CN113093522A - Closed-loop dynamic matrix control method for continuous stirring reaction kettle - Google Patents

Closed-loop dynamic matrix control method for continuous stirring reaction kettle Download PDF

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CN113093522A
CN113093522A CN202110303498.9A CN202110303498A CN113093522A CN 113093522 A CN113093522 A CN 113093522A CN 202110303498 A CN202110303498 A CN 202110303498A CN 113093522 A CN113093522 A CN 113093522A
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谢磊
石尧
张志铭
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Zhejiang University ZJU
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Abstract

The invention discloses a closed-loop dynamic matrix control method for a continuous stirring reaction kettle, which comprises the following steps: (1) step testing is carried out on the reaction process of the continuous stirring reaction kettle, and a model of a process object is obtained; (2) calculating a feedforward response model and constructing a generalized process object; (3) collecting input and output of process control, constructing an optimization problem, and calculating input of a generalized process object; (4) converting the input of the generalized process object into the input of the process object; (5) and (5) repeating the step (3) and the step (4) to realize the process control of the continuous stirring reaction kettle. The method has good robustness and stability, improves the dynamic characteristic of the control of the continuous stirring reaction kettle, and improves the economic benefit.

Description

Closed-loop dynamic matrix control method for continuous stirring reaction kettle
Technical Field
The invention relates to the field of control algorithms in industrial process control systems, in particular to a closed-loop dynamic matrix control method for a continuous stirring reaction kettle.
Background
Model predictive control technology is a class of model-based computer control methods that were developed in the 70's of the 20 th century, and which, over 40 years of development, has become the most successful modern advanced control technology applied to the process industry after PID. The model predictive control technology has the capability of processing problems in aspects of coupling among multiple variables and constraints on output and intermediate variables, and provides an effective solution for complex industrial processes with multiple variables and constraints.
As one representative of the model predictive Control technique, the dynamic matrix Control algorithm was proposed and published in advance by us shell engineers Cutler in 1980 at the Conference on Automatic Control Conference. Dynamic matrix control algorithms are widely used in the industry because they use a class of non-parametric models that are easily available at the actual engineering site, i.e., finite step response models. When the continuous stirring reaction kettle is used for controlling the treatment concentration and the temperature, the dependence on a model prediction control algorithm is very prominent due to the characteristics of hysteresis, nonlinearity, reverse response and the like of the system. However, conventional dynamic matrix control algorithms still have certain deficiencies in handling dynamics and parameter adjustments. The implementer often cannot effectively estimate the influence of parameter adjustment on closed-loop dynamics, so that the period for deploying and implementing the control algorithm is prolonged, and the implementation progress of the project is delayed.
Aiming at the problems, the academic world provides a plurality of methods for adjusting parameters of a dynamic matrix control algorithm, and certain praise is obtained in the industry. Although the stability of the dynamic matrix control algorithm in the methods is well guaranteed, the closed-loop dynamic performance under the methods cannot achieve the expected dynamic characteristics even after multiple times of debugging because the controller parameters only have a qualitative relation but not a quantitative relation to the closed-loop dynamic result.
Aiming at the problems and the defects of the current dynamic matrix control algorithm in engineering practice, the improved dynamic matrix control algorithm which can ensure that the closed-loop dynamic result can reach the expected result as far as possible and has the characteristics of simplicity, high efficiency, small calculated amount and easy implementation is very important.
Disclosure of Invention
Based on the defects in the prior art, the invention provides a closed-loop dynamic matrix control method for a continuous stirring reaction kettle, which can effectively control the concentration, the temperature and the pressure in the continuous stirring reaction kettle, can ensure that a closed-loop dynamic result under an improved dynamic matrix control algorithm reaches an expected result as far as possible, and has the characteristics of simplicity, high efficiency, small calculated amount and easiness in implementation.
A closed-loop dynamic matrix control method for a continuous stirring reaction kettle comprises the following steps:
(1) step testing is carried out on the reaction process of the continuous stirring reaction kettle, and a model of a process object is obtained;
