CN107976942B - 2D constraint fault-tolerant control method for intermittent process of infinite time domain optimization - Google Patents
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Abstract
The invention belongs to the field of advanced control of an automation technology, and particularly relates to an infinite time domain optimized intermittent process 2D constraint fault-tolerant control method. Designing an iterative learning control law aiming at an interference constraint fault control system model, introducing a state error and an output error, converting a dynamic model of an original system into a closed-loop system model expressed in a prediction form by using a Roesser model, and converting the design constraint iterative learning control law into a determined constraint updating law; and providing an update law real-time online design for ensuring the stability of the robustness asymptotic of the closed-loop system in a Linear Matrix Inequality (LMI) constraint form according to the designed infinite optimization performance index and the 2D system Lyapunov stability theory. The invention solves the problems that the control performance can not be perfected along with the increment of the batch and the control of the intermittent process with uncertain initial value, and finally achieves the purposes of saving energy, reducing consumption, reducing cost and reducing the occurrence of accidents damaging personal safety.
Description
Technical Field
The invention belongs to the field of advanced control of an automation technology, and particularly relates to an infinite time domain optimized intermittent process 2D constraint fault-tolerant control method.
Background
The intermittent process becomes one of the most important production modes in modern manufacturing industry, and along with the increase of production scale and the increase of complexity of production steps, uncertainty existing in actual production becomes increasingly prominent, so that the efficient and stable operation of a system is influenced, and even the quality of products is threatened. These complex operating conditions, in turn, increase the probability of system failure. Among them, actuator failure is a common failure, which affects the operation of the process and reduces the control performance, even endangers the personal safety. Although control methods such as iterative learning reliable fault-tolerant control and the like appear in the batch processing process, the control problem that the system still stably runs when an actuator fails can be well solved. However, for equipment with high precision, the possibility of failure occurrence is extremely low, if no failure occurs, the equipment is reliably controlled to use, so that resource waste is caused, the cost is increased in the past, and the environment-friendly concept of energy conservation and emission reduction is obviously not met. In the event of a serious fault, the reliable control law may completely lose control, which may lead to system breakdown, resulting in significant property loss and casualties.
In addition, although the robust iterative learning reliable control strategy adopted at the present stage can effectively resist the influence caused by uncertainty and faults in the production link, ensure the stability of the system and maintain the control performance of the system, the control law is obtained by solving based on the whole production process and belongs to global-covering optimization control in the control effect, namely the same control law is used all the time.
However, during actual operation, especially under the influence of disturbance and fault, the state of a constraint system (the constraint system means that both the operating variable and the controlled variable of the constraint system need to satisfy physical constraints) cannot change completely according to the obtained control law action; if the system state at the current moment deviates from the set value to a certain extent, the same control law is still continuously adopted, the deviation of the system state is increased gradually along with the lapse of time, and the existing robust iterative learning reliable control method cannot solve the problem of the deviation of the system state, which inevitably has adverse effects on the stable operation and the control performance of the system.
The Model Predictive Control (MPC) can well meet the requirement of real-time update and correction of the control law, and the optimal control law at each moment is obtained through rolling optimization and feedback correction, so that the system state can be ensured to run along the set track as much as possible. However, in the prior art, a one-dimensional infinite time domain control law is mostly adopted, a learning process is lacked among batches, and the control effect is not improved along with the increment of the batches; there is also a process that only considers batch-to-batch "learning" and this approach does not achieve the control problem of an intermittent process where the initial value is uncertain. It is clear that the discussion of the infinite time domain optimization problem for the constraint system with uncertainty and fault is left to be further. Therefore, a new control method is urgently needed to make up the defects of the existing method so as to achieve the aims of saving energy, reducing consumption, reducing cost, even reducing the occurrence of accidents which harm human safety and the like in the batch production process.
Most of the existing prediction control technologies design a control law in a one-dimensional direction, only the time direction or the batch direction is considered, only the time direction is considered, so that each batch is only simply repeated, and the control performance cannot be improved along with the increment of the batch; the control problem of the intermittent process with uncertain initial values cannot be realized only by considering the batch direction.
Disclosure of Invention
In order to solve the existing technical problems, the invention provides an infinite time domain optimized intermittent process 2D constraint fault-tolerant control method, which effectively solves the control problems that the control performance cannot be improved along with the increment of batches and the intermittent process with uncertain initial values is controlled, realizes the real-time optimization of a system in a variable constraint range regardless of faults, and finally achieves the aims of saving energy and reducing consumption, reducing cost, reducing the occurrence of personal safety hazards and the like.
