CN111123874B - Fractional-order LQG-reference-based method for determining performance of rotary cement kiln in firing process - Google Patents
Fractional-order LQG-reference-based method for determining performance of rotary cement kiln in firing process Download PDFInfo
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- 238000000034 method Methods 0.000 title claims abstract description 83
- 239000004568 cement Substances 0.000 title claims abstract description 46
- 238000010304 firing Methods 0.000 title claims abstract description 26
- 238000005526 cement kiln firing Methods 0.000 claims description 10
- 230000014509 gene expression Effects 0.000 claims description 6
- 238000012546 transfer Methods 0.000 claims description 4
- 230000010354 integration Effects 0.000 claims description 3
- 239000011159 matrix material Substances 0.000 claims description 3
- 238000004886 process control Methods 0.000 claims description 3
- 239000000126 substance Substances 0.000 claims description 3
- 239000006185 dispersion Substances 0.000 claims description 2
- 238000013404 process transfer Methods 0.000 claims 1
- 238000005265 energy consumption Methods 0.000 abstract description 2
- 239000003245 coal Substances 0.000 description 14
- 238000002347 injection Methods 0.000 description 12
- 239000007924 injection Substances 0.000 description 12
- 238000004519 manufacturing process Methods 0.000 description 3
- 239000002994 raw material Substances 0.000 description 3
- 230000009286 beneficial effect Effects 0.000 description 1
- 230000007547 defect Effects 0.000 description 1
- 239000007921 spray Substances 0.000 description 1
- 238000005507 spraying Methods 0.000 description 1
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- G05B19/00—Programme-control systems
- G05B19/02—Programme-control systems electric
- G05B19/418—Total factory control, i.e. centrally controlling a plurality of machines, e.g. direct or distributed numerical control [DNC], flexible manufacturing systems [FMS], integrated manufacturing systems [IMS] or computer integrated manufacturing [CIM]
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- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B2219/00—Program-control systems
- G05B2219/30—Nc systems
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Abstract
The invention relates to a method for determining the performance of a rotary cement kiln in a firing process based on a fractional-order LQG standard. The method comprises the steps of firstly collecting operation data of the rotary cement kiln in the burning process, establishing a fractional order model of the rotary cement kiln in the burning process, further using a fractional order LQG standard to obtain the optimal input variance and output variance of the rotary cement kiln in the burning process according to the fractional order model, and finally establishing a performance balance curve of the rotary cement kiln in the burning process. The invention can ensure the control precision of the rotary cement kiln in the firing process, simultaneously has better input performance, and realizes the stable high-precision control and low-energy consumption control of the rotary cement kiln in the firing process.
Description
Technical Field
The invention belongs to the field of automatic industrial process control, and relates to a method for determining the firing process performance of a rotary cement kiln based on a fractional-order LQG standard.
Background
In the process of burning the rotary cement kiln, a plurality of controllers of a process control loop have good performance at the initial stage of operation, but after the rotary cement kiln is operated for a period of time, the performance of the controllers can be reduced under the influence of a complex industrial environment, so that the control precision of a control system is reduced, the quality of cement clinker is finally reduced, the operation cost of an enterprise is increased, and resources are wasted.
Most of the traditional methods are based on the MVC reference, but the MVC reference has poor robustness performance, and cannot realize the balance with the input performance, and meanwhile, the existing LQG reference can only be used in the integer order process.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a method for determining the firing process performance of a rotary cement kiln based on a fractional LQG standard.
