CN110764414A - Robust predictive control method for multi-stage batch asynchronous switching process aiming at multiple interferences - Google Patents

Robust predictive control method for multi-stage batch asynchronous switching process aiming at multiple interferences Download PDF

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CN110764414A
CN110764414A CN201911049076.2A CN201911049076A CN110764414A CN 110764414 A CN110764414 A CN 110764414A CN 201911049076 A CN201911049076 A CN 201911049076A CN 110764414 A CN110764414 A CN 110764414A
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施惠元
彭博
苏成利
郝佳静
李平
文馨
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Liaoning Shihua University
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Abstract

A robust predictive control method for a multi-stage batch asynchronous switching process aiming at various interferences belongs to the advanced control field of industrial processes and comprises the following steps: the method comprises the following steps: establishing a state space model of a multi-stage batch asynchronous switching system with various interferences; step two: converting the constructed state space model of the asynchronous switching system into an expanded state space model of the asynchronous switching system; step three: designing a controller based on the extended model; step four: calculating a controller gain; step five: the average residence time for each stage is calculated. The invention effectively avoids the occurrence of asynchronous state, leads the system to operate stably, quickly and accurately, can improve the production efficiency and the product quality, effectively reduces the energy loss and improves the economic benefit of factories.

Description

Robust predictive control method for multi-stage batch asynchronous switching process aiming at multiple interferences
Technical Field
The invention belongs to the field of advanced control of industrial processes, and relates to a robust predictive control method for a multi-stage batch asynchronous switching process aiming at various interferences.
Background
With the development of economy, the variety of products is increased, the market demand change is accelerated, and the proportion of batch processes in industrial production is increased. At present, batch processes are widely applied to industries such as food, chemical industry, pharmacy, plastic processing and the like. The traditional control method has limitations due to the complexity of the batch process and the gradually increasing requirement on the control precision. In addition, when the switching system switches between different stages, there is a situation that the controller cannot switch in time, and at this time, the controller in the previous stage cannot well control the next stage. In the past research, the control method for the multistage batch asynchronous switching process is an iterative learning method, and because the models of the system are changed due to different interferences on the system at different times, the performance of the system is reduced by the iterative learning method for processing the next batch process by using the information of the previous batch, which not only increases some unnecessary energy consumption, but also reduces the product quality and even leads to the system being out of control. Therefore, it is very necessary to research a control method that combines stability, rapidity, and robustness for a multi-stage batch asynchronous switching process with uncertainty, interval time-varying time lag, external unknown interference, and input/output constraints.
At present, a mainstream control method for the multi-stage batch asynchronous switching process is an iterative learning method, under ideal conditions, the control method can effectively control the multi-stage batch process, but the control effect of iterative learning is greatly reduced due to the influence of various interferences in actual production.
Disclosure of Invention
In order to solve the technical problem, the invention provides a robust predictive control method for a multi-stage batch asynchronous switching process aiming at various interferences. The method can still stably work when the system is influenced by uncertainty, interval time-varying time lag, external unknown interference and input and output constraints and the controller is not switched over, thereby ensuring the safe and stable operation of equipment. Meanwhile, a brand new design scheme is provided for the control of the multi-stage batch asynchronous switching system, and the method has very important significance for realizing the ultimate goal of leading the industry of China to the global technical system.
The invention aims to enable the control system to have robust performance indexes and simultaneously reserve the advantage of solving the control law through rolling optimization in predictive control. The method is characterized in that a robust prediction idea is applied at the initial stage of design, the influence of factors such as uncertainty of a system, interval time-varying time lag, external unknown interference and the like on the system is fully considered during design, a discrete multi-stage batch asynchronous switching system with uncertainty, interval time-varying time lag, unknown interference and input-output constraint is represented in a state space form, then an output tracking error is introduced into the state space, and a new expanded state space model is established. Meanwhile, in order to overcome unknown disturbance, an H-infinity performance index is introduced.
And finally, giving a system stability condition based on LMI constraint so as to solve a control law capable of simultaneously stabilizing the system. And calculating the minimum running time of each synchronous stage and the maximum running time of each asynchronous stage by using a mode-related average residence time method, thereby realizing the early switching of the controller.