The technical scheme adopted by the invention is as follows:
the 2D constraint fault-tolerant control method for the intermittent process of infinite time domain optimization comprises the following steps:
A. constructing an intermittent process model with disturbance and actuator fault, wherein the intermittent process model with disturbance and actuator fault (1) is represented by (1a) and (1 b):
and the input and output constraints thereof meet:
where t represents time, k represents batch,
in (1) is the state of the system,
is an input to the system that is,
is the actual output of the system and is,
respectively are upper bound constraint values of input and actual output,
is an unknown disturbance outside the system, and
Δ a is the perturbation matrix of the unknown uncertain system, Δ a (t, k) ═ D Δ (t, k) E, Δ (t, k) ΔT(t,k)≤I，{A,B2,C2{ D, E } is a constant matrix of appropriate dimensions, I is an identity matrix of appropriate dimensions; defining different alpha values to indicate different fault types of the actuator, and indicating partial failure fault when alpha is more than 0; when alpha is 0, the failure is completely failed, and the problem of an optimal controller is not involved;
for partial actuator failure, α > 0 should satisfy the following form:
wherein α (α. ltoreq.1), and
is a known constant;
B. converting an intermittent process dynamic model with interference and actuator faults into a closed-loop system model represented in a predicted value mode, and introducing the following iterative learning control law into the model (1):
u(t,k)＝u(t,k-1)+r(t,k),u(0,k)＝0,t＝0,1,2,…T (3)
where u (0, k) is the initial value of the iteration, typically set to 0,
an iterative learning update law;
the state error and the output error in the batch direction are defined as follows:
k(f(t,k))＝f(t,k)-f(t,k-1) (4a)
the model (1) and the iterative learning control law (3) are used for obtaining:
wherein,
the error model of the dimension expansion is written in the following form using the Roesser model:
wherein:
C3＝[0 0 I]，
and assume that
The horizontal and vertical state components of the adaptive dimensional vector are assigned, and Z (t, k) is the controlled output of the system;
C. an iterative learning control law is designed for an intermittent process model with interference and actuator faults,
designing a 2D predictive fault-tolerant controller for the model (6) to achieve minimum optimal control under maximum disturbance and maximum fault, even if the model (6) reaches steady state and meets the following robust performance indexes at each moment:
and (3) limiting:
and Q (Q > 0) and R (R > 0) are weighting matrices of appropriate dimensions, R (t + i | t, k) is the predicted value input at time t to t + i, and R (t, k) ═ R (t | t, k),
represents an input increment;
defining a state feedback control law to ensure that the system achieves secondary stability, wherein the selected updating law is as follows:
the closed-loop predictive model of (6) is expressed as
The stability of the system is proved by using a 2D Lyapunov function, wherein the Lyapunov function is defined as follows:
wherein
The model (6) can still run smoothly within the fault tolerance range, and the following requirements must be met:
(1) the 2D lyapunov function is inequality constrained:
(2) there exists a matrix M of appropriate dimensionsjH, Y and a non-singular matrix G of appropriate dimensions, arbitrary scalar > 0, theta > 0, gammajA > 0 may make the following matrix inequality true:
Wherein, T1 ═ - (G + G)T-Mj),
At this time, the optimal performance index satisfies J∞(t,k)≤θ；
The robust update law gain is K (t, K) ═ YG-1；
Therefore, the further update law is represented as:
and (3) substituting the value into u (t, k) ═ u (t, k-1) + r (t, k), so as to obtain a 2D constraint iterative learning control law design u (t, k), continuously repeating (11a) - (11b) at the next moment, continuously solving a new controlled variable u (t, k), and sequentially circulating.
Adjusting matrixes Q (Q > 0) and R (R > 0), giving initial values x (t | t, K), solving equations (11a) - (11d), finding Y and G when theta is minimum, wherein x (t | t, K) is different at different moments, and K (t, K) is also changed continuously along with time; if the system is not in fault, a normal system controller is utilized; when the value of K (t, K) differs depending on the failure, and α is equal to 0, the inequality (11a) β is equal to β0At this time, the equation (11a) may not satisfy the condition of being less than zero, which is reflected in that the controller is not functioning in the actual process, the system is unstable, and the state quickly deviates from the original trajectory. At this point, the equipment should be checked and even the process should be shut down. In this regard, the occurrence of accidents that endanger human safety is reduced.
Compared with the prior art, the invention has the beneficial effects that: the method has the advantages and beneficial effects that an iterative learning control law is designed on the basis of an interference fault control system model, a state error and an output error are introduced, a dynamic model of an original system is converted into a closed-loop system model expressed in a prediction mode by a Roesser model, and the designed iterative learning control law is converted into a determined updating law; according to designed infinite optimization performance indexes and a 2D system Lyapunov stability theory, an update law real-time online design for ensuring asymptotic stability of the robustness of a closed-loop system is provided in a Linear Matrix Inequality (LMI) constraint form, the control problems that the control performance cannot be improved along with increment of batches and an intermittent process with uncertain initial values are effectively solved, and the system can be optimized in real time in a variable constraint range regardless of faults. Finally, the purposes of saving energy, reducing consumption, reducing cost and reducing the occurrence of accidents damaging personal safety are achieved. Generally, the control law is designed by using the design method, so that the system can be ensured to stably operate within a fault allowable range, the aims of saving energy, reducing consumption, reducing cost and the like are fulfilled, and the aims of reducing the occurrence of personal safety hazards and the like can be fulfilled.
Drawings
FIG. 1 is a flow chart of an intermittent process 2D constraint fault-tolerant control method of infinite time domain optimization.
FIG. 2 is a graph of tracking performance due to differences in R in quadratic forms in accordance with an embodiment of the present invention.
Fig. 3 is a graph comparing the tracking performance of two different methods when R is 200000 according to an embodiment of the present invention.
Fig. 4 is a graph of the output tracking contrast of two different methods when R is 200000 according to an embodiment of the present invention.
Fig. 5 is a graph comparing the tracking performance of two different methods when α is 0 according to an embodiment of the present invention.
Fig. 6 is a graph of output tracking comparison of two different methods when α is 0 according to an embodiment of the present invention.
FIG. 7 is a comparison of update laws for two different methods according to an embodiment of the present invention.
Detailed Description
The invention is described in detail below with reference to the figures and specific embodiments.
As shown in fig. 1, the method for 2D constrained fault-tolerant control of an intermittent process by infinite time domain optimization includes the following steps:
A. constructing an intermittent process model with disturbance and actuator fault, wherein the intermittent process model with disturbance and actuator fault (1) is represented by (1a) and (1 b):
and the input and output constraints thereof meet:
where t represents time, k represents batch,
in (1) is the state of the system,
is an input to the system that is,
is the actual output of the system and is,
respectively are upper bound constraint values of input and actual output,
is an unknown disturbance outside the system, and
Δ a is the perturbation matrix of the unknown uncertain system, Δ a (t, k) ═ D Δ (t, k) E, Δ (t, k) ΔT(t,k)≤I，{A,B2,C2{ D, E } is a constant matrix of appropriate dimensions, I is an identity matrix of appropriate dimensions; defining different alpha values to indicate different fault types of the actuator, and indicating partial failure fault when alpha is more than 0; when alpha is 0, the failure is completely failed, and the problem of an optimal controller is not involved;
for partial actuator failure, α > 0 should satisfy the following form:
in the formulaα(α1 or less), and
is a known constant;
B. converting an intermittent process dynamic model with interference and actuator faults into a closed-loop system model represented in a predicted value mode, and introducing the following iterative learning control law into the model (1):
u(t,k)＝u(t,k-1)+r(t,k),u(0,k)＝0,t＝0,1,2,…T (3)
where u (0, k) is the initial value of the iteration, typically set to 0,
an iterative learning update law;
the state error and the output error in the batch direction are defined as follows:
k(f(t,k))＝f(t,k)-f(t,k-1) (4a)
the model (1) and the iterative learning control law (3) are used for obtaining:
wherein,
the error model of the dimension expansion is written in the following form using the Roesser model:
wherein:
C3＝[0 0 I]，
and assume that
The horizontal and vertical state components of the adaptive dimensional vector are assigned, and Z (t, k) is the controlled output of the system;
C. an iterative learning control law is designed for an intermittent process model with interference and actuator faults,
designing a 2D predictive fault-tolerant controller for the model (6) to achieve minimum optimal control under maximum disturbance and maximum fault, even if the model (6) reaches steady state and meets the following robust performance indexes at each moment:
and (3) limiting:
and Q (Q > 0) and R (R > 0) are weighting matrices of appropriate dimensions, R (t + i | t, k) is the predicted value input at time t to t + i, and R (t, k) ═ R (t | t, k),
represents an input increment;
defining a state feedback control law to ensure that the system achieves secondary stability, wherein the selected updating law is as follows:
the closed-loop predictive model of (6) is expressed as
The stability of the system is proved by using a 2D Lyapunov function, wherein the Lyapunov function is defined as follows:
wherein
The model (6) can still run smoothly within the fault tolerance range, and the following requirements must be met:
(1) the 2D lyapunov function is inequality constrained:
(2) there exists a matrix M of appropriate dimensionsjH, Y and a non-singular matrix G of appropriate dimensions, arbitrary scalar > 0, theta > 0, gammajA > 0 may make the following matrix inequality true:
Wherein, T1 ═ - (G + G)T-Mj),
At this time, the optimal performance index satisfies J∞Theta is not less than (t, k); the robust update law gain is K (t, K) ═ YG-1；
Therefore, the further update law is represented as:
and (3) substituting the value into u (t, k) ═ u (t, k-1) + r (t, k), so as to obtain a 2D constraint iterative learning control law design u (t, k), continuously repeating (11a) - (11b) at the next moment, continuously solving a new controlled variable u (t, k), and sequentially circulating.
Adjusting the matrices Q (Q > 0) and R (R > 0), giving initial values
Solving equations (11a) - (11d), finding Y and G with the smallest theta, and different time
Will be different, K (t, K) will also change constantly over time; if the system is not in fault, a normal system controller is utilized; when the value of K (t, K) differs depending on the failure, and α is equal to 0, the inequality (11a) β is equal to β0At this time, the equation (11a) may not satisfy the condition of being less than zero, which is reflected in that the controller is not functioning in the actual process, the system is unstable, and the state quickly deviates from the original trajectory.
Examples
The injection molding process is a complex industrial manufacturing process, and the quality of the injection molded product depends on material parameters, machine parameters, process parameters, and the interaction of these parameters. The quality of injection-molded products includes many aspects such as appearance quality, dimensional accuracy, and mechanical (optical, electrical) properties, etc. The quality concerns vary from user to user. These quality indicators are determined by the material used in the process, the mold, and the accuracy of control of the process parameters. Meanwhile, various interference factors exist in different links in the injection molding process.
Injection molding is essentially a multi-stage batch process for producing a product, with one or more key parameters in each major stage being critical to the quality of the final product. The injection speed in the injection phase, the dwell pressure in the dwell phase and the melt temperature in the plastification phase are the key process variables in these phases, so that these parameters must be controlled stably and accurately in order to ensure the quality of the products produced.
The pressure maintaining stage is an important stage for determining the product quality, and in the stage, because the low-temperature mold has a cooling effect, in order to prevent the melt in the mold cavity from reversely flowing and prevent the product from shrinking due to cooling of the melt, the injection nozzle still maintains a certain pressure. Thus, the nozzle pressure is the most important controlled variable at this stage, this pressure also being referred to as the packing pressure.
Control of dwell pressure has long been a concern to the plastics industry and related researchers. Although a great deal of research work has proven the importance of the dwell pressure, the research on the dwell phase is still relatively small, because on the one hand the dwell analysis requires the results of the mold filling analysis as initial conditions, and on the other hand the problem is further complicated because extensive research on the dwell phase necessitates consideration of the compressibility of the melt, requiring consideration of more physical parameters.
In addition, in the injection molding process, the opening degree of the control valve is large, so that although the possibility of clogging can be reduced to a certain extent and the occurrence of a failure can be effectively prevented, for a system having a high degree of precision, the possibility of the occurrence of a failure itself is low, and the large opening degree of the valve causes waste of raw materials and an increase in cost in the control process. Therefore, it is important to solve this problem.
Aiming at valve faults and existing disturbances which may occur in the system, the invention designs a 2D prediction fault-tolerant control law by organically combining learning control and feedback control under the condition of constrained variables, and performs closed-loop control on pressure maintaining pressure.
Solving the above algorithm, the initial time controller gain is obtained as (this time is considered as normal case):
Kis normal＝[-0.0065 -0.0040 0.0041]；
Failure occurred in 30 batches with values: α is 0.6, the controller gain is:
Kfault of＝[-0.0085 -0.0068 0.0045]；
The constraint of the updating law meets the condition that | r (t + i | t, k) | is less than or equal to 0.1.
The control effect of the controller is as follows: as shown in fig. 2, if the minimum performance index is to be obtained, the given matrix in the quadratic form needs to be adjusted, and when the tracking performance is the best, the controller at that time is obtained, and the controller is compared with the conventional method, and the following four graphs are comparative result graphs. Fig. 3 clearly shows that the tracking performance of the method is better, and even zero-error tracking can be achieved later, although the tracking performance is poor for several batches initially and after a fault. FIG. 4 is a tracing diagram of the output trajectory of the system, in which the control effect of the initial batch and the several batches after the fault is still not ideal, but once the control effect is stable, the tracing effect is extremely good, and is particularly obvious at a step point; fig. 5 and 6 show the control effect after the system completely fails, and obviously, no matter which control method, the control effect is not expected, and in this case, the check should be stopped. FIG. 7 is a representation of the update law, from which it can be seen that the change of the update law of the method is very gradual, and better control performance can be seen.
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 2D constraint fault-tolerant control method for the intermittent process of infinite time domain optimization is characterized by comprising the following steps of: the method comprises the following steps:
A. constructing a constrained intermittent process model with disturbance and actuator faults, wherein the intermittent process model with disturbance and actuator faults (1) is represented by (1a) and (1 b):
and the input and output constraints thereof meet:
where t represents time, k represents batch,
in (1) is the state of the system,
is an input to the system that is,
is the actual output of the system and is,
respectively are upper bound constraint values of input and actual output,
is an unknown disturbance outside the system, and
Δ a is the perturbation matrix of the unknown uncertain system, Δ a (t, k) ═ D Δ (t, k) E, Δ (t, k) ΔT(t,k)≤I，{A,B2,C2{ D, E } is a constant matrix of appropriate dimensions, I is an identity matrix of appropriate dimensions; defining different alpha values to indicate different fault types of the actuator, and indicating partial failure fault when alpha is more than 0; when alpha is 0, the failure is completely failed, and the problem of an optimal controller is not involved;
for partial actuator failure, α > 0 should satisfy the following form:
in the formulaα(α1 or less), and
is a known constant;
B. converting an intermittent process model with interference and actuator faults into a closed-loop system model represented in a predicted value mode, and introducing the following iterative learning control law into the model (1):
u(t,k)＝u(t,k-1)+r(t,k),u(0,k)＝0,t＝0,1,2,…T (3)
where u (0, k) is the initial value of the iteration, typically set to 0,
an iterative learning update law;
the state error and the output error in the batch direction are defined as follows:
k(f(t,k))＝f(t,k)-f(t,k-1) (4a)
the model (1) and the iterative learning control law (3) are used for obtaining:
wherein,
the error model of the dimension expansion is written in the following form using the Roesser model:
wherein:
C3＝[0 0 I]，
and assume that
The horizontal and vertical state components of the adaptive dimensional vector are assigned, and Z (t, k) is the controlled output of the system;
C. an iterative learning control law is designed for an intermittent process model with interference and actuator faults,
designing a 2D predictive fault-tolerant controller for the model (6) to achieve minimum optimal control under maximum disturbance and maximum fault, even if the model (6) reaches steady state and meets the following robust performance indexes at each moment:
and (3) limiting:
and Q (Q > 0) and R (R > 0) are weighting matrices of appropriate dimensions, R (t + i | t, k) is the predicted value input at time t to t + i, and R (t, k) ═ R (t | t, k),
represents an input increment;
defining a state feedback control law to ensure that the system achieves secondary stability, wherein the selected updating law is as follows:
the closed-loop predictive model of (6) is expressed as
The stability of the system is proved by using a 2D Lyapunov function, wherein the Lyapunov function is defined as follows:
wherein
The model (6) can still run smoothly within the fault tolerance range, and the following requirements must be met:
(1) the 2D lyapunov function is inequality constrained:
(2) there exists a matrix M of appropriate dimensionsjH, Y and a non-singular matrix G of appropriate dimensions, arbitrary scalar > 0, theta > 0, gammajA > 0 may make the following matrix inequality true:
wherein,
at this time, the optimal performance index satisfies J∞(t,k)≤θ；
The robust update law gain is K (t, K) ═ YG-1；
Therefore, the further update law is represented as:
and (3) substituting the value into u (t, k) ═ u (t, k-1) + r (t, k), so as to obtain a 2D constraint iterative learning control law design u (t, k), continuously repeating (11a) - (11b) at the next moment, continuously solving a new controlled variable u (t, k), and sequentially circulating.
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| CN109100941B (en) * | 2018-10-11 | 2022-01-04 | 海南师范大学 | Multi-stage intermittent process two-dimensional anti-interference prediction controller design method |
| CN109212971B (en) * | 2018-10-11 | 2022-02-18 | 海南师范大学 | Multi-stage intermittent process 2D linear secondary tracking fault-tolerant control method |
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