CN103064293A - Chemical process decoupling non-minimal realization state space linear quadric form control method - Google Patents

Chemical process decoupling non-minimal realization state space linear quadric form control method Download PDF

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CN103064293A
CN103064293A CN 201310018108 CN201310018108A CN103064293A CN 103064293 A CN103064293 A CN 103064293A CN 201310018108 CN201310018108 CN 201310018108 CN 201310018108 A CN201310018108 A CN 201310018108A CN 103064293 A CN103064293 A CN 103064293A
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decoupling
input
matrix
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张日东
吴锋
张乐
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Hangzhou Dianzi University
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Hangzhou Dianzi University
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Abstract

The invention relates to a chemical process decoupling non-minimal realization state space linear quadric form control method. According to an existing traditional and simple control method, control parameters are fully depended on experience of technical workers, and therefore control effect is unsatisfying. According to method, a decoupling state space model is established based on a chemical process model so as to obtain basic process characteristics; a linear quadric form control loop is established based on the decoupling state space model; and parameters of a linear quadric form controller are computed to carry out linear quadric form control on the whole of process objects. By means of data acquisition, process processing, mechanism forecasting, data drive, optimization and the like, the chemical process decoupling non-minimal realization state linear quadric form control method is achieved, and the chemical process decoupling non-minimal realization state linear quadric form control method can effectively improve control accuracy and stability, effectively bring convenience to design of controllers, guarantee improvement of performance, and meanwhile meet given production performance indexes.