(2) calculating a feedforward response model and constructing a generalized process object;
(3) collecting input and output of process control, constructing an optimization problem, and calculating input of a generalized process object;
(4) converting the input of the generalized process object into the input of the process object;
(5) and (5) repeating the step (3) and the step (4) to realize the process control of the continuous stirring reaction kettle.
Further, in the step (1), a step response model is used as a model of the process object of the continuous stirred tank reactor.
Further, in step (2), the method for calculating the feedforward response model includes:
(2-1) determining an expected closed-loop response model;
(2-2), solving the following optimization problem:
Figure BDA0002987210230000031
s.t.
Figure BDA0002987210230000032
Figure BDA0002987210230000033
wherein the content of the first and second substances,
Figure BDA0002987210230000034
a feed forward response model, representing the need for optimization, sigma represents the summation,
Figure BDA0002987210230000035
the jth parameter of the step response model representing the process object,
Figure BDA0002987210230000036
i-th parameter, N, representing the expected closed-loop response modelmRepresenting the model length, beta representing the stability coefficient, s.t. representing that the constraint is satisfied;
(2-3), adjusting the stability coefficient beta, and determining an actual closed-loop response model:
Figure BDA0002987210230000037
wherein, the first and second guide rollers are arranged in a row,
Figure BDA0002987210230000038
the jth parameter of the step response model representing the process object,
Figure BDA0002987210230000039
the ith parameter representing the actual expected closed-loop response model,
Figure BDA00029872102300000310
the jth parameter representing the feedforward response model.
Further, in the step (3), the specific form of constructing the optimization problem is as follows:
Figure BDA00029872102300000311
s.t.
Figure BDA00029872102300000312
Figure BDA00029872102300000313
ΔUk∈[ΔUmin,ΔUmax]
Uk∈[Umin,Umax]
Yk∈[Ymin,Ymax]
wherein, JkIs an objective function, Δ VkIs a differential generalized process object input vector to be optimized,
Figure BDA00029872102300000314
is the output open-loop prediction vector of the process object, YkIs the output closed-loop prediction vector of the process object, DMIs the actual desired closed-loop dynamic matrix, av (k) is the current time instant differential generalized process object input vector,
Figure BDA00029872102300000315
is an open-loop prediction vector, Δ U, of the input to a differential process objectkIs a closed-loop prediction vector, Δ D, of the differential process object inputsLIs a dynamic matrix of differential feedforward responses, Δ UminIs the lower bound vector, Δ U, of the differential process object inputsmaxIs the upper bound vector, U, of the differential process object inputskIs a process object input vector, UminIs a lower bound vector, U, of the process object inputmaxIs the upper bound vector of the process object input, YkIs a process object output vector, YminIs a lower bound vector of process object outputs, YmaxIs the upper bound vector of the process object output.
Further, in the step (4), the specific method of conversion is:
calculating a closed-loop prediction vector for the differential process object input:
Figure BDA0002987210230000041
taking the first element of the vector as the input increment of the process object
Δu(k)＝ΔUk(1)
Wherein Δ u (k) represents the input delta of the process object，ΔUk(1) The first element of the closed-loop prediction vector representing the differential process object input.
Further, in the step (5), a specific method for realizing the process control of the continuous stirring reaction kettle is as follows: and (4) superposing the input increment of the process object obtained in the step (4) on the input signal of the current process object.
Compared with the prior art, the invention has the following beneficial effects:
1. the invention can effectively improve the closed loop dynamic state, and leads the closed loop dynamic result to be as close as possible to the expected result by introducing the corresponding concept of feedback and the related optimization problem.
2. The invention replaces the common feedback dynamic matrix control scheme with a relatively concise and intuitive feedforward scheme, so that the parameter adjustment is relatively simple.
3. The invention has the capability of processing complex working conditions, for example, the inverse response of a non-minimum phase system can be effectively inhibited.
Drawings
FIG. 1 is a schematic flow diagram of the process of the present invention;
FIG. 2 is a graph of the results of various response models in an embodiment of the present invention;
fig. 3 is a diagram illustrating a change situation of a set value and an output value of a process object according to an embodiment of the present invention.
Detailed Description
The invention will be described in further detail below with reference to the drawings and examples, which are intended to facilitate the understanding of the invention without limiting it in any way.
This example describes the invention of a closed-loop dynamic matrix control method for a continuous stirred tank reactor, taking the problem of controlling the relative temperature in a continuous stirred tank reactor as an example.
