CN107942669B - Limited rolling time domain hybrid tracking control method for batch injection molding process - Google Patents

Limited rolling time domain hybrid tracking control method for batch injection molding process Download PDF

Info

Publication number
CN107942669B
CN107942669B CN201711232764.3A CN201711232764A CN107942669B CN 107942669 B CN107942669 B CN 107942669B CN 201711232764 A CN201711232764 A CN 201711232764A CN 107942669 B CN107942669 B CN 107942669B
Authority
CN
China
Prior art keywords
model
switching
stage
injection molding
different stages
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Active
Application number
CN201711232764.3A
Other languages
Chinese (zh)
Other versions
CN107942669A (en
Inventor
王立敏
罗卫平
余维燕
王鹏
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Hainan Normal University
Original Assignee
Hainan Normal University
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Hainan Normal University filed Critical Hainan Normal University
Priority to CN201711232764.3A priority Critical patent/CN107942669B/en
Publication of CN107942669A publication Critical patent/CN107942669A/en
Application granted granted Critical
Publication of CN107942669B publication Critical patent/CN107942669B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Classifications

    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
    • G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
    • G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
    • G05B13/042—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators in which a parameter or coefficient is automatically adjusted to optimise the performance

Abstract

The invention belongs to the field of advanced control of industrial processes, and relates to a limited rolling time domain hybrid tracking control method for a batch injection molding process. The method comprises the steps of firstly, establishing input and output models in different stages by collecting input and output data, then selecting appropriate state variables to establish a multi-stage state space model, further converting the state space model into an extended state space model containing the state variables and output tracking errors, representing the extended state space model by using a switching system model, then selecting performance indexes containing terminal states aiming at different stages, and obtaining an optimal hybrid control law by combining a Riccati equation and boundary conditions. The control law has more flexible adjustment by adding the adjustable weighting coefficient and ensures that the system obtains better control performance. Finally, aiming at different stages, a residence time method depending on the Lyapunov function is designed, the result obtained by the method does not need to refer to any other variable, the method is simple and easy to implement, the running time of the system can be shortened, and the production efficiency is improved.