Description

Chemical process decoupling non-minimum realization state space linear quadratic control method
Technical Field
The invention belongs to the technical field of automation, and relates to a chemical process decoupling non-minimum realization state space linear quadratic control method.
Background
The chemical process is an important component of the flow industrial process in China, and the requirement is to supply qualified industrial products so as to meet the requirement of industrial development in China. As an important main body of industrial production, the improvement of the level of the industrial production process plays an important role in improving the economic benefit of the whole industry. For this reason, the individual main process parameters of the production process have to be strictly controlled. With the development of industry and the increasing requirements on the quality of products, energy consumption and environmental protection, the control precision requirement on the industrial process is more and more strict, and although the traditional control method meets certain requirements, the control level is difficult to further improve, and the process becomes more complex. Simple single-loop process control cannot meet the requirements of control precision and stability, the product yield is low, and the device efficiency is low. At present, the control in the actual industry basically adopts the traditional simple control means, the control parameters completely depend on the experience of technicians, the production cost is increased, and the control effect is not ideal. The chemical process control and optimization technology in China is relatively lagged behind, the energy consumption is high, the control performance is poor, the automation degree is low, the requirements of energy conservation and emission reduction and indirect environmental protection are difficult to adapt, and one of the direct influence factors is the control scheme problem of the system.
Disclosure of Invention
The invention aims to provide a linear quadratic control method for a chemical process decoupling non-minimum realization state space, aiming at the defects of the existing chemical process system control technology. The method makes up the defects of the traditional control mode, ensures that the control has higher precision and stability, ensures simple form and meets the requirements of the actual industrial process.
Firstly, establishing a decoupling state space model based on a chemical process model, and excavating basic process characteristics; then establishing a linear quadratic control loop based on the decoupling state space model; and finally, performing linear quadratic control on the whole process object by calculating the parameters of the linear quadratic controller.
The technical scheme of the invention is that a chemical process decoupling non-minimum realization state space linear quadratic control method is established by means of data acquisition, process processing, prediction mechanism, data driving, optimization and the like, and the method can effectively improve the control precision and the control stability.
The method comprises the following steps:
(1) a decoupling state space model is established by utilizing a chemical process model, and the specific method comprises the following steps:
firstly, acquiring input and output data of a chemical process, and establishing an input and output model by using the data as follows:
Figure 2013100181089100002DEST_PATH_IMAGE002
wherein
Figure 2013100181089100002DEST_PATH_IMAGE004
、
Figure 2013100181089100002DEST_PATH_IMAGE006
、
Figure 2013100181089100002DEST_PATH_IMAGE008
Are respectively output vectors
Figure 2013100181089100002DEST_PATH_IMAGE010
Transformation, transfer function matrix, input vectorTransforming;
Figure 2013100181089100002DEST_PATH_IMAGE012
，
Figure 2013100181089100002DEST_PATH_IMAGE014
，
Figure 2013100181089100002DEST_PATH_IMAGE016
Figure 2013100181089100002DEST_PATH_IMAGE018
,
Figure 2013100181089100002DEST_PATH_IMAGE020
,,
Figure 2013100181089100002DEST_PATH_IMAGE024
representing the transfer function of each loop of the process,
Figure 2013100181089100002DEST_PATH_IMAGE026
and
Figure 2013100181089100002DEST_PATH_IMAGE028
are respectively the first
Figure 2013100181089100002DEST_PATH_IMAGE030
Of input and output variables
Figure 952555DEST_PATH_IMAGE010
The transformation is carried out by changing the parameters of the image,，
Figure 384673DEST_PATH_IMAGE010
for the discrete transform operator of a computer controlled system,