As shown in fig. 1, a closed-loop dynamic matrix control method for a continuous stirred tank reactor, comprising:
step 1, carrying out step test on the reaction of the continuous stirring reaction kettle, obtaining a model of the relative temperature control problem, and inputting the model as the flow of reactants. In this embodiment, the sampling period is 30 seconds, as shown in fig. 2.
And 2, calculating a feedforward response model off line. The specific implementation mode is as follows:
step 2-1, the desired closed-loop response model is first determined, in this example set to a step process to facilitate demonstrating the closed-loop tracking features of the present invention.
Step 2-2, solving the optimization problem
Figure BDA0002987210230000051
s.t.
Figure BDA0002987210230000052
Figure BDA0002987210230000053
Wherein
Figure BDA0002987210230000054
A feed forward response model, representing the need for optimization, sigma represents the summation,
Figure BDA0002987210230000055
the jth parameter of the step response model representing the process object,
Figure BDA0002987210230000056
i-th parameter, N, representing the expected closed-loop response modelmRepresenting the model length, set to 21 in this example, and beta representing the stability factor, set to 0.05 in this example.
Step 2-3, determining an actual closed-loop response model according to the feedforward response model obtained in the step 2-2
Figure BDA0002987210230000057
Wherein the content of the first and second substances,
Figure BDA0002987210230000058
the jth parameter of the step response model representing the process object,
Figure BDA0002987210230000061
the ith parameter representing the actual expected closed-loop response model,
Figure BDA0002987210230000062
the jth parameter representing the feedforward response model. Figure 2 shows the results of the response models for this example after calculation.
And 3, calculating a quadratic programming problem on line, and solving a decision variable of the generalized object process.
The quadratic programming problem solved is as follows:
Figure BDA0002987210230000063
s.t.
Figure BDA0002987210230000064
Figure BDA0002987210230000065
ΔUk∈[ΔUmin,ΔUmax]
Uk∈[Umin,Umax]
Yk∈[Ymin,Ymax]
wherein, JkIs an objective function, Δ VkIs a differential generalized process object input vector to be optimized,
Figure BDA0002987210230000066
is the output open-loop prediction vector of the process object, YkIs the output closed-loop prediction vector of the process object, DMIs a practically expected closed-loop dynamic matrixΔ V (k) is the current time instant difference generalized process object input vector,
Figure BDA0002987210230000067
is an open-loop prediction vector, Δ U, of the input to a differential process objectkIs a closed-loop prediction vector, Δ D, of the differential process object inputsLIs a dynamic matrix of differential feedforward responses, Δ UminAnd Delta UmaxIn this case, no setting is made, i.e. no constraint is made on the amplitude of the input variation, UkIs a process object input vector, UminIs the lower limit vector of the process object input, set to-1, U in this casemaxIs the upper vector of the process object inputs, set to 2, Y in this casekIs a process object output vector, YminIs the lower limit vector of the process object output, which is not planned in this case, YmaxIs the upper vector of the process object output, which is set to 1.1 in this case.
And 4, converting the generalized process object into process object input and applying the process object input to the process object after the generalized process object is input. The specific method of conversion is as follows:
calculating a closed-loop prediction vector for the differential process object input:
Figure BDA0002987210230000068
taking the first element of the vector as the input increment of the process object
Δu(k)＝ΔUk(1)
Where Δ U (k) represents the input increment of the process object, Δ Uk(1) The first element of the closed-loop prediction vector representing the differential process object input.
And 5, superposing the input increment of the process control obtained in the step 4 on the input signal of the current process control. And continuously repeating the step 3 and the step 4.
As shown in fig. 3, at the 30 th second, the set value has a step change from 0 to 1, and the process object output has a small overshoot at about 250 th second, but still can be controlled within the specified constraint range, and the process object completes tracking in about 300 seconds, and becomes stable.
The output value change of the process object shows that the method can quickly and accurately realize the expected closed-loop characteristic, is simple and convenient to operate, has strong robustness and has high practical application value.
The embodiments described above are intended to illustrate the technical solutions and advantages of the present invention, and it should be understood that the above-mentioned embodiments are only specific embodiments of the present invention, and are not intended to limit the present invention, and any modifications, additions and equivalents made within the scope of the principles of the present invention should be included in the scope of the present invention.