Description

Limited rolling time domain hybrid tracking control method for batch injection molding process
Technical Field
The invention belongs to the field of advanced control of industrial processes, and relates to a limited rolling time domain hybrid tracking control method for a batch injection molding process.
Background
Injection molding processes are widely used in plastic processing and other related fields, and although some research has been made on injection molding processes, they still pose a challenge in terms of high-precision control of modern plastic processing. The main reasons are the complex dynamic characteristics and the variable process conditions. The injection molding process is a typical multi-stage intermittent process, each batch mainly comprises two stages of injection and pressure maintaining, the variables to be controlled in the injection stage and the pressure maintaining stage are respectively injection speed and pressure maintaining pressure, the variables controlled in the two different stages are different, the control targets are different, when the stage is switched to the other stage, and the length of the operation time of each stage directly influences the production efficiency and the product quality. It is clear that it is crucial to design a high-precision controller and the switching conditions of the adjacent phases and the run time of each phase for such a production process.
High-precision control for a single phase is mature at present, but the single process does not involve switching conditions nor run-time. Although there has been some research effort on multiple stages, the controller gain cannot be adjusted throughout the process. In actual industrial control, due to factors such as drift, process nonlinearity and system external interference existing in actual working conditions, the control performance of the control system may be reduced after the control system operates for a period of time. If the controller is not repaired in time to improve the control quality, the economic benefit obtained by the control system is reduced.
Therefore, it is necessary to provide a more effective control method for seeking suitable switching conditions and operation time at different stages of batch injection molding process and solving the problems of mold mismatch and interference in control.
Disclosure of Invention
The invention aims to seek the appropriate switching condition and running time at different stages of batch injection molding process; and secondly, providing a limited rolling time domain tracking control method for batch injection molding process for improving the tracking performance and anti-interference performance of the control method in the batch process. The method comprises the steps of firstly, establishing input and output models in different stages by collecting input and output data, then selecting appropriate state variables to establish a multi-stage state space model, further converting the state space model into an extended state space model containing the state variables and output tracking errors, representing the extended state space model by using a switching system model, then selecting performance indexes containing terminal states aiming at different stages, and obtaining an optimal hybrid control law by combining a Riccati equation and boundary conditions. The control law has more flexible adjustment by adding the adjustable weighting coefficient and ensures that the system obtains better control performance. Finally, aiming at different stages, a residence time method depending on the Lyapunov function is designed, the result obtained by the method does not need to refer to any other variable, the method is simple and easy to implement, the running time of the system can be shortened, and the production efficiency is improved.
The limited rolling time domain hybrid tracking control method for the batch injection molding process comprises the following specific steps:
step 1, aiming at different stages in the batch process, establishing a switching system model of a controlled object based on a state space model, specifically:
step 1, aiming at different stages in the batch injection molding process, establishing a switching system model of a controlled object based on a state space model, specifically:
1.1 firstly, acquiring input and output data of a batch injection molding process, and establishing a corresponding stage model of the batch process by using the data, wherein the form is as follows:
Ai(z-1)yi(z)＝Bi(z-1)ui(z)
Figure BDA0001488450560000021
Figure BDA0001488450560000022
wherein, yi(z)，ui(z) z-transforms of the output and input, respectively, of the ith stage, ai,biAre respectively polynomial Ai(z-1)，Bi(z-1) M, n are each Ai(z-1)，Bi(z-1) The maximum order of (d);
1.2 the model in step 1.1 is further processed, introducing a delta difference operator, yi(k)∈R,ui(k) E.R is respectively an output variable and an input variable of the ith stage of the batch process at the moment k; obtaining an error model:
Figure BDA0001488450560000023
Figure BDA0001488450560000031