The invention is realized by the following technical scheme:
the robust predictive control method for the multi-stage batch asynchronous switching process aiming at various interferences comprises the following steps:
the method comprises the following steps: establishing a state space model of a multi-stage batch asynchronous switching system with various interferences;
an actual multi-phase batch process can be represented as a state space model with uncertainty, time-varying time-lag between intervals, and unknown external disturbances as follows:
in the formula (I), the compound is shown in the specification,
Figure BDA0002254860700000012
w (k) is a table representing system state, inputs, outputs and unknown ambient at discrete time instances kInterference, d (k), is a time-varying time-lag dependent on discrete k-time, satisfying:
dm≤d(k)≤dM(2)
in the formula (d)MAnd dmRespectively an upper and a lower bound of the time lag,
Figure BDA0002254860700000021
Ap，
Figure BDA0002254860700000022
Bpand CpIs a constant matrix of the corresponding dimension, and
Figure BDA0002254860700000023
and
Figure BDA0002254860700000024
is an uncertain perturbation at discrete k instants, which can be expressed as:
Figure BDA0002254860700000025
and is
ΔpT(k)Δp(k)≤Ip
In the formula, Np,Hp,
Figure BDA0002254860700000026
Is a matrix of known constants of corresponding dimensions, Δp(k) Is an uncertain perturbation dependent on discrete time k;
defining a system state and a controller synchronous stage as a stable state, and defining a system state and a controller asynchronous stage as an unstable state, so that when the system runs in the p-1 stage and the p-1 stage, the system needs to go through two stages of p instability and p stability according to the stage classification of the system state; therefore, the state space model of the p-th stage containing uncertainty, interval time-varying time lag and external unknown disturbance can be expressed as follows:
Figure BDA0002254860700000028
wherein formula (4a) is a p-stable state and formula (4b) is a p-unstable state;
when the switching between the phases occurs, the state of the previous phase is related to the state of the next phase, and thus can be represented by the following formula:
xp(Tp-1)＝Φp-1xp-1(Tp-1) (5)
in the formula
Figure BDA0002254860700000029
State transition matrixes of two adjacent stages are obtained;
since whether a phase of the system switches depends on its state, the switching signal of the system can be expressed as:
Figure BDA00022548607000000210
in the formula Mυ(k)+1(x (k) < 0 is the system's switching condition;
furthermore, when the switching conditions are triggered, at different stages, the switching time is an important factor affecting the quality and yield of the product, this time T being dependent on the known state of the systempCan be expressed as:
Tp＝min{k＞Tp-1|Mp(x(k))＜0},T0＝0 (7)
because the stable state and the unstable state exist in the same stage, the invention respectively uses the time of the two conditions as TpSAnd TpUThen the time series of the system can be expressed as:
Figure BDA00022548607000000211
step two: converting the constructed state space model of the asynchronous switching system into an expanded state space model of the asynchronous switching system;
in order to obtain a system incremental state space model, a state space incremental model of a stable state and an unstable state can be obtained by subtracting a state space at a time k from a state space at a time k +1 by using equation (4), and as a result, equation (9a) is the state space incremental model of the stable state and equation (9b) is the state space incremental model of the unstable state:
Figure BDA0002254860700000031
Figure BDA0002254860700000032
in the formula (I), the compound is shown in the specification,
Figure BDA0002254860700000034
by rp(k) The setting value of the p stage is shown, the output tracking error of the system is ep(k)＝yp(k)-rp(k) Therefore, the equations of the output tracking error of the p-th stage system in the stable state and the unstable state are respectively obtained as follows:
Figure BDA0002254860700000035
introducing the state variables of the output tracking error and the increment into the new state space variables to obtain a new expanded state space model, wherein the results are as follows:
Figure BDA0002254860700000036
in the formula (I), the compound is shown in the specification,
Figure BDA0002254860700000039
Figure BDA00022548607000000310
Figure BDA00022548607000000312
because the states of two adjacent stages are related to each other, the relationship between the expanded new state space variables is as follows:
Figure BDA0002254860700000041