The technical scheme of the invention is as follows: firstly, collecting operation data of a cement rotary kiln in a burning process, establishing a fractional order model of the cement rotary kiln in the burning process, further using a fractional order LQG standard to obtain the optimal input variance and output variance of the cement rotary kiln in the burning process according to the fractional order model, and finally establishing a performance balance curve of the cement rotary kiln in the burning process, wherein the specific steps are as follows:
step 1, establishing a fractional order model of a controlled object in a rotary cement kiln firing process, which comprises the following specific steps:
1-1, firstly, collecting real-time operation data of a rotary cement kiln in a firing process, and establishing a fractional order dispersion time model of the rotary cement kiln in the firing process under the condition of uncertain interference, which is expressed in the following form:
Yk＝Gp(z-1)Uk+Gd(z-1)ξk
wherein, UkProcess input representing time k, YkIndicating the process output, ξ, at time kkRepresents a variance of time k of
Zero mean discrete white noise of (z)-1Representing the delay operator in the z-domain. The process and interference transfer functions are described as follows:
wherein, T (z)-1) Is a filter for improving system robustness and suppressing interference, D is a difference operator, and D is 1-z-1。A(z-1),B(z-1),T(z-1) Represents a polynomial defined as follows:
A(z-1)＝A1+A2z-1+…+Arz-r
B(z-1)＝B1+B2z-1+…+Bsz-s
T(z-1)＝T1+T2z-1+…+Tqz-q
1-2, designing an LQG objective function as follows:
wherein, JLQGRepresenting the LQG objective function, P representing the step size, P being the control input weight, Δ Uk+j-1For control input at a future time k + j-1, Yk+j|kFor j-step forward prediction output at the time k, the following can be calculated by a model after disturbance simplification:
wherein A is0(z-1),B0(z-1) Representing the ideal process polynomial with the disturbance filter coefficients removed.
1-3, adding the fractional order definite integral operator into the objective function of 1-2 to obtain a fractional order LQG objective function:
wherein I represents a fractional order integration operator, JFLQGRepresenting a fractional order LQG objective function, e1，e2Each represents an arbitrary order integral number, D represents a fractional order differential operator, Δ Uk-1Representing the process control input at time k-1, TsFor the sample length, the above equation can be continued to be discrete using the fractional GL definition, and the following objective function can be obtained:
wherein symbols ←, → represent the past and future, respectively,1，2is represented by1，2A finite-dimensional weighting matrix is constructed.
The coefficient polynomial is expressed by the following formula:
X＝e1、e2,
step 2, solving a performance determination curve of the rotary cement kiln in the firing process, and specifically comprising the following steps:
2-1. at time k, the inputs and outputs at time k-1 and the inputs and outputs at times prior thereto are known, the fractional order objective function shown in step 1-3 is further transformed into:
wherein the content of the first and second substances,
wherein, Ui(i-0, 1, …, k, k +1, …, p) represents the process input at time i, Yi(i-0, 1, …, k, k +1, …, p) represents the process output at time i.
2-2. without considering the constraints, in a closed-loop system, minimizing the objective function shown in equation step 2-1, the following linear time-invariant control law can be derived:
wherein, S (z)-1)，R(z-1) Indicating feedback controlDevice Gc(z-1) Numerator and denominator polynomials.
And 2-3, substituting the linear time-invariant control law obtained in the step 2-2 into the process model described in the formula step 1-1 to further obtain the following input and output expressions:
further using Parseval theory, display expressions of process input variance and process output variance are obtained:
wherein, Var (Y)k) Represents the process output variance, Var (U)k) Representing the process input variance.
2-4, changing the weight r in the objective function in the step 2-1, and then continuously solving a new process output variance Var (Y) according to the steps 2-1 to 2-3k) Process input variance Var (U)k) And solving a plurality of groups of data, and establishing a coordinate system by using x and y axes respectively to obtain a performance determination curve of the rotary cement kiln in the firing process.
The invention has the beneficial effects that: the invention can ensure the control precision of the rotary cement kiln in the firing process, simultaneously has better input performance, and realizes the stable high-precision control and low-energy consumption control of the rotary cement kiln in the firing process.
Drawings
Fig. 1 is a fractional order LQG performance determination curve.
Detailed Description
Taking the firing process of a cement rotary kiln as an example:
in the cement flow production process, the rotary cement kiln firing process is an important ring in cement production. After the cement raw material is prepared, the cement raw material continues to enter the cement rotary kiln, at the moment, the coal spraying kiln head of the rotary kiln starts to spray coal to the rotary kiln, the rotary kiln is heated, the cement clinker reacts, and the cement raw material is gradually converted into the cement clinker as the temperature of a burning zone of the rotary kiln rises to a certain degree.