Figure 2013100181089100002DEST_PATH_IMAGE034
is composed of
Figure 229263DEST_PATH_IMAGE010
The inverse number of (c) is,
Figure 2013100181089100002DEST_PATH_IMAGE036
the number of input and output variables of the process is the number stored in the data acquisition unitAccordingly;
further selecting an adjoint matrix decoupling array for the equation as follows:
Figure 2013100181089100002DEST_PATH_IMAGE038
wherein,is a companion matrix decoupling array which is,is composed of
Figure 649487DEST_PATH_IMAGE006
The companion matrix of (a).
Combining the adjoint matrix decoupling array and the process input and output model to obtain:
Figure 2013100181089100002DEST_PATH_IMAGE044
wherein,is the obtained model of the decoupling process,is composed of
Figure 382957DEST_PATH_IMAGE006
The determinant (c) of (a),
Figure 2013100181089100002DEST_PATH_IMAGE050
to be composed of
Figure 353187DEST_PATH_IMAGE006
Is a diagonal matrix of elements.
Figure 2013100181089100002DEST_PATH_IMAGE052
Processing the decoupling process model into
Figure 927650DEST_PATH_IMAGE036
Discrete equation form for a single variable process:
Figure 2013100181089100002DEST_PATH_IMAGE054
whereinAnd
Figure 2013100181089100002DEST_PATH_IMAGE058
are respectively the firstThe output and input variables of the individual processes,，
Figure 2013100181089100002DEST_PATH_IMAGE062
and
Figure 2013100181089100002DEST_PATH_IMAGE064
are respectively
Figure 801857DEST_PATH_IMAGE056
Anda coefficient matrix polynomial of (a);
Figure 2013100181089100002DEST_PATH_IMAGE068
whereinAre the coefficients of the respective coefficients that are,to move backwards
Figure 2013100181089100002DEST_PATH_IMAGE074
The step-by-step operators are calculated,
Figure 2013100181089100002DEST_PATH_IMAGE076
is the resulting model order;
passing the discrete equation model of the univariate process through a backward shift operator
Figure 2013100181089100002DEST_PATH_IMAGE078
Processing into a state space form:
Figure 2013100181089100002DEST_PATH_IMAGE082
。
wherein,
Figure 2013100181089100002DEST_PATH_IMAGE084
、
Figure 2013100181089100002DEST_PATH_IMAGE086
are respectively the first
Figure 2013100181089100002DEST_PATH_IMAGE088
The value of the variable at the time of day,
Figure 2013100181089100002DEST_PATH_IMAGE090
is as follows
Figure 2013100181089100002DEST_PATH_IMAGE092
The value of the input delta variable at the time,
Figure 2013100181089100002DEST_PATH_IMAGE094
、
Figure 2013100181089100002DEST_PATH_IMAGE096
are respectively the first
Figure 2013100181089100002DEST_PATH_IMAGE098
The output delta and input delta values at the time,
Figure 2013100181089100002DEST_PATH_IMAGE100
、
Figure 2013100181089100002DEST_PATH_IMAGE102
、
Figure 2013100181089100002DEST_PATH_IMAGE104
respectively corresponding state matrix, input matrix and output matrix,
Figure 2013100181089100002DEST_PATH_IMAGE106
to take the transposed symbol.
Figure 2013100181089100002DEST_PATH_IMAGE108
Figure 2013100181089100002DEST_PATH_IMAGE112
(2) The linear quadratic controller is designed based on the decoupling state space model, and the specific method comprises the following steps:
a. the objective function defining the linear quadratic controller is:
Figure 2013100181089100002DEST_PATH_IMAGE114
wherein,
Figure 2013100181089100002DEST_PATH_IMAGE116
in order to be the objective function, the target function,
Figure 2013100181089100002DEST_PATH_IMAGE118
and
Figure 2013100181089100002DEST_PATH_IMAGE120
respectively, a weighting matrix for the state variables and the output variables.
b. Calculating parameters of the linear quadratic controller, specifically:
Figure 2013100181089100002DEST_PATH_IMAGE122
wherein
Figure 2013100181089100002DEST_PATH_IMAGE124
Is as follows
Figure 590427DEST_PATH_IMAGE092
The value of the variable at the time of day,
Figure 2013100181089100002DEST_PATH_IMAGE126
and feeding back a coefficient vector for the controller.
The chemical process decoupling non-minimum realization state space linear quadratic control method provided by the invention makes up the defects of the traditional control, effectively facilitates the design of a controller, ensures the improvement of the control performance and simultaneously meets the given production performance index.
The control technology provided by the invention can effectively reduce the error between the ideal process parameters and the actual process parameters, further make up for the defects of the traditional controller, and simultaneously ensure that the control device is operated in the optimal state, so that the process parameters in the production process are strictly controlled.