and selecting a non-minimum state space variable Deltax0 i(k)TThe form is as follows:
Δx0 i(k)T＝[Δyi(k)T,Δyi(k-1)T,…,Δyi(k-n+1)T,Δui(k-1)T,Δui(k-2)T,…,Δui(k-m+1)T]
wherein, Δ x0 i(k) Is (m-1) × p + nxq, p being the dimension of the input variable and q being the dimension of the output variable;
obtaining a new ith stage state space model according to the above:
Figure BDA0001488450560000032
Figure BDA0001488450560000033
wherein the content of the first and second substances,
Figure BDA0001488450560000034
Figure BDA0001488450560000035
Figure BDA0001488450560000036
wherein the content of the first and second substances,
Figure BDA0001488450560000037
is an identity matrix of dimension p,
Figure BDA0001488450560000038
is a q-dimensional identity matrix;
1.3 for better tracking performance, an output tracking error e is defined for phase ii(k)＝yi(k)-ri(k)And combining the step 1.2 to obtain the following tracking error form:
Figure BDA0001488450560000039
wherein r isi(k) The expected output of the stage i at the moment k;
1.4, aiming at the ith stage, selecting a new state variable again, further expanding the model to obtain a new expanded state space model, and enabling the model to comprise the state variable and an output tracking error, wherein the form of the model is as follows:
zi(k+1)＝Aizi(k)+BiΔui(k)
wherein the content of the first and second substances,
Figure BDA0001488450560000041
matrix Ai0 in (1) represents a zero matrix;
1.5 the system is reproduced as a switching system model:
z(k+1)＝Aσ(k)z(k)+Bσ(k)Δu(k).
wherein σ (k) Z + →NWhere {1,2, …, N } denotes a switching signal, which may be time or system state dependent, N is the number of phases of the subsystem, and the switching sequence is defined as S: ═ T: { (T)0,T1,T2,...,Tt,.. }; all the time intervals of the successive interruptions satisfy Tt+1-Tt≥τi,t＝0,1,2,...,，TtRepresents the T-th switching time, T0Is the initial time, τiFor the dwell time of the different phases and whose value depends on the Lyapunov function, Aσ(k),Bσ(k)The above formula model 1.4 represents for different phases;
step 2, designing controllers and switching signals sigma (k) of different stages in the batch injection molding process to obtain switching conditions and operating time of different stages, specifically:
2.1 considering the non-minimum realization expansion state space model containing the free terminal state, selecting the corresponding performance index form as follows:
Figure BDA0001488450560000042
wherein Q isi，Ri，
Figure BDA0001488450560000043
Weight matrixes respectively representing the state variable, the controlled input and the terminal state of the ith stage,
Figure BDA0001488450560000044
optimizing the time domain for rolling;
Figure BDA0001488450560000045
respectively as the starting end and the terminal end;
2.2, according to the performance indexes in the step 2.1, obtaining the optimal control laws of the controllers in different stages, wherein the form is as follows:
Figure BDA0001488450560000046
Figure BDA0001488450560000047
Figure BDA0001488450560000051
2.3 applying the control quantity obtained in the step 2.2 to the controlled object:
ui(k)＝Δui(k)+ui(k-1)
2.4 at the next moment, repeating the steps 2.1 to 2.3 to continuously solve new control quantity, and circulating in sequence;
2.5 design the switching signal to σ (k) for different phases;
2.5.1 for the switching system in step 1.5, different stage controllers are designed as follows:
Δui(k)＝-Kizi(k)
wherein the content of the first and second substances,
Figure BDA0001488450560000052
for each phase i, the switching system may become:
z(k+1)＝(Ai-BiKi)z(k)
2.5.2 for the ith subsystem, the following Lyapunov function is selected:
Vi(k)＝zT(k)Pi(k)z(k)
wherein, Pi(k)，i∈N,NThat {1,2, …, N } is dependent on the residence time τiA matrix of (a); then:
Figure BDA0001488450560000053
if the switching system is stable, Δ V must be presenti(k) < 0, which is equivalent to:
Figure BDA0001488450560000054
Figure BDA0001488450560000055
Figure BDA0001488450560000056
combining with step 2.2, solving the inequality to obtain tau at different stagesi。
Compared with the prior art, the invention has the beneficial effects that: aiming at an injection section and a pressure maintaining section which are two important stages to be controlled in the injection molding process, the switching condition and the operation time are designed, and the high-efficiency production is realized. Aiming at the condition that the controller is mismatched and interfered by a model, the controller which is more flexible to adjust by increasing the weight coefficient which can be adjusted is designed, the control quality of the controller is improved, and better control performance is realized. The method has the advantages that other parameters are not required to be set, the value is directly obtained, the method is simple and easy to implement, and the method is obviously superior to other methods, such as an average residence time method, namely the average value of residence time of the system in each stage. The average residence time method often assumes that a certain variable in its conditions is given, which undoubtedly increases the run time of a certain phase, thus extending the run time of the whole production process. Therefore, the method provided by the invention ensures the stable operation of the system and has the optimal control performance, and improves the production efficiency under the condition of ensuring the product quality.