order to
Figure BDA0002254860700000042
Then
Figure BDA0002254860700000043
Step three: designing a controller based on the extended model;
based on the models (11a) and (11b), the stable phase and unstable phase control laws are respectively designed as follows:
Figure BDA0002254860700000044
Figure BDA0002254860700000045
in the formula (I), the compound is shown in the specification,
Figure BDA0002254860700000046
for the controller gain of the controller, in order to construct a closed-loop system, equations (13a) and (13b) are respectively substituted into equations (11a) and (11b), and the state space models of the closed-loop system in the stable state and the unstable state are obtained as follows:
Figure BDA0002254860700000047
Figure BDA0002254860700000048
in the formula (I), the compound is shown in the specification,
Figure BDA0002254860700000049
based on the extended models (14a) and (14b), the system optimization problem can be converted into the following min-max optimization problem respectively:
Figure BDA00022548607000000410
the constraint conditions are as follows:
Figure BDA0002254860700000051
in the formulaAnd
Figure BDA0002254860700000053
corresponding dimension weighting matrixes for system state variables and control inputs respectively; u. ofp(k + i | k) is a predicted input value at time k + i; y isp(k + i) is that the system is inA predicted output value at time k + i in a steady state;
Figure BDA0002254860700000054
an upper bound for the p-th stage system input;
Figure BDA0002254860700000055
an upper bound for the p-th stage system output;
step four: calculating controller gain
Figure BDA0002254860700000056
Solving for the unknown matrix by solving for a Linear Matrix Inequality (LMI) based onCalculating a controller gain;
Figure BDA0002254860700000058
Figure BDA0002254860700000059
Figure BDA00022548607000000510
Figure BDA00022548607000000511
Figure BDA00022548607000000512
Figure BDA00022548607000000513
wherein the content of the first and second substances,
Figure BDA00022548607000000514
Figure BDA0002254860700000061
are all positive definite symmetric matrices, matrices
Figure BDA0002254860700000062
And scalar quantity
Figure BDA0002254860700000063
Figure BDA0002254860700000063
0≤dm≤dM(ii) a And is
Figure BDA0002254860700000064
Represents the lyapunov function of the system at the p-th stage steady state,
Figure BDA0002254860700000065
a Lyapunov function representing the system at the p stage of instability; in addition, the method can be used for producing a composite material
Figure BDA0002254860700000066
Figure BDA0002254860700000067
Figure BDA0002254860700000068
Figure BDA0002254860700000069
Figure BDA00022548607000000610
Figure BDA00022548607000000611
Figure BDA0002254860700000071
Figure BDA0002254860700000072
Figure BDA0002254860700000074
Figure BDA0002254860700000075
Figure BDA0002254860700000076
Step five: calculating the average residence time of each stage;
according to the LMI in the fourth step, the corresponding LMI of each step can be calculated
Figure BDA0002254860700000077
The average residence time of the system in the stable and unstable phases
Figure BDA0002254860700000078
As shown in formulas (22a) and (22b), respectively:
Figure BDA0002254860700000079
Figure BDA0002254860700000081
wherein the content of the first and second substances,
Figure BDA0002254860700000082
for the minimum average residence time of the system in the stationary phase,
Figure BDA0002254860700000083
the maximum average residence time of the system in the unstable phase.
Compared with the prior art, the invention has the beneficial effects that: the invention provides a robust prediction control strategy based on modal-dependent average residence time for a multi-stage batch asynchronous switching system with uncertainty, interval time-varying time lag and external unknown interference. On one hand, the designed controller can ensure the stable operation of the system when the system is subjected to uncertainty, interval time-varying time lag and external unknown interference. On the other hand, the maximum operation time of the unstable stage can be obtained through calculation, so when the system is switched from the p-1 stage to the p-th stage, the controller can be switched in advance according to the calculated maximum operation time, and the influence of an uncontrollable period, in which the state of the controller is inconsistent with that of the system, on the system is avoided. In addition, unlike the way that the running time is given by the traditional experience method, the method can give the running time of each stage by calculation, thereby improving the production efficiency of the system.
