the obtained optimal control increment and apply it to the actual process: u(k)=u(k-1)+Δu(k).

7. The method for predictive control of a large time-delay process based on a fixed-dimensional state space model according to claim 6, characterized in that: The prediction time domain P of the model predictive control takes a value of 1.

8. The method for predictive control of a large time-delay process based on a fixed-dimensional state space model according to claim 1, characterized in that: The step S4 specifically includes: At each sampling time k, obtain the actual output y of the process p (k), calculate the corrected process output y pc (k), update the state vector x(k), using the calculation formula Δu(k) = -(γ T Qγ+R) -1 γ T Qθx(k) calculates the optimal control increment and applies the control quantity u(k)=u(k-1)+Δu(k) to the controlled process.

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