Detailed Description
The present invention will be further described with reference to the following specific examples.
The limited rolling time domain hybrid tracking control method for the batch injection molding process comprises the following specific steps:
step 1, aiming at different stages in the batch process, establishing a switching system model of a controlled object based on a state space model, specifically:
step 1, aiming at different stages in the batch injection molding process, establishing a switching system model of a controlled object based on a state space model, specifically:
1.1 firstly, acquiring input and output data of a batch injection molding process, and establishing a corresponding stage model of the batch process by using the data, wherein the form is as follows:
Ai(z-1)yi(z)＝Bi(z-1)ui(z)
Figure BDA0001488450560000061
Figure BDA0001488450560000062
wherein, yi(z)，ui(z) z-transforms of the output and input, respectively, of the ith stage, ai,biAre respectively polynomial Ai(z-1)，Bi(z-1) M, n are each Ai(z-1)，Bi(z-1) The maximum order of (d);
1.2 the model in step 1.1 is further processed, introducing a delta difference operator, yi(k)∈R,ui(k) E.R is respectively an output variable and an input variable of the ith stage of the batch process at the moment k; obtaining an error model:
Figure BDA0001488450560000063
and selecting a non-minimum state space variable Deltax0 i(k)TThe form is as follows:
Δx0 i(k)T＝[Δyi(k)T,Δyi(k-1)T,…,Δyi(k-n+1)T,Δui(k-1)T,Δui(k-2)T,…,Δui(k-m+1)T]
wherein, Δ x0 i(k) Is (m-1) × p + nxq, p being the dimension of the input variable and q being the dimension of the output variable;
obtaining a new ith stage state space model according to the above:
Figure BDA0001488450560000071
Figure BDA0001488450560000072
wherein the content of the first and second substances,
Figure BDA0001488450560000073
Figure BDA0001488450560000074
Figure BDA0001488450560000075
wherein the content of the first and second substances,
Figure BDA0001488450560000076
is an identity matrix of dimension p,
Figure BDA0001488450560000077
is a q-dimensional identity matrix;
1.3 for better tracking performance, an output tracking error e is defined for phase ii(k)＝yi(k)-ri(k) And combining the step 1.2 to obtain the following tracking error form:
Figure BDA0001488450560000078
wherein r isi(k) The expected output of the stage i at the moment k;
1.4, aiming at the ith stage, selecting a new state variable again, further expanding the model to obtain a new expanded state space model, and enabling the model to comprise the state variable and an output tracking error, wherein the form of the model is as follows:
zi(k+1)＝Aizi(k)+BiΔui(k)
wherein the content of the first and second substances,
Figure BDA0001488450560000081
matrix Ai0 in (1) represents a zero matrix;
1.5 the system is reproduced as a switching system model:
z(k+1)＝Aσ(k)z(k)+Bσ(k)Δu(k).
wherein σ (k) Z + →NWhere {1,2, …, N } denotes a switching signal, which may be time or system state dependent, N is the number of phases of the subsystem, and the switching sequence is defined as S: ═ T: { (T)0,T1,T2,...,Tt,.. }; all continuously interruptedThe time interval satisfies Tt+1-Tt≥τi,t＝0,1,2,...,，TtRepresents the T-th switching time, T0Is the initial time, τiFor the dwell time of the different phases and whose value depends on the Lyapunov function, Aσ(k),Bσ(k)The above formula model 1.4 represents for different phases;
step 2, designing controllers and switching signals sigma (k) of different stages in the batch injection molding process to obtain switching conditions and operating time of different stages, specifically:
2.1 considering the non-minimum realization expansion state space model containing the free terminal state, selecting the corresponding performance index form as follows:
Figure BDA0001488450560000082
wherein Q isi，Ri，
Figure BDA0001488450560000083
Weight matrixes respectively representing the state variable, the controlled input and the terminal state of the ith stage,
Figure BDA0001488450560000084
optimizing the time domain for rolling;
Figure BDA0001488450560000085
respectively as the starting end and the terminal end;
2.2, according to the performance indexes in the step 2.1, obtaining the optimal control laws of the controllers in different stages, wherein the form is as follows:
Figure BDA0001488450560000086
Figure BDA0001488450560000087
Figure BDA0001488450560000088
2.3 applying the control quantity obtained in the step 2.2 to the controlled object:
ui(k)＝Δui(k)+ui(k-1)
2.4 at the next moment, repeating the steps 2.1 to 2.3 to continuously solve new control quantity, and circulating in sequence;
2.5 design the switching signal to σ (k) for different phases;
2.5.1 for the switching system in step 1.5, different stage controllers are designed as follows:
Δui(k)＝-Kizi(k)
wherein the content of the first and second substances,
Figure BDA0001488450560000091
for each phase i, the switching system may become:
z(k+1)＝(Ai-BiKi)z(k)
2.5.2 for the ith subsystem, the following Lyapunov function is selected:
Vi(k)＝zT(k)Pi(k)z(k)
wherein, Pi(k)，i∈N,NThat {1,2, …, N } is dependent on the residence time τiA matrix of (a); then:
Figure BDA0001488450560000092
if the switching system is stable, Δ V must be presenti(k) < 0, which is equivalent to:
Figure BDA0001488450560000093
Figure BDA0001488450560000094
Figure BDA0001488450560000095
combining with step 2.2, solving the inequality to obtain tau at different stagesi。
Examples
The injection molding process is a typical batch production process, and each batch mainly comprises three steps, i.e., an injection section → a pressure holding section → a cooling section. In the injection section, the forward movement of the screw extrudes the melt (formed by heating the raw material by the heating ring) stored at the front end of the machine barrel forward, flows through the pouring channel, the runner and the sprue, and enters the closed mold cavity (mold cavity). When the mold cavity is completely filled, the molding process is switched from the injection section to the pressure maintaining section. In the hold pressure section, the screw is advanced at a very low speed to maintain a certain nozzle pressure. A small amount of melt continues into the mold cavity to compensate for the volume shrinkage due to material cooling and solidification. Once the gate of the mold having the smallest cross-sectional area is substantially solidified, the hold pressure section is stopped and the process enters the cooling section, ideally at which time the melt flow should stop. Plasticizing the injection mechanism in a cooling section to prepare for the next cycle; at the same time, the material in the mold cavity continues to cool until it is fully solidified. And finally, opening the mold, and ejecting the product by the ejector pin to finish a cycle.
Therefore, the injection molding process mainly comprises an injection section, a pressure maintaining section and a cooling section. The control effects of the injection section and the pressure maintaining section have direct influence on the final quality of the product, wherein the injection speed of the injection section and the pressure maintaining section have the greatest influence on the control effect of the corresponding stage, and the given value needs to be controlled and tracked. Both parameters are controlled by the respective valve, the valve opening influencing the parameter. Furthermore, at the injection stage, when the cavity pressure reaches a certain value, the process enters the hold pressure stage, and thus the cavity pressure needs to be detected but does not need to be directly controlled at the injection stage. Only the high-temperature finished product is cooled in the cooling section, and no control measures are taken; therefore, it is necessary to establish a hybrid state space model of the injection section and the pressure maintaining section in the injection molding process.
The frequency domain mathematical model of the injection section and the pressure maintaining section in the existing injection molding process is as follows:
the injection section frequency domain mathematical model is as follows: (1-0.9291 z)-1-0.03191z-2)IV＝(8.687z-1-5.617z-2)VO，
The frequency domain mathematical model of the pressure maintaining section is as follows: (1-1.317 z)-1+0.3259z-2)NP＝(171.8Z-1-156.8Z-2)VO；
Wherein IV represents the injection speed of the injection section, and the set value is 40 mm/s; NP represents the die cavity pressure, and the set value of the pressure maintaining section is 300 bar; VO represents the valve opening.
The input and output model of the two stages of the injection molding process is rewritten into the equivalent switching system augmentation model by the step 1 as follows:
z(k+1)＝Aσ(k)z(k)+Bσ(k)Δu(k),σ(k)＝{1,2}
the injection section is defined as stage 1, and the pressure holding section as stage 2, i.e., σ (t, k) is 1, and σ (t, k) is 2, which respectively represent stage 1 and stage 2.
And 2, designing a corresponding controller which can be flexibly adjusted in real time according to different stages so as to improve the control quality of the controller, and solving the defect that the gain of the controller can not be adjusted in the whole process in the existing method. Finally, aiming at different stages, a residence time method depending on the Lyapunov function is designed, the result obtained by the method does not need to refer to any other variable, the method is simple and easy to implement, the running time of the system is shortened, and the production efficiency is improved.
The foregoing is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, various modifications and decorations can be made without departing from the principle of the present invention, and these modifications and decorations should also be regarded as the protection scope of the present invention.