Detailed Description
Taking the control of the hearth pressure process of the coking heating furnace as an example:
the coking furnace hearth pressure process control is described herein as an example. The process is a multivariable coupling process, and the hearth pressure is not only influenced by the opening of a flue baffle, but also influenced by the fuel quantity and the intake air flow. The adjusting means adopts the opening degree of the flue baffle, and other influences are used as uncertain factors.
(1) Establishing a decoupling state space model, wherein the specific method comprises the following steps:
firstly, a data acquisition unit is used for acquiring input data (flue baffle opening) and output data (heating furnace hearth pressure) of a chemical process, and an input and output model is established as follows:
Figure DEST_PATH_IMAGE128
wherein,
Figure DEST_PATH_IMAGE130
,
Figure DEST_PATH_IMAGE132
,
Figure 268664DEST_PATH_IMAGE022
,
Figure DEST_PATH_IMAGE134
a transfer function equation representing the pressure process of the hearth of the heating furnace,
Figure DEST_PATH_IMAGE136
respectively the opening of the flue baffle and the pressure data of the hearth of the heating furnace
Figure DEST_PATH_IMAGE138
Transforming;
then three variables are defined、
Figure DEST_PATH_IMAGE142
、
Figure DEST_PATH_IMAGE144
The following were used:
Figure DEST_PATH_IMAGE146
the input data and output data of the above process are represented as:
Figure 781422DEST_PATH_IMAGE002
further selecting an adjoint matrix decoupling array for the equation as follows:
wherein,
Figure 4779DEST_PATH_IMAGE040
is a companion matrix decoupling array which is,
Figure 285326DEST_PATH_IMAGE042
is composed of
Figure 657401DEST_PATH_IMAGE006
The companion matrix of (a).
And developing the process model to obtain:
Figure 790442DEST_PATH_IMAGE044
wherein,
Figure 906166DEST_PATH_IMAGE046
is the obtained model of the decoupling process,
Figure 309728DEST_PATH_IMAGE048
is composed ofThe determinant (c) of (a),
Figure 410725DEST_PATH_IMAGE050
to be composed of
Figure 64560DEST_PATH_IMAGE006
Is a diagonal matrix of elements.
Figure 821163DEST_PATH_IMAGE052
Processing the decoupling process model intoDiscrete representation of a single univariate process:
Figure 141210DEST_PATH_IMAGE054
wherein,
Figure 598736DEST_PATH_IMAGE056
、
Figure DEST_PATH_IMAGE148
are respectively the first
Figure 475425DEST_PATH_IMAGE030
The output and input variables of the individual processes,
Figure 861669DEST_PATH_IMAGE062
、
Figure 191020DEST_PATH_IMAGE064
are respectively
Figure 452237DEST_PATH_IMAGE056
、
Figure 767722DEST_PATH_IMAGE148
The polynomial of the coefficient matrix of (a),
Figure 761086DEST_PATH_IMAGE076
is the order of the model obtained and,
Figure 577732DEST_PATH_IMAGE070
are the coefficients of the respective coefficients that are,
Figure 377061DEST_PATH_IMAGE072
to move backwards
Figure 962763DEST_PATH_IMAGE074
And (5) step operators.
Figure 956389DEST_PATH_IMAGE068
Passing the discrete equation model of the univariate process through a backward shift operator
Figure 260331DEST_PATH_IMAGE078
Processing into a state space form:
Figure 535455DEST_PATH_IMAGE080
wherein,、
Figure 638726DEST_PATH_IMAGE086
are respectively the first
Figure 928500DEST_PATH_IMAGE088
The value of the variable at the time of day,
Figure 69631DEST_PATH_IMAGE090
is as follows
Figure 629925DEST_PATH_IMAGE092
The value of the input delta variable at the time,、
Figure 414527DEST_PATH_IMAGE096
are respectively the firstThe output delta and input delta values at the time,
Figure 275615DEST_PATH_IMAGE100
、
Figure 280481DEST_PATH_IMAGE102
、
Figure 780732DEST_PATH_IMAGE104
respectively corresponding state matrix, input matrix and output matrix,
Figure 201349DEST_PATH_IMAGE106
to take the transposed symbol.
。
Figure 410537DEST_PATH_IMAGE108
Figure 398085DEST_PATH_IMAGE110
(2) A linear quadratic controller of a hearth pressure state space model is designed, and the specific method comprises the following steps:
the first step is as follows: the objective function defining the linear quadratic controller is:
Figure 309988DEST_PATH_IMAGE114
wherein,
Figure 594339DEST_PATH_IMAGE116
in order to be the objective function, the target function,
Figure 131500DEST_PATH_IMAGE118
and
Figure 221815DEST_PATH_IMAGE120
respectively, a weighting matrix for the state variables and the output variables.
The second step is that: calculating parameters of the linear quadratic controller, specifically:
Figure 403398DEST_PATH_IMAGE122
wherein
Figure 153923DEST_PATH_IMAGE126
And feeding back a coefficient vector for the controller.