Claims (6)

1. A closed-loop dynamic matrix control method for a continuous stirring reaction kettle is characterized by comprising the following steps:
(1) step testing is carried out on the reaction process of the continuous stirring reaction kettle, and a model of a process object is obtained;
(2) calculating a feedforward response model and constructing a generalized process object;
(3) collecting input and output of process control, constructing an optimization problem, and calculating input of a generalized process object;
(4) converting the input of the generalized process object into the input of the process object;
(5) and (5) repeating the step (3) and the step (4) to realize the process control of the continuous stirring reaction kettle.
2. The closed-loop dynamic matrix control method for the continuous stirred tank reactor according to claim 1, wherein in step (1), a step response model is used as the model of the process object of the continuous stirred tank reactor.
3. The closed-loop dynamic matrix control method for the continuous stirred tank reactor as claimed in claim 1, wherein the method for calculating the feedforward response model in the step (2) is:
(2-1) determining an expected closed-loop response model;
(2-2), solving the following optimization problem:
Figure FDA0002987210220000011
s.t.
Figure FDA0002987210220000012
Figure FDA0002987210220000013
wherein the content of the first and second substances,
Figure FDA0002987210220000014
a feed forward response model, representing the need for optimization, sigma represents the summation,
Figure FDA0002987210220000015
the jth parameter of the step response model representing the process object,
Figure FDA0002987210220000016
i-th parameter, N, representing the expected closed-loop response modelmRepresenting the model length, beta representing the stability coefficient, s.t. representing that the constraint is satisfied;
(2-3), adjusting the stability coefficient beta, and determining an actual closed-loop response model:
Figure FDA0002987210220000021
wherein, the first and second guide rollers are arranged in a row,
Figure FDA0002987210220000022
the jth parameter of the step response model representing the process object,
Figure FDA0002987210220000023
the ith parameter representing the actual expected closed-loop response model,
Figure FDA0002987210220000024
the jth parameter representing the feedforward response model.
4. The closed-loop dynamic matrix control method for the continuous stirred tank reactor as claimed in claim 1, wherein in the step (3), the specific form of the optimization problem is constructed as follows:
Figure FDA0002987210220000025
s.t.
Figure FDA0002987210220000026
Figure FDA0002987210220000027
ΔUk∈[ΔUmin,ΔUmax]
Uk∈[Umin,Umax]
Yk∈[Ymin,Ymax]
wherein, JkIs an objective function, Δ VkIs a differential generalized process object input vector to be optimized,
Figure FDA0002987210220000028
is the output open-loop prediction vector of the process object, YkIs the output closed-loop prediction vector of the process object, DMIs the actual desired closed-loop dynamic matrix, av (k) is the current time instant differential generalized process object input vector,
Figure FDA0002987210220000029
is an open-loop prediction vector, Δ U, of the input to a differential process objectkIs a closed-loop prediction vector, Δ D, of the differential process object inputsLIs a dynamic matrix of differential feedforward responses, Δ UminIs the lower bound vector, Δ U, of the differential process object inputsmaxIs the upper bound vector, U, of the differential process object inputskIs a process object input vector, UminIs a lower bound vector, U, of the process object inputmaxIs the upper bound vector of the process object input, YkIs a process object output vector, YminIs a lower bound vector of process object outputs, YmaxIs the upper bound vector of the process object output.
5. The closed-loop dynamic matrix control method for the continuous stirring reaction kettle as claimed in claim 4, wherein in the step (4), the specific method for switching is as follows:
calculating a closed-loop prediction vector for the differential process object input:
Figure FDA0002987210220000031
taking the first element of the vector as the input increment of the process object
Δu(k)＝ΔUk(1)
Where Δ U (k) represents the input increment of the process object, Δ Uk(1) The first element of the closed-loop prediction vector representing the differential process object input.
6. The closed-loop dynamic matrix control method for the continuous stirred tank reactor as claimed in claim 1, wherein in the step (5), the specific method for realizing the process control of the continuous stirred tank reactor is as follows: and (4) superposing the input increment of the process object obtained in the step (4) on the input signal of the current process object.
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