Drawings
FIG. 1 is a diagram of the output response of a synchronous switching method system;
FIG. 2 is a control input diagram of a synchronous switching method system;
FIG. 3 is a system error diagram of a synchronous handover method;
FIG. 4 is a diagram of the output response of the asynchronous handover method system proposed by the present invention;
FIG. 5 is a control input diagram of the asynchronous switching method system proposed by the present invention;
FIG. 6 is a system error diagram of the asynchronous handover method proposed by the present invention;
FIG. 7 is a simplified illustration of an injection molding process: (a) an injection stage, (b) a pressure maintaining stage, (c) a cooling stage, (d) a mold opening and part ejection stage;
FIG. 8 is a flow chart of the steps of the present invention.
Detailed Description
The invention is described in detail below with reference to the figures and specific embodiments.
Example (b): the invention aims at the injection stage and the pressure maintaining stage in the injection molding process for simulation. The simulation respectively adopts a synchronous switching method and an asynchronous switching method provided by the invention. The output response and control input images for both methods are shown in fig. 1-6.
As can be seen from fig. 1 and 2, when the pressure in the chamber reaches the switching condition of 350bar, the system state is switched from the injection stage to the pressure holding stage, but the controller does not complete the switching, and there is a time difference of 21s between the switching of the system state and the switching of the controller. The system is now in an asynchronous handoff state.
As can be seen from fig. 1 and 4, the occurrence of the asynchronous switching state cannot be avoided by using the synchronous switching method, so that the system is obviously unstable in the asynchronous switching state. And the adoption of the asynchronous switching method successfully avoids the asynchronous switching state and ensures the stable operation of the system.
The asynchronous switching method designed by the invention is used for preventing the system from asynchronous switching, and a switching signal of the controller is given in advance before the system is switched, so that the system state and the controller are switched simultaneously. As can be seen from fig. 4 and 5, the switching signal of the controller is given in advance before the state switching, so that the switching time of the controller is the same as the switching time of the system state, thereby avoiding the unstable state of asynchronous switching of the system.
As can be seen from fig. 3 and fig. 6, the system error of the asynchronous handover method is significantly smaller than that of the synchronous handover method when the system is handed over.
In conclusion, the method designed by the invention can effectively avoid the influence of the asynchronism of the system state and the controller on the stable operation of the system, provides a brand-new design scheme for the control of the multi-stage batch asynchronous switching system, and has very important significance for realizing the ultimate goal of leading the global technical system in China industry.
Plastic products are widely used in life due to their advantages of low cost, strong plasticity, etc. The plastics industry is a very important place in the world today, and in recent years the production processes for plastic products have developed at a high rate. As one of the important methods for processing plastic products, injection molding is increasingly widely used in the production of plastic products due to its advantages of high production speed, high efficiency, accurate product size, easy replacement, etc.
It is well known that the injection molding process is a common multi-stage batch process. FIG. 7 shows four important stages of injection molding, namely injection, pressure holding, cooling and demolding. The injection and pressure holding stages have a great influence on the product quality. To ensure a uniform filling of the material during the injection phase, a good control of the injection speed is required. Either too fast or too slow injection rate can affect product quality. During the dwell phase, the pressure in the mold cavity must be ensured to prevent shrinkage of the plastic due to cooling. Therefore, controlling the injection speed and pressure in the chamber to ensure stability of the injection stage and the dwell stage is very important to achieve high quality production. The invention takes the switching between the injection molding stage and the pressure maintaining stage in the injection molding as an example to verify the effectiveness of the designed controller.
By repeating the test, the injection speed (IV) model corresponding to the Valve Opening (VO) can be identified during the injection phase as:
Figure BDA0002254860700000091
the model of Nozzle Pressure (NP) for Injection Velocity (IV) is:
Figure BDA0002254860700000092
during the dwell phase, the model for Valve Opening (VO) and Nozzle Pressure (NP) is:
Figure BDA0002254860700000093
the switching conditions between the two phases are: m1(x(k))＝350-[0 0 1]x1(k)＜0。
Then the state space model with uncertainty, interval time-varying time lag and external unknown interference after the two stages of injection molding and pressure maintaining in the injection molding process are as follows:
when p is 1, the system is in the injection molding stage, and when p is 2, the system is in the pressure maintaining stage. Wherein
1≤d(k)≤3,
Figure BDA0002254860700000095
C1＝[1 0 0],
Figure BDA0002254860700000096
Figure BDA0002254860700000097
Figure BDA0002254860700000099
w1(k)＝0.5×[Δ4Δ5Δ6]T,w2(k)＝0.5×[Δ9Δ10]T,|Δii|≤1,ii＝1,2,L,10.