Claims (1)

1. The limited rolling time domain hybrid tracking control method for the batch injection molding process is characterized by comprising the following steps of: the method comprises the following specific steps:
step 1, aiming at different stages in the batch injection molding process, establishing a switching system model of a controlled object based on a state space model, specifically:
1.1 firstly, acquiring input and output data of a batch injection molding process, and establishing a corresponding stage model of the batch process by using the data, wherein the form is as follows:
Ai(z-1)yi(z)＝Bi(z-1)ui(z)
Figure FDA0001488450550000011
Figure FDA0001488450550000012
wherein, yi(z)，ui(z) z-transforms of the output and input, respectively, of the ith stage, ai,biAre respectively polynomial Ai(z-1)，Bi(z-1) M, n are each Ai(z-1)，Bi(z-1) The maximum order of (d);
1.2 the model in step 1.1 is further processed, introducing a delta difference operator, yi(k)∈R,ui(k) E.R is respectively an output variable and an input variable of the ith stage of the batch process at the moment k; obtaining an error model:
Figure FDA0001488450550000013
and selecting non-minimum state space variables
Figure FDA0001488450550000014
The form is as follows:
Δx0 i(k)T＝[Δyi(k)T,Δyi(k-1)T,…,Δyi(k-n+1)T,Δui(k-1)T,Δui(k-2)T,…,Δui(k-m+1)T]
wherein, Δ x0 i(k) Is (m-1) × p + nxq, p being the dimension of the input variable and q being the dimension of the output variable;
obtaining a new ith stage state space model according to the above:
Figure FDA0001488450550000015
Figure FDA0001488450550000016
wherein the content of the first and second substances,
Figure FDA0001488450550000027
Figure FDA0001488450550000021
Figure FDA0001488450550000022
wherein the content of the first and second substances,
Figure FDA0001488450550000023
is an identity matrix of dimension p,
Figure FDA0001488450550000024
is a q-dimensional identity matrix;
1.3 for better tracking performance, an output tracking error e is defined for phase ii(k)＝yi(k)-ri(k) And combining the step 1.2 to obtain the following tracking error form:
Figure FDA0001488450550000025
wherein r isi(k) The expected output of the stage i at the moment k;
1.4, aiming at the ith stage, selecting a new state variable again, further expanding the model to obtain a new expanded state space model, and enabling the model to comprise the state variable and an output tracking error, wherein the form of the model is as follows:
zi(k+1)＝Aizi(k)+BiΔui(k)
wherein the content of the first and second substances,
Figure FDA0001488450550000026
matrix Ai0 in (1) represents a zero matrix;
1.5 the system is reproduced as a switching system model:
z(k+1)＝Aσ(k)z(k)+Bσ(k)Δu(k)；
wherein σ (k) is Z+→NWhere {1,2, …, N } denotes a switching signal, which may be time or system state dependent, N is the number of phases of the subsystem, and the switching sequence is defined as S: ═ T: { (T)0,T1,T2,...,Tt,.. }; all the time intervals of the successive interruptions satisfy Tt+1-Tt≥τi,t＝0,1,2,...，TtRepresents the T-th switching time, T0Is the initial time, τiFor the dwell time of the different phases and whose value depends on the Lyapunov function, Aσ(k),Bσ(k)The above formula model 1.4 represents for different phases;
step 2, designing controllers and switching signals sigma (k) of different stages in the batch injection molding process to obtain switching conditions and operating time of different stages, specifically:
2.1 considering the non-minimum realization expansion state space model containing the free terminal state, selecting the corresponding performance index form as follows:
Figure FDA0001488450550000031
wherein Q isi，Ri，
Figure FDA0001488450550000032
Weight matrixes respectively representing the state variable, the controlled input and the terminal state of the ith stage,
Figure FDA0001488450550000033
optimizing the time domain for rolling;
Figure FDA0001488450550000034
respectively as the starting end and the terminal end;
2.2, according to the performance indexes in the step 2.1, obtaining the optimal control laws of the controllers in different stages, wherein the form is as follows:
Figure FDA0001488450550000035
Figure FDA0001488450550000036
Figure FDA0001488450550000037
2.3 applying the control quantity obtained in the step 2.2 to the controlled object:
ui(k)＝Δui(k)+ui(k-1)
2.4 at the next moment, repeating the steps 2.1 to 2.3 to continuously solve new control quantity, and circulating in sequence;
2.5 design the switching signal to σ (k) for different phases;
2.5.1 for the switching system in step 1.5, different stage controllers are designed as follows:
Δui(k)＝-Kizi(k)
wherein the content of the first and second substances,
Figure FDA0001488450550000038
for each phase i, the switching system may become:
z(k+1)＝(Ai-BiKi)z(k)
2.5.2 for the ith subsystem, the following Lyapunov function is selected:
Vi(k)＝zT(k)Pi(k)z(k)
wherein, Pi(k)，i∈N,NThat {1,2, …, N } is dependent on the residence time τiA matrix of (a); then:
Figure FDA0001488450550000041
if the switching system is stable, Δ V must be presenti(k) < 0, which is equivalent to:
Figure FDA0001488450550000042
Figure FDA0001488450550000043
Figure FDA0001488450550000044
combining with step 2.2, solving the inequality to obtain tau at different stagesi。
CN201711232764.3A 2017-11-30 2017-11-30 Limited rolling time domain hybrid tracking control method for batch injection molding process Active CN107942669B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN201711232764.3A CN107942669B (en) 2017-11-30 2017-11-30 Limited rolling time domain hybrid tracking control method for batch injection molding process