Step 1, establishing a fractional order model of a controlled object in a rotary cement kiln firing process, which comprises the following specific steps:
1-1, firstly, collecting real-time operation data of a rotary cement kiln in a firing process, and establishing a fractional order discrete time model of the rotary cement kiln in the firing process under the condition of uncertain interference, which is expressed in the following form:
Yk＝Gp(z-1)Uk+Gd(z-1)ξk
wherein, UkIndicating the opening degree of the kiln head coal injection input valve at the time of k, YkIndicating the temperature of the rotary kiln at time k, ξkRepresents a variance of time k of
Zero mean discrete white noise of (z)-1Representing the delay operator in the z-domain. The process and interference transfer functions are described as follows:
wherein, T (z)-1) Is a filter for improving system robustness and suppressing interference, delta is a difference operator, and is 1-z-1。A(z-1),B(z-1),T(z-1) Represents a polynomial defined as follows:
A(z-1)＝A1+A2z-1+…+Arz-r
B(z-1)＝B1+B2z-1+…+Bsz-s
T(z-1)＝T1+T2z-1+…+Tqz-q
1-2, designing an LQG objective function of a rotary cement kiln firing process, which is as follows:
wherein, JLQGExpressing the firing process of the rotary cement kiln with an LQG objective function, P expressing the step length, r being the weighted value of the opening degree of the coal injection input valve at the kiln head, DUk+j-1Inputting the opening change of a valve for the kiln head coal injection at the future k + j-1 moment, Yk+j|kAnd (3) for the j-step forward predicted output of the temperature of the rotary kiln at the time k, calculating by using a cement rotary kiln firing process model after disturbance simplification:
wherein A is0(z-1),B0(z-1) And expressing the ideal rotary cement kiln firing process polynomial after the disturbance filter coefficient is removed.
1-3, adding the fractional order definite integral operator to the objective function in the step 1-2 to obtain a fractional order LQG objective function in the rotary cement kiln firing process:
wherein I represents a fractional order integration operator, JFLQGRepresents a fractional order LQG objective function in the rotary cement kiln firing process,1，2all represent an arbitrary order integral number, D represents a fractional order differential operator, DUk-1Representing the variation of the opening of the kiln head coal injection input valve at the time of k-1, TsFor the sample length, the above equation can be continued to be discrete using the fractional GL definition, and the following objective function can be obtained:
whereinThe symbols ←, → represent the past and future, respectively,1，2is represented by1，2A finite-dimensional weighting matrix is constructed.
The coefficient polynomial is expressed by the following formula:
X＝1、e2,
step 2, designing a performance determination curve of the rotary cement kiln in the firing process, and specifically comprising the following steps:
and 2-1, when the opening change of the kiln head coal injection input valve and the temperature of the rotary kiln at the time k and the time k-1 and the opening change of the kiln head coal injection input valve and the temperature of the rotary kiln at the previous time are known, further converting the fractional order objective function shown in the step 1-3 into the following steps:
wherein the content of the first and second substances,
wherein, Ui(i is 0,1, …, k, k +1, …, p) represents the variation of the opening of the kiln head coal injection inlet valve at the time of i, and Y represents the variation of the opening of the kiln head coal injection inlet valve at the time of ii(i ═ 0,1, …, k, k +1, …, p) represents the rotary kiln temperature at time i.
2-2, in the rotary cement kiln burning process, under the condition of not considering constraint and in a closed loop system, minimizing the objective function shown in the step 2-1, and deducing the following linear time-invariant control law:
wherein, S (z)-1)，R(z-1) Feedback controller G for indicating rotary cement kiln firing processc(z-1) Numerator and denominator polynomials.
And 2-3, substituting the linear time-invariant control law obtained in the step 2-2 into the rotary cement kiln firing process model described in the step 1-1 to obtain the following expressions of kiln head coal injection input valve opening and rotary kiln temperature:
and further using Parseval theory to obtain display expressions of the opening variance of the kiln head coal injection input valve and the temperature variance of the rotary kiln:
wherein, Var (Y)k) Denotes the temperature variance of the rotary kiln, Var (U)k) And the opening variance of the coal injection inlet valve of the kiln head is represented.
