Robust fault-tolerant tracking and anti-interference dynamic output feedback control method for packing system of injection molding machine

Abstract

The present application relates to a robust fault-tolerant tracking and anti-interference dynamic output feedback control method for the pressure maintaining system of an injection molding machine, belonging to the field of advanced control of industrial processes, comprising the following steps: Step one: design a dynamic output feedback switching controller with probability; Step two: establish a closed-loop discrete system actuator random failure model containing controller state deviation; Step three: sufficient condition for system asymptotic stability when the system is not affected by external disturbance and variable output set value; Step four: sufficient condition for system asymptotic stability when the system is affected by external disturbance and variable output set value; This method proposes a new scheme for the control of the pressure maintaining stage of injection molding with parameter uncertainty, unknown external disturbance and time-varying set value under the condition that the state variables are not completely measurable; This scheme combines the theories of stochastic control, robust predictive control and dynamic output feedback, which not only guarantees the tracking performance of the system, but also reduces the energy consumption of the equipment.

Description

TECHNICAL FIELD

[0001] The patent belongs to the field of advanced control of industrial processes, and relates to a robust fault-tolerant tracking and anti-interference dynamic output feedback control method for a pressure maintaining system of an injection molding machine. BACKGROUND

[0002] With the increasing complexity of modern industrial processes, the control system in actual industrial production often has the situation that state variables cannot be obtained. Assuming that all state variables are measurable is idealized, and only output variables and part of state variables are available in actual industrial production. Injection molding, as one of the intermittent processes, is a widely used process operation equipment in modern society. The injection molding process is generally divided into four steps of injection, pressure maintaining, cooling and demolding. In the injection stage, it is necessary to ensure the filling of the material in the mold cavity. In the pressure maintaining stage, the pressure in the film cavity is ensured to ensure the temperature of the plastic and prevent the material from shrinking, so that the subsequent production steps can be carried out smoothly, so the pressure maintaining stage is the key stage of the injection molding production process. The key of the pressure maintaining process is to ensure the smoothness of the nozzle pipe, otherwise the nozzle pipe will be blocked, which will cause the system to fail. The initial value of the nozzle pressure is different for different production equipment, and due to the influence of equipment aging and external interference, the control performance of the equipment by PID control or adaptive control method is poor. Most of the current control methods for the pressure maintaining stage use state feedback to design fault-tolerant feedback controllers. The controller will run continuously during the operation of the system, which ensures the control performance of the system, but sacrifices the low energy consumption and high efficiency production goal. And the controller designed by state feedback ignores the unobtainable state variables in the production process, which will cause the control system to make wrong judgments, resulting in the inconsistency between the production output and the expected output, causing losses.

[0003] The device will have a certain probability of failure during operation, and also has a certain probability of recovery, if the traditional fault-tolerant control method is used to control the system, not only will cause unnecessary high energy consumption, low efficiency, but also make the system in normal operation period appears violent fluctuations. Especially for the fault rate is extremely low high-precision equipment, the traditional fault-tolerant control is continuously used, will cause great waste of resources, which is contrary to the theme of energy saving and emission reduction. The patent for the state variable is not completely measurable, modeling uncertainty, unknown bounded external disturbance and time-varying set value of injection molding pressure maintaining stage pressure control system proposed injection molding machine pressure maintaining system robust fault-tolerant tracking and anti-disturbance dynamic output feedback control method. On the one hand, the occurrence of failure is random, that is, unpredictable when and where to occur. In order to solve this problem, the patent is based on the characteristics of the next state of the system only related to the previous time, the random fault is processed by conditional probability. On the other hand, it is ideal to assume that all state variables are available, which does not meet the characteristics of the actual production process that only part of the state variables are available. If this problem is not solved, during the operation of the equipment, the control system may make wrong judgment because of the inaccuracy of the state variable, and then lead to the deterioration of the control performance of the injection molding pressure maintaining stage, and even seriously affect the stability of the system, thus causing a lot of loss. Therefore, it is necessary to design a kind of control method which can accurately state variable, stable and efficient for injection molding pressure maintaining stage, has become the inevitable demand of actual production. SUMMARY

[0004] In order to solve the above technical problems, the patent proposes a robust fault-tolerant tracking and anti-disturbance dynamic output feedback control method for injection molding machine pressure maintaining system. This method is aimed at the model uncertainty, time-varying set value, unknown bounded external disturbance and actuator random failure of the control system, combines random control theory, dynamic output feedback theory, model predictive control theory and robust control, and better controls the pressure of injection molding pressure maintaining stage in the required range.

[0005] Firstly, the incremental discrete state space model of the injection molding pressure-holding stage with model uncertainty, unknown bounded external disturbance and partial actuator faults is established. For the random characteristics of actuator faults, the probability representation method of actuator random faults is constructed. In order to enable the system to track the set value, the output tracking error function is established. According to the incremental discrete state space model, the probability representation method and the tracking error function, the random discrete state space model containing tracking error and time-varying set value is obtained. This model not only reduces the tracking error and accurately tracks the set value, but also deals with the time-varying set value. On this basis, considering that the state variables are not completely measurable, the dynamic output feedback fault-tolerant controller is designed using the measurable system output, which not only improves the control accuracy of the system, but also improves the degree of freedom and flexibility of the control system. Moreover, the conventional controller can be used when the system is running normally, and the fault-tolerant controller can be used when the system fails, thereby reducing energy consumption and saving resources.

[0006] The method is implemented by the following technical solutions:

[0007] Step one: design a dynamic output feedback switching controller with probability;

[0008] Plastic products as a new type of material not only facilitate people's daily life, but also greatly promote the development of industry; however, the advancement of plastic product production requires the progress of injection molding process, but the input-output relationship of the pressure control system of the injection molding pressure-holding stage is affected by factors such as incomplete measurement of state variables; the input-output relationship of the pressure-holding system is represented as follows:

[0009] (1)

[0010] wherein is the system state at discrete k time, and are the state variables that are not completely measured, is the system cavity pressure at discrete k time, is the valve opening at discrete k time; is the state matrix containing uncertainty at discrete k time, is the state matrix, is the state matrix disturbance caused by model uncertainty, is the input matrix, is the output matrix.

[0011] In the control system design, it is usually assumed that all state variables can be effectively used for feedback control and can be used as any initial condition of system operation. But this assumption is idealized, not all state variables can be used for feedback in actual industrial production, that is, only part of the state variables can be used. Since the occurrence of actuator failure of system (1) is uncertain, that is, the time and location of occurrence cannot be predicted, if fault-tolerant control (FTC) is always used, it will cause energy waste. But the occurrence of system failure is premise and bounded random, so predict whether the system is fault at the current time and the next time in the form of event probability, that is, , under the premise of event occurred, the probability of event occurred.

[0012] Considering the case of incomplete measurement of state variables and random failure of actuators, while reducing the system calculation, the following dynamic output feedback switching controller with probability is designed:

[0013] (2)

[0014] Where represents the normal operation of the system and , represents the failure of the system and , , , and are controller gains, which can be obtained by steps three and four, is the controller state deviation, is the available system output deviation, is the backward shift operator.

[0015] Step two: establish a closed-loop discrete system actuator random failure model containing controller state deviation;

[0016] In the case of actuator random failure, system (1) is improved to a system that can adjust the system state and output error respectively; and since controller (2) itself has state variables, the closed-loop system actuator random failure model based on the improved system and controller (2) will give the system better control performance; it not only can make the system play a good control effect in the environment of incomplete measurement of state variables, but also can independently adjust the controller state, system state and output error, which not only improves the control efficiency, but also reduces energy consumption.

[0017] In addition to the case of incomplete measurement of state variables, system (1) will also be affected by external disturbances and variable set values. After further processing of external disturbances on system (1), it will be combined with output tracking error ​ After the dimension expansion, the system contains the variable set point term, and the controller (2) is introduced, and the closed-loop discrete system actuator random failure model containing the system state deviation, output error and controller state deviation can be obtained, as shown in the following:

[0018] (3)

[0019] wherein is the closed-loop system state variable at discrete k time, is the state variable after dimension expansion, is the state matrix of the closed-loop system containing uncertainty at discrete k time, is the state matrix of the closed-loop system, is the state matrix disturbance caused by the uncertainty of the closed-loop system model, is the unified matrix of the uncertainty of the closed-loop system, is the parameter uncertainty matrix, is the state matrix of the uncertainty of the closed-loop system, is the state matrix containing uncertainty after dimension expansion, , and is the input matrix of the closed-loop system, is the input matrix after dimension expansion, is the variable set point matrix of the closed-loop system, is the variable set point matrix after dimension expansion, is the unit matrix of the corresponding dimension, is the disturbance matrix of the closed-loop system, is the disturbance matrix after dimension expansion, is the output matrix of the closed-loop system, is the output matrix after dimension expansion, is the tracking error matrix, , is the secondary tracking error matrix, is the variable set point at discrete k+1 time, is the external disturbance after dimension expansion, is the output of the closed-loop system at discrete k time, is the output matrix, is the tracking error at discrete k time, is the tracking error matrix, is the fault operator.

[0020] Step three: sufficient condition for system asymptotic stability when the system is not affected by external disturbance and variable output set point;

[0021] First, define the Lyapunov function ,in, It is a positive definite symmetric matrix. Performance indicators , This represents the expected value in mathematics. For the stability of the system to be guaranteed, the system must satisfy... ,in , and This is a probability value. and This is a probability estimate.

[0022] Further define the transformation matrix , It is an n-dimensional full-rank matrix. , X and Y are both n-dimensional symmetric positive definite matrices. It is an n-dimensional full-rank matrix. (From...) We know M and N can be derived from... The singular value decomposition is obtained. And it can be known that... ,and then diagonal matrix .

[0023] The system has input constraints and output constraints. For input constraints, the following conditions must be met: For output constraints, the following must be satisfied: .

[0024] We can obtain The sufficient condition for the stability of a system is:

[0025] When, given a scalar ,constant , If a positive definite scalar exists Positive definite matrix ,matrix Symmetric positive definite matrix and appropriate dimension matrix For system (3) to be asymptotically stable under controller (2), the following LMI conditions and inequalities must be satisfied:

[0026] (4)

[0027] (5)

[0028] (6)

[0029] (7)

[0030] (8)

[0031] where

[0032] ,

[0033] ,

[0034] is a 7x7 symmetric transposed matrix, * represents the transposition of the symmetric position matrix,

[0035] , , , , , , , , and are transformation matrices, X and Y are symmetric positive definite matrices, N and M are matrices of corresponding dimensions, and are weighting matrices, and are fault factors, are the 1 / 2 power of the probability of normal at current time and normal at next time, the 1 / 2 power of the probability of normal at current time and failure at next time, the 1 / 2 power of the probability of failure at current time and normal at next time, and the 1 / 2 power of the probability of failure at current time and failure at next time, respectively, is a positive definite scalar that needs to be solved by linear matrix inequality, is a known scalar, , , , , and are probability values;

[0036] By solving the conditional equations (4)-(8), the gain of the controller (2) is obtained ;

[0037] Step four: sufficient condition for system asymptotic stability when the system is affected by external disturbance and variable output set value;

[0038] If the system (3) satisfies where Then system (3) under any bounded disturbance Given an initial condition of 0, it has Robust performance.

[0039] If system (3) satisfies ,in Then the system (3) changes the set value Given an initial condition of 0, it has Tracking performance.

[0040] Then in At that time, build Performance indicators .

[0041] Here Under performance indicators, And any initial conditions, such as , can make The result is correct. The subsequent proof process in step four is similar to that in step three, except that... This will not be described in detail here. The final result is... The sufficient condition for the stability of a system is:

[0042] When, given a scalar ,constant , If a positive definite scalar exists Positive definite matrix ,matrix Symmetric positive definite matrix and appropriate dimension matrix For system (3) to be asymptotically stable under controller (2), the following LMI conditions and inequalities must be satisfied:

[0043] (9)

[0044] (10)

[0045] (11)

[0046] (12)

[0047] (13)

[0048] in

[0049] ,

[0050] , is a 10-by-5 symmetric transpose matrix,

[0051] ,

[0052] , represents the transpose of the symmetric position matrix, , , , , , , , and are transformation matrices, X and Y are symmetric positive definite matrices, N and M are matrices of corresponding dimensions, and are weighting matrices, and are fault factors, are 1 / 2 power of the probability of normal at current time and normal at next time, 1 / 2 power of the probability of normal at current time and failure at next time, 1 / 2 power of the probability of failure at current time and normal at next time, and 1 / 2 power of the probability of failure at current time and failure at next time, respectively, is a positive definite scalar that needs to be solved by linear matrix inequality, is a known scalar, , , , , and are probability values;

[0053] By solving the conditional equations (9)-(13), the gain of the controller (2) is obtained under the influence of external disturbance and variable output set value on the system .

[0054] When the state variable cannot be completely obtained, when the dynamic output feedback switching controller with probability acts on the injection molding pressure maintaining stage, even if the stability of the closed-loop system is affected by the random failure of the actuator and external disturbance, and the tracking performance is affected by the change of the output set value, the closed-loop control system still has stability and convergence, and tracking performance.

[0055] Compared with the prior art, the method has the beneficial effects that: a robust fault-tolerant tracking and anti-interference dynamic output feedback control method is proposed for the pressure control system in the injection molding pressure maintaining stage. On the one hand, unlike other methods that assume that all system states are available, and then design a state feedback controller. Based on the dynamic output feedback theory, combined with the stochastic control theory, a dynamic output feedback switching controller with probability is designed for the case that the state variables cannot be completely obtained and the actuator has random faults. On the other hand, considering the influence of external disturbance and variable set value on the system performance, the method designs a robust performance index and tracking performance index, respectively, to improve the anti-interference ability of the system and suppress the influence of the variable output set value on the tracking performance. On the other hand, the single system state variable is deepened into a closed-loop system state variable containing the system state, the output error and the controller state deviation, which improves the regulation freedom of the system. In summary, a robust fault-tolerant tracking and anti-interference dynamic output feedback control method is designed for the pressure maintaining system, which has low conservativeness, good tracking effect and strong anti-interference ability.

[0056] drawings

[0057] Figure 1 the system output response when the fault probability is 0.195 and the recovery probability is 0.002 in the embodiment;

[0058] Figure 2 the system control input when the fault probability is 0.195 and the recovery probability is 0.002 in the embodiment;

[0059] Figure 3 the system tracking performance when the fault probability is 0.195 and the recovery probability is 0.002 in the embodiment;

[0060] Figure 4 the step flowchart of the patent. DETAILED DESCRIPTION

[0061] The patent will be described in detail below in combination with the drawings and specific embodiments.

[0062] Embodiment:

[0063] The patent is researched for the pressure control system in the injection molding pressure maintaining stage. Based on the incremental model that can reduce the system calculation amount, a robust fault-tolerant tracking and anti-interference dynamic output feedback control method is adopted for simulation. The initial model of the pressure control system is described as formula (1).

[0064] In order to verify that the robust fault-tolerant tracking and anti-interference dynamic output feedback control method for the injection molding pressure maintaining system proposed by the patent is feasible and effective, the system state initial value is set to ; the error between the output set value and the actual output is defined , 1000 is the total number of system running steps; as Figure 1 shown, the output setting value is , , , , , ; set .

[0065] The application effect of the method is shown in Figure 1 , Figure 2 and Figure 3 . Figure 1 is the output response of the system, and the figure contains the control effect of the method and the comparative method. As Figure 1 can be seen, unlike the comparative method, the method quickly controls the injection molding pressure holding stage pressure to the vicinity of the set value when the actuator fails. At the same time, for the overall control effect, the control ability of the method is obviously better than that of the comparative method, which better ensures the control accuracy of the system. As Figure 2 can be seen, the overall control input of the method is smooth and stable, and there is no large fluctuation under the control of the comparative method, thereby ensuring the stability of the system. As Figure 3 can be seen, compared with the comparative method, the method greatly improves the tracking performance of the system, meeting the needs of practical application.

[0066] The injection molding machine pressure holding system robust fault-tolerant tracking and anti-disturbance dynamic output feedback control method is feasible and effective for the injection molding pressure holding stage pressure control system. Through the analysis of the simulation results, it is concluded that when there is external disturbance and output setting value change in the injection molding pressure holding stage, the method can make the system have strong anti-interference ability and optimal tracking performance. And the application of the method does not need to consider the incomplete availability of state variables too much, which makes the system have low conservativeness. Therefore, the injection molding machine pressure holding system robust fault-tolerant tracking and anti-disturbance dynamic output feedback control method can well meet the actual control demand, and proposes a new scheme for the design of the injection molding pressure holding stage pressure control system with external disturbance and output setting value change, which has good application value and application prospect.

Claims

1. Robust fault-tolerant tracking and anti-interference dynamic output feedback control method for packing system of injection molding machine, characterized in that, Step one: design a dynamic output feedback switching controller with probability; The input-output relationship of the holding system is shown as follows: (1) wherein is the discrete k-time system state, and is the incompletely measured state variable, is the discrete k-time system lumen pressure, is the discrete k-time valve opening; is the discrete k-time state matrix including uncertainty, is the state matrix, is the state matrix disturbance caused by model uncertainty, is the input matrix, is the output matrix; For system (1), in the control system design, it is usually assumed that all state variables can be effectively used for feedback control and can be used as any initial condition of system operation; but this assumption is idealized, and in actual industrial production, not all state variables can be used for feedback, that is, only part of the state variables can be used; and the occurrence of actuator failure is uncertain, that is, the time and position of occurrence cannot be predicted, and if fault-tolerant control is always used, it will lead to energy waste; Considering the case of incomplete measurement of state variables and random failure of actuators, while reducing the system calculation, the following dynamic output feedback switching controller with probability is designed: (2) wherein represents normal operation of the system and , represents a fault in the system and , , , and is the controller gain, which can be solved by steps three and four, is the controller state deviation, is the available system output deviation, is the backward shift operator; Step two: establish a closed-loop discrete system actuator random failure model containing controller state deviation; In the case of actuator random failure, system (1) is improved to a system that can adjust the system state and output error respectively; and since the controller (2) itself has state variables, the closed-loop system actuator random failure model based on the improved system and the controller (2) will give the system better control performance; it not only can make the system play a good control effect in the environment of incomplete measurement of state variables, but also can independently adjust the controller state, system state and output error, which not only improves the control efficiency, but also reduces the energy consumption; The system (1) is affected by external disturbance and variable set value in addition to the case that the state variable is not completely measurable. The system (1) is further processed in view of the external disturbance, and the processed result is combined with the output tracking error After the dimension expansion, the system contains a variable set value term, The scalar expected output is introduced. The controller (2) is introduced, and a closed-loop discrete system actuator random failure model containing system state deviation, output error and controller state deviation is obtained, as shown in the following formula: (3) wherein is the state variable of the closed loop system at discrete k time instant, is the state variable after dimension extension, is the state matrix of the closed loop system containing uncertainty at discrete k time instant, is the state matrix of the closed loop system, is the state matrix disturbance caused by the model uncertainty of the closed loop system, is the unified matrix of the uncertainty of the closed loop system, is the parameter uncertainty matrix, is the state matrix of the uncertainty of the closed loop system, is the state matrix containing uncertainty after dimension extension, and is the input matrix of the closed loop system, is the input matrix after dimension extension, is the variable set point matrix of the closed loop system, is the variable set point matrix after dimension extension, is the identity matrix of corresponding dimension, is the disturbance matrix of the closed loop system, is the disturbance matrix after dimension extension, is the output matrix of the closed loop system, is the output matrix after dimension extension, is the tracking error matrix, , is the secondary tracking error matrix, is the variable set point at discrete k+1 time instant, is the external disturbance after dimension extension, is the output of the closed loop system at discrete k time instant, is the output matrix, is the tracking error at discrete k time instant, is the tracking error matrix, is the fault operator;​ Step three: sufficient condition for system asymptotic stability when the system is not affected by external disturbance and variable output set value; a given scalar a constant , if there exists a positive definite scalar a positive definite matrix a matrix a symmetric positive definite matrix and a matrix of appropriate dimensions such that the system (3) is asymptotically stable under the controller (2), the following LMI conditions and inequalities must be satisfied: (4) (5) (6) (7) (8) where ， ， is a 7 by 7 symmetric transpose matrix, * represents the transpose of the symmetric position matrix, , , , , , , , , and are transformation matrices, X and Y are symmetric positive definite matrices, N and M are matrices of corresponding dimensions, and are weighting matrices, and are fault factors, are 1 / 2 power of probability of normal at current time and normal at next time, 1 / 2 power of probability of normal at current time and fault at next time, 1 / 2 power of probability of fault at current time and normal at next time, and 1 / 2 power of probability of fault at current time and fault at next time, respectively, is a positive definite scalar which needs to be solved by linear matrix inequality, is a known scalar, , , , , and are probability values; By solving the conditional equations (4) - (8) under the condition that the system is not affected by external disturbances and by varying the output set value, the gain of the controller (2) is obtained ; Step four: sufficient condition for system asymptotic stability when the system is affected by external disturbance and variable output set value; a given scalar a constant , if there exists a positive definite scalar a positive definite matrix a matrix a symmetric positive definite matrix and a matrix of appropriate dimensions such that the system (3) is asymptotically stable under the controller (2), the following LMI conditions and inequalities must be satisfied: (9) (10) (11) (12) (13) where ， , is a 10 by 5 symmetric transpose matrix, ， , , * represents the transpose of the symmetric position matrix, , , , , , , , and are transformation matrices, X and Y are symmetric positive definite matrices, N and M are matrices of corresponding dimensions, and are weighting matrices, and are fault factors, are the 1 / 2 power of the probability of normal at the current time and normal at the next time, the 1 / 2 power of the probability of normal at the current time and failure at the next time, the 1 / 2 power of the probability of failure at the current time and normal at the next time, and the 1 / 2 power of the probability of failure at the current time and failure at the next time, respectively, is a positive definite scalar that needs to be solved by linear matrix inequality, is a known scalar, , , , , and are probability values; By solving the conditional equations (9) - (13) under the influence of external disturbances and varying output set values, the gain of the controller (2) is obtained .

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