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN201711232764.3A CN107942669B (en) 2017-11-30 2017-11-30 Limited rolling time domain hybrid tracking control method for batch injection molding process

Publications (2)

Publication Number Publication Date
CN107942669A CN107942669A (en) 2018-04-20
CN107942669B true CN107942669B (en) 2021-05-07

Family

ID=61947815

Family Applications (1)

Application Number Title Priority Date Filing Date
CN201711232764.3A Active CN107942669B (en) 2017-11-30 2017-11-30 Limited rolling time domain hybrid tracking control method for batch injection molding process

Country Status (1)

Country Link
CN (1) CN107942669B (en)

Families Citing this family (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN109212972B (en) * 2018-10-12 2021-12-03 海南师范大学 Limited rolling time domain hybrid 2D tracking control method for intermittent process
CN109719915A (en) * 2018-12-20 2019-05-07 山东科技大学 A kind of T-S fuzzy model and the application in injection moulding process control
CN110780649B (en) * 2019-10-17 2022-08-02 海南师范大学 Prediction tracking control optimization method for hybrid limited model of industrial process

Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
EP2221687A1 (en) * 2009-02-24 2010-08-25 Siemens Aktiengesellschaft Method for controlling the recipe of a batch process
CN104932263A (en) * 2015-06-03 2015-09-23 辽宁石油化工大学 Minimum operation time control method of multistage intermittent process
CN105334751A (en) * 2015-11-26 2016-02-17 杭州电子科技大学 Design method for stability controller of batched injection molding process
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
CN105607591A (en) * 2015-12-10 2016-05-25 辽宁石油化工大学 Control method enabling minimum operating time of batch process in controller asynchronous switching
JP2017129988A (en) * 2016-01-19 2017-07-27 富士通株式会社 Batch control system, batch control program, and batch control method

Family Cites Families (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JP2004527860A (en) * 2001-05-25 2004-09-09 パラメトリック・オプティミゼーション・ソリューションズ・リミテッド Improved process control
CN103279123B (en) * 2013-05-21 2015-12-23 沈阳化工大学 Intermittent control system is carried out to the method for segment failure supervision
CN103713521B (en) * 2013-12-31 2017-01-11 广州市香港科大霍英东研究院 2D controller design method for interval time lag in injection modeling process
CN105607631B (en) * 2016-03-24 2018-01-19 辽宁工业大学 The weak fault model control limit method for building up of batch process and weak fault monitoring method