2-4, changing the weight r in the objective function in the step 2-1, and then continuously solving a new rotary kiln temperature variance Var (Y) according to the steps 2-1 to 2-3k) Opening variance Var (U) of coal injection input valve at kiln headk) And solving a plurality of groups of data, and establishing a coordinate system by using x and y axes respectively to obtain a performance determination curve of the rotary cement kiln in the firing process, which is shown in figure 1.
Claims (2)
1. The method for determining the performance of the rotary cement kiln in the firing process based on the fractional order LQG standard is characterized by comprising the following steps of:
step 1, establishing a fractional order model of a controlled object in a rotary cement kiln firing process, which comprises the following specific steps:
1-1, collecting real-time operation data of a rotary cement kiln in a firing process, and establishing a fractional order dispersion time model of the rotary cement kiln in the firing process under the condition of uncertain interference, which is expressed in the following form:
Yk＝Gp(z-1)Uk+Gd(z-1)ξk
wherein, UkProcess input representing time k, YkIndicating the process output, ξ, at time kkRepresents a variance of time k of
Zero mean discrete white noise of (z)-1Representing a delay operator under the z-domain; gp(z-1) As a function of the process, Gd(z-1) Is an interference transfer function;
1-2, designing an LQG objective function as follows:
wherein, JLQGRepresenting the LQG objective function, P representing the step size, P being the control input weight, Δ Uk+j-1For control input at a future time k + j-1, Yk+j|kFor j-step forward prediction output at the time k, the following can be calculated by a model after disturbance simplification:
wherein A is0(z-1),B0(z-1) Representing an ideal process polynomial with the disturbance filter coefficients removed;
1-3, adding the fractional order definite integral operator into the objective function of 1-2 to obtain a fractional order LQG objective function:
wherein I represents a fractional order integration operator, JFLQGRepresenting a fractional order LQG objective function,1，2each represents an arbitrary order integral number, D represents a fractional order differential operator, Δ Uk-1Representing the process control input at time k-1, TsFor the sample length, the above equation can be continued to be discrete using the fractional GL definition, and the following objective function can be obtained:
wherein symbols ←, → represent the past and future, respectively,1，2is represented by1，2Constructing a weighting matrix of finite dimensions;
step 2, solving a performance determination curve of the rotary cement kiln in the firing process, and specifically comprising the following steps:
2-1. at time k, the inputs and outputs at time k-1 and the inputs and outputs at times prior thereto are known, the fractional order objective function shown in step 1-3 is further transformed into:
wherein the content of the first and second substances,
wherein, Ui(i-0, 1, …, k, k +1, …, p) represents the process input at time i, Yi(i ═ 0,1, …, k, k +1, …, p) represents the process output at time i;
2-2. without considering the constraints, in a closed-loop system, minimizing the objective function shown in equation step 2-1, the following linear time-invariant control law can be derived:
wherein, S (z)-1)，R(z-1) Indicating a feedback controller Gc(z-1) Numerator and denominator polynomials of (a);
and 2-3, substituting the linear time-invariant control law obtained in the step 2-2 into the process model described in the formula step 1-1 to further obtain the following input and output expressions:
further using Parseval theory, display expressions of process input variance and process output variance are obtained:
wherein, Var (Y)k) Represents the process output variance, Var (U)k) Represents the process input variance, T (z)-1) Is a filter for improving system robustness and suppressing interference, A (z)-1),B(z-1) Represents a polynomial;
2-4, changing the weight p in the objective function in the step 2-1, and then continuously solving a new process output variance Var (Y) according to the steps 2-1 to 2-3k) Process input variance Var (U)k) And solving a plurality of groups of data, and establishing a coordinate system by using x and y axes respectively to obtain a performance determination curve of the rotary cement kiln in the firing process.
2. The method for determining the performance of the rotary cement kiln in the firing process based on the fractional-order LQG standard as claimed in claim 1, is characterized in that:
process transfer function Gp(z-1) And interference transfer function Gd(z-1) The specific description is as follows:
where Δ is a difference operator, Δ ═ 1-z-1；A(z-1),B(z-1),T(z-1) Is defined as follows:
A(z-1)＝A1+A2z-1+…+Arz-r
B(z-1)＝B1+B2z-1+…+Bsz-s
T(z-1)＝T1+T2z-1+…+Tqz-q。
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