Claims (1)

1. The chemical process decoupling non-minimum realization state space linear quadratic control method is characterized by comprising the following specific steps:
the decoupling state space model is established by utilizing a chemical process model, and the specific method comprises the following steps:
firstly, acquiring input and output data of a chemical process, and establishing an input and output model by using the data as follows:
Figure 2013100181089100001DEST_PATH_IMAGE002
wherein
Figure 2013100181089100001DEST_PATH_IMAGE004
、、
Figure DEST_PATH_IMAGE008
Are respectively output vectors
Figure DEST_PATH_IMAGE010
Transformation, transfer function matrix, input vectorTransforming;
Figure DEST_PATH_IMAGE012
，，
Figure DEST_PATH_IMAGE016
Figure DEST_PATH_IMAGE018
,
Figure DEST_PATH_IMAGE020
,,
Figure DEST_PATH_IMAGE024
each loop representing a processThe function of the transfer function is such that,
Figure DEST_PATH_IMAGE026
and
Figure DEST_PATH_IMAGE028
are respectively the first
Figure DEST_PATH_IMAGE030
Of input and output variables
Figure 889449DEST_PATH_IMAGE010
The transformation is carried out by changing the parameters of the image,
Figure DEST_PATH_IMAGE032
，for the discrete transform operator of a computer controlled system,is composed of
Figure 299494DEST_PATH_IMAGE010
The inverse number of (c) is,
Figure DEST_PATH_IMAGE036
the number of the input and output variables of the process is the number, and the input and output data are data stored in a data acquisition unit;
further selecting an adjoint matrix decoupling array for the equation as follows:
wherein,is a companion matrix decoupling array which is,
Figure DEST_PATH_IMAGE042
is composed of
Figure 437345DEST_PATH_IMAGE006
The companion matrix of (a);
combining the adjoint matrix decoupling array and the process input and output model to obtain:
wherein,
Figure DEST_PATH_IMAGE046
is the obtained model of the decoupling process,is composed of
Figure 516070DEST_PATH_IMAGE006
The determinant (c) of (a),
Figure DEST_PATH_IMAGE050
to be composed of
Figure 531300DEST_PATH_IMAGE006
Is a diagonal matrix of elements;
processing the decoupling process model intoDiscrete equation form for a single variable process:
Figure DEST_PATH_IMAGE054
whereinAndare respectively the firstThe output and input variables of the individual processes,
Figure DEST_PATH_IMAGE060
，
Figure DEST_PATH_IMAGE062
andare respectively
Figure 609218DEST_PATH_IMAGE056
And
Figure DEST_PATH_IMAGE066
a coefficient matrix polynomial of (a);
Figure DEST_PATH_IMAGE068
wherein
Figure DEST_PATH_IMAGE070
Are the coefficients of the respective coefficients that are,
Figure DEST_PATH_IMAGE072
to move backwards
Figure DEST_PATH_IMAGE074
The step-by-step operators are calculated,
Figure DEST_PATH_IMAGE076
is the resulting model order;
passing the discrete equation model of the univariate process through a backward shift operator
Figure DEST_PATH_IMAGE078
Processing into a state space form:
Figure DEST_PATH_IMAGE080
Figure DEST_PATH_IMAGE082
；
wherein,
Figure DEST_PATH_IMAGE084
、
Figure DEST_PATH_IMAGE086
are respectively the first
Figure DEST_PATH_IMAGE088
The value of the variable at the time of day,
Figure DEST_PATH_IMAGE090
is as follows
Figure DEST_PATH_IMAGE092
The value of the input delta variable at the time,
Figure DEST_PATH_IMAGE094
、
Figure DEST_PATH_IMAGE096
are respectively the first
Figure DEST_PATH_IMAGE098
Output change of timeThe delta quantity and the input delta value,
Figure DEST_PATH_IMAGE100
、
Figure DEST_PATH_IMAGE102
、
Figure DEST_PATH_IMAGE104
respectively corresponding state matrix, input matrix and output matrix,
Figure DEST_PATH_IMAGE106
taking a transposed symbol;
Figure DEST_PATH_IMAGE110
Figure DEST_PATH_IMAGE112
designing a linear quadratic controller based on the decoupling state space model, wherein the specific method comprises the following steps:
a. the objective function defining the linear quadratic controller is:
Figure DEST_PATH_IMAGE114
wherein,
Figure DEST_PATH_IMAGE116
in order to be the objective function, the target function,
Figure DEST_PATH_IMAGE118
and
Figure DEST_PATH_IMAGE120
weighting matrices for state variables and output variables, respectively;
b. the parameters of the linear quadratic controller are calculated,
Figure DEST_PATH_IMAGE122
wherein
Figure DEST_PATH_IMAGE124
Is as follows
Figure 53188DEST_PATH_IMAGE092
The value of the variable at the time of day,
Figure DEST_PATH_IMAGE126
and feeding back a coefficient vector for the controller.
CN 201310018108 2013-01-18 2013-01-18 Chemical process decoupling non-minimal realization state space linear quadric form control method Pending CN103064293A (en)

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Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN104317194A (en) * 2014-09-23 2015-01-28 杭州电子科技大学 Temperature control method for non-minimal state space model predictive control optimization
CN105353619A (en) * 2015-11-26 2016-02-24 杭州电子科技大学 Rolling time domain tracking control method for batch injection molding process
CN113534661A (en) * 2021-06-03 2021-10-22 太原理工大学 Resistance furnace temperature control method based on Kalman filtering and non-minimum state space

Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN104317194A (en) * 2014-09-23 2015-01-28 杭州电子科技大学 Temperature control method for non-minimal state space model predictive control optimization
CN105353619A (en) * 2015-11-26 2016-02-24 杭州电子科技大学 Rolling time domain tracking control method for batch injection molding process
CN105353619B (en) * 2015-11-26 2018-12-21 杭州电子科技大学 A kind of rolling time horizon tracking and controlling method of batch injection moulding process
CN113534661A (en) * 2021-06-03 2021-10-22 太原理工大学 Resistance furnace temperature control method based on Kalman filtering and non-minimum state space

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Application publication date: 20130424