The parameters of the two phase controllers are respectively:
Figure BDA00022548607000000910
calculated minimum mean residence time T for the injection phase186s, shortest mean residence time T of the pressure holding stage292s, the maximum time of operation of the unstable state between the two phases is T12＝21s。
The input-output constraints of the system are:
the set values of the two stages are respectively:
Figure BDA0002254860700000102
in summary, the present invention takes the switching between the injection stage and the pressure maintaining stage in the injection molding process as an example to verify the stability and effectiveness of the designed controller. Simulation results show that the designed controller can calculate the average residence time of the stable state and the longest running time of the unstable state in each stage, and can give out a switching signal of the controller in advance before the system state is switched according to the calculated time, so that the occurrence of an asynchronous state is effectively avoided, the system can stably, quickly and accurately run, the production efficiency and the product quality can be improved, the energy loss is effectively reduced, and the economic benefit of a factory is improved.

Claims (6)

1. The robust predictive control method for the multi-stage batch asynchronous switching process aiming at various interferences is characterized by comprising the following steps of: the method comprises the following steps:
the method comprises the following steps: establishing a state space model of a multi-stage batch asynchronous switching system with various interferences;
step two: converting the constructed state space model of the asynchronous switching system into an expanded state space model of the asynchronous switching system;
step three: designing a controller based on the extended model;
step four: calculating controller gain
Figure FDA0002254860690000011
Step five: the average residence time for each stage is calculated.
2. The robust predictive control method of a multi-stage batch asynchronous switching process to multiple disturbances according to claim 1 wherein: the first step specifically comprises the following steps:
the state space model with uncertainty, interval time-varying time lag and external unknown disturbance is as follows:
Figure FDA0002254860690000012
in the formula (I), the compound is shown in the specification,
Figure FDA0002254860690000013
w (k) represents the system state, input, output and unknown external interference at discrete k time, d (k) is time-varying time lag depending on discrete k time, and satisfies the following conditions:
dm≤d(k)≤dM(2)
in the formula (d)MAnd dmRespectively an upper and a lower bound of the time lag,
Figure FDA0002254860690000014
Ap，Bpand CpIs a constant matrix of the corresponding dimension, and
Figure FDA0002254860690000016
and
Figure FDA0002254860690000017
is an uncertain perturbation at discrete k instants, expressed as:
Figure FDA0002254860690000018
and is
ΔpT(k)Δp(k)≤Ip
In the formula, Np,Hp,
Figure FDA0002254860690000019
Is a matrix of known constants of corresponding dimensions, Δp(k) Is an uncertain perturbation dependent on discrete time k;
defining a system state and a controller synchronous stage as a stable state, and defining a system state and a controller asynchronous stage as an unstable state, so that when the system runs in the p-1 stage and the p-1 stage, the system needs to go through two stages of p instability and p stability according to the stage classification of the system state; therefore, the state space model of the p-th stage containing uncertainty, interval time-varying time lag and external unknown disturbance is expressed as the following formula:
Figure FDA00022548606900000110
Figure FDA00022548606900000111
wherein formula (4a) is a p-stable state and formula (4b) is a p-unstable state;
when the switching between the phases occurs, the state of the previous phase is related to the state of the next phase, and thus can be represented by the following formula:
xp(Tp-1)＝Φp-1xp-1(Tp-1) (5)
in the formula
Figure FDA00022548606900000112
State transition matrixes of two adjacent stages are obtained;
since whether a phase of the system is switched depends on its state, the switching signal of the system is expressed as:
Figure FDA00022548606900000113
in the formula Mυ(k)+1(x (k) < 0 is the system's switching condition;
when the switching conditions are triggered, at different stages, the switching time is an important factor affecting the quality and yield of the product, depending on the known state of the system, time TpIs shown as：
Tp＝min{k＞Tp-1|Mp(x(k))＜0},T0＝0 (7)
Because the stable state and the unstable state exist in the same stage, the time of the two conditions is respectively used as TpSAnd TpUAnd then the time sequence of the system is represented as:
Figure FDA0002254860690000021
3. the robust predictive control method of a multi-stage batch asynchronous switching process to multiple disturbances according to claim 1 wherein: the second step specifically comprises the following steps:
in order to obtain a system incremental state space model, a state space incremental model of a stable state and an unstable state can be obtained by subtracting a state space at a time k from a state space at a time k +1 by using equations (4a) and (4b), and the results are as follows, where equation (9a) is the state space incremental model of the stable state and equation (9b) is the state space incremental model of the unstable state:
Figure FDA0002254860690000022
Figure FDA0002254860690000023
in the formula (I), the compound is shown in the specification,
Figure FDA0002254860690000024
Figure FDA0002254860690000025
by rp(k) The setting value of the p stage is shown, the output tracking error of the system is ep(k)＝yp(k)-rp(k) To obtain the p stage systemThe output tracking error of (1) in the stable state and the unstable state is respectively expressed by the following formula:
Figure FDA0002254860690000026
introducing the state variables of the output tracking error and the increment into a new state space variable to obtain a new expanded state space model, wherein the result is as follows:
Figure FDA0002254860690000027
Figure FDA0002254860690000031
in the formula (I), the compound is shown in the specification,
Figure FDA0002254860690000032
Figure FDA0002254860690000034
Figure FDA0002254860690000035
because the states of two adjacent stages are related to each other, the relationship between the expanded new state space variables is as follows:
Figure FDA0002254860690000037
order to
Figure FDA0002254860690000038
Then
Figure FDA0002254860690000039
4. The robust predictive control method of a multi-stage batch asynchronous switching process to multiple disturbances according to claim 1 wherein: the third step specifically comprises the following steps:
based on the models (11a) and (11b), the stable phase and unstable phase control laws are respectively designed as follows:
Figure FDA00022548606900000311
in the formula (I), the compound is shown in the specification,
Figure FDA00022548606900000312
for the controller gain of the controller, in order to construct a closed-loop system, equations (13a) and (13b) are respectively substituted into equations (11a) and (11b), and the state space models of the closed-loop system in the stable state and the unstable state are obtained as follows:
Figure FDA0002254860690000041
in the formula (I), the compound is shown in the specification,
Figure FDA0002254860690000043
based on the extended models (14a) and (14b), respectively converting the system optimization problem into the following min-max optimization problem:
Figure FDA0002254860690000044
the constraint conditions are as follows:
Figure FDA0002254860690000045
in the formula
Figure FDA0002254860690000046
And
Figure FDA0002254860690000047
corresponding dimension weighting matrixes for system state variables and control inputs respectively; u. ofp(k + i | k) is a predicted input value at time k + i; y isp(k + i) is a predicted output value at the k + i moment when the system is in a stable state;
Figure FDA0002254860690000048
an upper bound for the p-th stage system input;
Figure FDA0002254860690000049
the upper bound of the system output for the p-th stage.
5. The robust predictive control method of a multi-stage batch asynchronous switching process to multiple disturbances according to claim 1 wherein: the fourth step specifically comprises the following steps:
solving for the unknown matrix by solving for the linear matrix inequality, based on
Figure FDA00022548606900000410
Calculating controller gain
Figure FDA00022548606900000412
Figure FDA0002254860690000051
Figure FDA0002254860690000052
Figure FDA0002254860690000053
Figure FDA0002254860690000054
Figure FDA0002254860690000055
Wherein the content of the first and second substances,
Figure FDA0002254860690000056
Figure FDA0002254860690000057
are all positive definite symmetric matrices, matrices
Figure FDA0002254860690000058
And scalar quantityθp＞0,0≤dm≤dM(ii) a And is
Figure FDA00022548606900000510
Represents the lyapunov function of the system at the p-th stage steady state,
Figure FDA00022548606900000511
a Lyapunov function representing the system at the p stage of instability; in addition, the method can be used for producing a composite material
Figure FDA00022548606900000512
Figure FDA00022548606900000513
Figure FDA00022548606900000514
Figure FDA0002254860690000061
Figure FDA0002254860690000062
Figure FDA0002254860690000063
Figure FDA0002254860690000064
Figure FDA0002254860690000065
Figure FDA0002254860690000066
Figure FDA0002254860690000071
Figure FDA0002254860690000072
Figure FDA0002254860690000073
6. The robust predictive control method of a multi-stage batch asynchronous switching process to multiple disturbances according to claim 1 wherein: the fifth step specifically comprises the following steps:
calculating the corresponding relation of each stage according to the linear matrix inequality in the step four
Figure FDA0002254860690000074
The average residence time of the system in the stable and unstable phases
Figure FDA0002254860690000075
As shown in formulas (22a) and (22b), respectively:
Figure FDA0002254860690000076
Figure FDA0002254860690000077
wherein the content of the first and second substances,
Figure FDA0002254860690000078
for the minimum average residence time of the system in the stationary phase,the maximum average residence time of the system in the unstable phase.
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Cited By (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN111506033A (en) * 2020-05-08 2020-08-07 辽宁石油化工大学 Injection molding machine pressure maintaining fault-tolerant switching control method based on nozzle pressure
CN111812980A (en) * 2020-07-02 2020-10-23 淮阴工学院 Robust fault estimation method of discrete switching system based on unknown input observer
CN112180738A (en) * 2020-10-22 2021-01-05 辽宁石油化工大学 Robust fuzzy prediction control method for nonlinear injection molding asynchronous switching process
CN112213946A (en) * 2020-10-13 2021-01-12 辽宁石油化工大学 Robust prediction control method for time-varying track injection molding asynchronous switching process
CN112327971A (en) * 2020-10-27 2021-02-05 江南大学 Robust heuristic iterative learning control method of metal bar temperature distribution system
CN115755788A (en) * 2022-11-02 2023-03-07 辽宁石油化工大学 Robust asynchronous prediction tracking control method for low-delay multi-stage batch process

Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN104749958A (en) * 2015-03-25 2015-07-01 成都市优艾维机器人科技有限公司 Model-depended average dwell time asynchronous fuzzy control method of nonlinear switching system
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
CN108803338A (en) * 2018-06-28 2018-11-13 杭州电子科技大学 A kind of chemical industry multistage batch process iterative learning control method

Patent Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN104749958A (en) * 2015-03-25 2015-07-01 成都市优艾维机器人科技有限公司 Model-depended average dwell time asynchronous fuzzy control method of nonlinear switching system
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
CN108803338A (en) * 2018-06-28 2018-11-13 杭州电子科技大学 A kind of chemical industry multistage batch process iterative learning control method

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
HUIYUAN SHI等: "Robust Predictive Fault-Tolerant Control for Multi-Phase Batch Processes With Interval Time-Varying Delay", 《IEEE ACCESS 》 *

Cited By (8)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN111506033A (en) * 2020-05-08 2020-08-07 辽宁石油化工大学 Injection molding machine pressure maintaining fault-tolerant switching control method based on nozzle pressure
CN111812980A (en) * 2020-07-02 2020-10-23 淮阴工学院 Robust fault estimation method of discrete switching system based on unknown input observer
CN112213946A (en) * 2020-10-13 2021-01-12 辽宁石油化工大学 Robust prediction control method for time-varying track injection molding asynchronous switching process
CN112180738A (en) * 2020-10-22 2021-01-05 辽宁石油化工大学 Robust fuzzy prediction control method for nonlinear injection molding asynchronous switching process
CN112327971A (en) * 2020-10-27 2021-02-05 江南大学 Robust heuristic iterative learning control method of metal bar temperature distribution system
CN112327971B (en) * 2020-10-27 2021-06-15 江南大学 Robust heuristic iterative learning control method of metal bar temperature distribution system
WO2022088857A1 (en) * 2020-10-27 2022-05-05 江南大学 Robust heuristic iterative learning control method for metal bar temperature distribution system
CN115755788A (en) * 2022-11-02 2023-03-07 辽宁石油化工大学 Robust asynchronous prediction tracking control method for low-delay multi-stage batch process

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