Patent Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
EP2221687A1 (en) * 2009-02-24 2010-08-25 Siemens Aktiengesellschaft Method for controlling the recipe of a batch process
CN104932263A (en) * 2015-06-03 2015-09-23 辽宁石油化工大学 Minimum operation time control method of multistage intermittent process
CN105334751A (en) * 2015-11-26 2016-02-17 杭州电子科技大学 Design method for stability controller of batched injection molding process
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
CN105607591A (en) * 2015-12-10 2016-05-25 辽宁石油化工大学 Control method enabling minimum operating time of batch process in controller asynchronous switching
JP2017129988A (en) * 2016-01-19 2017-07-27 富士通株式会社 Batch control system, batch control program, and batch control method

Non-Patent Citations (3)

* Cited by examiner, † Cited by third party
Title
Average dwell time-based optimal iterative learning control for multi-phase batch processes;Limin Wang 等;《Journal of Process Control》;20161231;第40卷;1-12 *
Robust iterative learning fault-tolerant control for multi-phase batch processes with uncertainties;Limin Wang 等;《Industrial & Engineering Chemistry Research》;20170712;1-32 *
注塑过程中注射保压阶段最小运行时间控制方法;王立敏 等;《工程塑料应用》;20160430;第44卷(第4期);53-56 *

Also Published As

Publication number Publication date
CN107942669A (en) 2018-04-20

Similar Documents

Publication Publication Date Title
CN107918283B (en) Design method of anti-interference hybrid stable controller in batch injection molding process
CN107942669B (en) Limited rolling time domain hybrid tracking control method for batch injection molding process
CN107942667B (en) Injection molding process hybrid 2D tracking control method based on time-varying time lag and interference
CN104932263A (en) Minimum operation time control method of multistage intermittent process
CN107966902B (en) Constraint 2D tracking control method for uncertain intermittent process
CN108073077B (en) Linear quadratic hybrid fault-tolerant control method for batch process infinite time domain optimization
CN107976942B (en) 2D constraint fault-tolerant control method for intermittent process of infinite time domain optimization
CN103713521A (en) 2D controller design method for interval time lag in injection modeling process
Wang et al. H∞ design of 2D controller for batch processes with uncertainties and interval time-varying delays
CN109212971B (en) Multi-stage intermittent process 2D linear secondary tracking fault-tolerant control method
CN105607591B (en) A kind of batch process minimum run time control method of controller asynchronised handover
WO2021243779A1 (en) Injection molding self-adaptive compensation method based on melt viscosity fluctuation
CN103901773B (en) Method for designing 2D hybrid controller according to input delay
CN103934951A (en) Injection molding process for car bumpers
CN109100941B (en) Multi-stage intermittent process two-dimensional anti-interference prediction controller design method
CN104552852A (en) Method for iterative learning control of injection speed of nonlinear injection molding machine system
CN110764414A (en) Robust predictive control method for multi-stage batch asynchronous switching process aiming at multiple interferences
CN109991853B (en) Multi-stage intermittent process 2D input and output constraint tracking control method
CN109254531A (en) The optimal cost control method of multistage batch process with time lag and interference
CN104626469A (en) Intelligent temperature control type thin-walled injection molding mold
CN109212972B (en) Limited rolling time domain hybrid 2D tracking control method for intermittent process
CN108943637A (en) A kind of Shooting Technique
CN110780649B (en) Prediction tracking control optimization method for hybrid limited model of industrial process
CN111221313A (en) Quadratic fault-tolerant tracking control method for industrial process expansion state space
Jeong et al. Optimized digital proportional integral derivative controller for heating and cooling injection molding system

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant