Robust model predictive fault tolerant switching control method for injection molding hold pressure process with failure recovery

Abstract

The application discloses a robust model predictive fault tolerant switching control method for injection molding pressure maintaining process with fault recovery, which aims to realize random switching between normal control strategy and fault tolerant control strategy, so that the system can cope with uncertainties and potential faults in the running process in a probabilistic manner, and belongs to the field of advanced control of industrial processes. The method comprises the following steps: step 1, constructing a mathematical model of injection molding pressure maintaining process with fault recovery; step 2, designing a robust model predictive fault tolerant switching controller; and step 3, obtaining real-time control law gain, compensation coefficient and switching coefficient of the system by solving sufficient conditions of robust positive invariance set and terminal constraint set. The application innovates the design of the controller by introducing probability, so that the controller can dynamically adjust between normal and fault tolerant modes, and ensure safe and efficient operation of the system.

Description

Technical Field

[0001] The patent application belongs to the field of advanced industrial process control and relates to a robust model prediction fault-tolerant switching control method for injection molding holding pressure process with recoverable faults. Background Technology

[0002] Batch processes, a classic and indispensable production mode in modern industry, are characterized by batch-based, phased operations. Unlike continuous processes where raw materials are continuously input and products are continuously output, batch processes input a specific quantity of material into the equipment at once. Then, under strict control, a series of unit operations (such as heating, cooling, chemical reaction, mixing, or bio-fermentation) are executed according to a preset "formula" sequence. After all processes are completed, the entire batch of material is transferred to the next stage or produced as the final product. This "start-run-stop" cyclical operation gives it extremely high production flexibility, allowing the same set of equipment to produce a variety of different high-value-added products by adjusting process parameters and operating sequences, perfectly meeting the small-batch, multi-variety production needs of industries such as pharmaceuticals, specialty chemicals, and food and beverages. Although its absolute capacity is generally lower than that of continuous processes, the unique advantages of batch processes in product quality control, batch traceability, and responding to diversified market demands ensure that they maintain a strategically important position in many high-tech manufacturing fields. The patent application focuses on the holding pressure process of injection molding, a typical batch process, aiming to conduct in-depth analysis and optimization.

[0003] Time delays significantly impact the stability of injection molding processes. On one hand, they delay feedback signals, leading to oscillations in the system output; on the other hand, they reduce the system's response speed to control actions, weakening its ability to handle real-time dynamic changes. To address this challenge, the Lyapunov–Razumikhin functional (LRF) method, with its directness and efficiency, has become an important tool for analyzing systems with medium and low time delays. Unlike the Lyapunov–Krasovskii functional (LKF) method, which constructs complex functionals dependent on the entire time delay history, the core advantage of the LRF method lies in its "directness." It is based on the key idea that even with time delays, as long as the system state "returns" to a bounded range at a specific moment, the system's eventual stability is guaranteed. This method bypasses the complex processing of historical trajectories, directly utilizing the Lyapunov function of time-delay-free systems for analysis, thus greatly simplifying the derivation of stability conditions. However, this directness also determines the high sensitivity of the LRF method to the magnitude of the time delay. The dimension of the stability condition derived by the method is directly linked to the time delay value. As the time delay increases, the conservatism of the condition increases sharply, leading to a significant increase in solution complexity. Therefore, the LRF method is more suitable for scenarios with small or medium time delays. In such problems, it can quickly and effectively complete the stability determination with low computational cost.

[0004] As modern industrial systems continue to evolve towards greater integration and intelligence, their equipment structures are becoming increasingly complex, and their operating environments are becoming more demanding. This significantly increases the likelihood of actuator failure when subjected to extreme conditions such as high frequency and high voltage over extended periods. The increased system complexity further exacerbates the risk of fault propagation; localized faults can rapidly spread, leading to performance degradation or even overall system failure. Against this backdrop, fault-tolerant control (FTC), as a key technology for improving system reliability, has received widespread attention. Based on the fundamental requirements for safe system operation, FTC enables systems to complete their control tasks according to their original performance indicators (or with appropriate adjustments within permissible limits) even when significant changes occur in system components or the external environment, and maintains asymptotic stability after a fault occurs. Given the significant advantages of FTC in enhancing system fault tolerance, research on control strategies based on this framework has emerged continuously in recent years. However, most existing research on actuator failures focuses on permanent fault scenarios, assuming that the actuator remains in a fixed abnormal state after a fault occurs and does not recover with changes in system conditions. In real-world systems, fault behavior is often more complex: in addition to sudden, permanent faults, there exists a type of intermittent fault characterized by the spontaneous appearance and disappearance of fault phenomena, with actuators repeatedly switching between normal and abnormal states. The dynamic, time-varying characteristics of this type of fault not only increase the difficulty of system modeling and analysis but also place higher demands on the adaptability and robustness of control strategies, becoming a key challenge that urgently needs further investigation in current fault-tolerant control research. Summary of the Invention

[0005] To address the problems described above, the proposed patent proposes a robust model predictive fault-tolerant switching control method for the injection molding holding pressure process, which is characterized by uncertainty, low time delay, external unknown disturbances, and recoverable faults. The proposed patent first constructs a system model of the injection molding holding pressure process with recoverable faults, and designs a robust model predictive fault-tolerant switching controller based on the established model. Second, by solving for sufficient conditions of the robust positive definite invariant set and the terminal constraint set, the real-time control law gain, compensation coefficient, and switching coefficient of the system are obtained. Finally, according to the steps described above, the controller gain is solved and combined with the state transition matrix to determine whether the controller adopts conventional control or fault-tolerant control, realizing random switching between normal control strategy and fault-tolerant control strategy. This allows the system to cope with uncertainties and potential faults during operation in a probabilistic manner.

[0006] The patent application was achieved through the following methods:

[0007] Step 1: Construct a mathematical model of the injection molding holding pressure process with fault recovery capabilities;

[0008] To address the bounded and random characteristics of intermittent actuator failures, a conditional probability model can be established based on historical system operating data to characterize its statistical evolution. and Define the system in Under the condition of always being in a fault-free state, it runs until The conditional probabilities of being in a fault state or a stable state at time 1, respectively, are represented by their respective probability values ​​using... and express; and Define the system in Under the condition that the current time is already in a fault state, it runs until The conditional probability of remaining in a faulty state or recovering to a stable state at any given time is represented by the following probability values: and express; Indicates the current state of the system It runs stably at all times. Indicates the current Faults occur frequently. It is a random variable that follows a Bernoulli random distribution. Represents conditional probability;

[0009] In the controller design process, parameters are usually required. and However, in actual production conditions, accurately obtaining the values ​​of these two parameters is often very difficult. Therefore, we introduce the following form to represent the uncertainty of the parameters: and , and They are respectively and The estimated value, and Indicates the uncertain part. and These represent the boundaries of the uncertain part of the probability, respectively;

[0010] By introducing state increments and output tracking errors, the mathematical model of the injection molding holding pressure process with fault recovery is expressed as follows:

[0011]

[0012] in, Indicates the direction of time. Representing discrete time Next Switching signals within a time period and These represent system operation without faults and faults, respectively. and They represent discrete and The system state at any given moment. , and They represent discrete Real-time control inputs, external unknown interferences, and system outputs. For discrete The matrix of an uncertain system at time t, and satisfying , Let be the uncertainty matrix of the system, and , For discrete Uncertain system matrix at time , It is an uncertainty matrix that satisfies , For an identity matrix of the corresponding dimension, Let these represent the system matrix, output matrix, and input matrix of appropriate dimensions, respectively. Represents a known matrix with appropriate dimensions. Represents the interference matrix. This represents the system's tracking error expression. The coefficient matrix represents the expression for the tracking error of the system. It is a thing with upper and lower boundaries Failure factors, and Given a matrix, and , For ease of design, the failure factor is expressed as: , , Indicates discrete The system output tracking error at any given time;

[0013] Step 2: Design a robust model-predicted fault-tolerant switching controller;

[0014] Based on the mathematical model of the injection molding holding pressure process in equation (1), the following fault-tolerant switching controller is designed:

[0015]

[0016] in, , It is the controller gain;

[0017] Based on the fault-tolerant switching controller designed according to equation (2), the following closed-loop system model can be obtained:

[0018]

[0019] in, ,

[0020] ;

[0021] Step 3: Obtain the real-time control law gain, compensation coefficient, and switching coefficient of the system by solving the sufficient conditions of the robust positive definite invariant set and the terminal constraint set;

[0022]

[0023]

[0024]

[0025]

[0026] in, These are intermediate variables in the solution process. and Represents an unknown positive definite matrix. and These represent the state weighting matrix and the tracking weighting matrix, respectively. Indicates discrete Maximum control input at all times; , , , , , , , , , , , , , , , , , , , , , , , , , and To represent an unknown scalar, This is the upper bound of the performance metric. 0 indicates that the system is running stably, 1 indicates that the system has failed, * indicates the transpose of the matrix at the corresponding position in the LMI, and 0 indicates a zero matrix of the appropriate dimension.

[0027] The controller gain is calculated by following the steps above and combined with the state transition matrix to determine whether the controller adopts conventional control or fault-tolerant control. This enables random switching between normal control strategy and fault-tolerant control strategy, allowing the system to cope with uncertainties and potential faults during operation in a probabilistic manner.

[0028] This algorithm optimizes the controller parameters in real time along the time sequence during the pressure holding process of injection molding. Based on these parameters, the optimal control law can be calculated. After being implemented in the pressure holding stage of the injection molding process, it can drive the system output to gradually converge to the expected set value.

[0029] Compared to existing methods, the advantages of the patent application are:

[0030] To address the problems described above, the patent application proposes a robust model predictive fault-tolerant switching control method for injection molding holding pressure processes characterized by uncertainty, low time delay, unknown external disturbances, and recoverable faults. This method features fault-recoverable faults. By introducing a probabilistic switching strategy, this design achieves a paradigm shift in control strategy from the traditional "deterministic response" to a "probabilistic proactive adaptation." The controller no longer passively waits for faults to occur but makes forward-looking decisions based on the fault probability model, achieving random and smooth switching between different control modes. This method endows the control system with a higher level of intelligence, enabling it to bridge the gap between normal operation and complete fault tolerance in a probabilistic manner, thereby optimizing its dynamic performance while ensuring system stability. Furthermore, compared to the Lyapunov-Krasovskii method for addressing low-latency issues, the dimension of the V function in the Lyapunov-Razumikhin method is directly related to the time delay. This results in the LRF exhibiting significantly lower computational cost and lower conservatism compared to the LKF method in the case of low time delays, demonstrating its superiority.

[0031] Algorithm Steps

[0032] The following are the algorithm steps of a robust model prediction fault-tolerant switching control method for the injection molding holding pressure process with fault recovery.

[0033] Offline portion:

[0034] Step 1: Establish a state-space model based on the characteristics of the injection molding holding pressure process;

[0035] Step 2: Initialize model parameters, weight matrix, range of fault factors, and probability values.

[0036] Online section:

[0037] Step 1: Obtain the current system status .

[0038] Step 2: In discrete At each moment, solve for the sufficient conditions for system stability (4)-(7) to obtain the real-time control law gain of the system. , ), compensation coefficient ( , ) and switching coefficient ( , ).

[0039] Step 3: Calculate the average dwell time and simultaneously adjust the control law gain. , Substituting into equation (2) yields the control law. and use Calculate the optimal control input .

[0040] Step 4: Solve for the state transition matrix according to the steps shown above. This determines whether the controller should use conventional control or fault-tolerant control.

[0041] Step 5: Update the system's control inputs, which are applied to system (1).

[0042] Step 6: Let Return to step 2 until the system finishes running. Attached Figure Description

[0043] Figure 1 The injection molding process flow chart is as follows: (a) Injection stage, (b) Holding pressure stage, (c) Cooling stage, (d) Demolding stage.

[0044] Figure 2 The probability of failure is Below is a comparison chart of the output responses of the proposed method and the traditional method;

[0045] Figure 3 The probability of failure is Below is a comparison chart of the output responses of the proposed method and the traditional method;

[0046] Figure 4 The probability of failure is Below is a comparison chart of the output responses of the proposed method and the traditional method;

[0047] Figure 5 The probability of failure is The switching signal below;

[0048] Figure 6 The probability of failure is The switching signal below;

[0049] Figure 7 The probability of failure is The switching signal below;

[0050] Figure 8 The probability of failure is Tracking performance under these conditions;

[0051] Figure 9 The probability of failure is Tracking performance under these conditions;

[0052] Figure 10 The probability of failure is Tracking performance under these conditions;

[0053] Figure 11 This is a flowchart of the steps involved in the patent application. Detailed Implementation

[0054] The patent application will be further explained below with reference to the accompanying drawings and implementation examples:

[0055] A robust model-based predictive fault-tolerant switching control method for the injection molding holding pressure process with recoverable faults is characterized by the following specific steps:

[0056] Step 1: Construct a mathematical model of the injection molding holding pressure process with fault recovery capabilities;

[0057] To address the bounded and random characteristics of intermittent actuator failures, a conditional probability model can be established based on historical system operating data to characterize its statistical evolution. and Define the system in Under the condition of always being in a fault-free state, it runs until The conditional probabilities of being in a fault state or a stable state at time 1, respectively, are represented by their respective probability values ​​using... and express; and Define the system in Under the condition that the current time is already in a fault state, it runs until The conditional probability of remaining in a faulty state or recovering to a stable state at any given time is represented by the following probability values: and express; Indicates the current state of the system It runs stably at all times. Indicates the current Faults occur frequently. It is a random variable that follows a Bernoulli random distribution. Represents conditional probability;

[0058] In the controller design process, parameters are usually required. and However, in actual production conditions, accurately obtaining the values ​​of these two parameters is often very difficult. Therefore, we introduce the following form to represent the uncertainty of the parameters: and , and They are respectively and The estimated value, and Indicates the uncertain part. and These represent the boundaries of the uncertain part of the probability, respectively;

[0059] By introducing state increments and output tracking errors, the mathematical model of the injection molding holding pressure process with fault recovery is expressed as follows:

[0060]

[0061] in, Indicates the direction of time. Representing discrete time Next Switching signals within a time period and These represent system operation without faults and faults, respectively. and They represent discrete and The system state at any given moment. , and They represent discrete Real-time control inputs, external unknown interferences, and system outputs. For discrete The matrix of an uncertain system at time t, and satisfying , Let be the uncertainty matrix of the system, and , For discrete Uncertain system matrix at time , It is an uncertainty matrix that satisfies , For an identity matrix of the corresponding dimension, Let these represent the system matrix, output matrix, and input matrix of appropriate dimensions, respectively. Represents a known matrix with appropriate dimensions. Represents the interference matrix. This represents the system's tracking error expression. The coefficient matrix represents the expression for the tracking error of the system. It is a thing with upper and lower boundaries Failure factors, and Given a matrix, and , For ease of design, the failure factor is expressed as: , , Indicates discrete The system output tracking error at any given time;

[0062] Step 2: Design a robust model-predicted fault-tolerant switching controller;

[0063] Based on the mathematical model of the injection molding holding pressure process in equation (1), the following fault-tolerant switching controller is designed:

[0064]

[0065] in, , It is the controller gain;

[0066] Based on the fault-tolerant switching controller designed according to equation (2), the following closed-loop system model can be obtained:

[0067]

[0068] in, ,

[0069] ;

[0070] Step 3: Obtain the real-time control law gain, compensation coefficient, and switching coefficient of the system by solving the sufficient conditions of the robust positive definite invariant set and the terminal constraint set;

[0071]

[0072]

[0073]

[0074]

[0075] in, These are intermediate variables in the solution process. and Represents an unknown positive definite matrix. and These represent the state weighting matrix and the tracking weighting matrix, respectively. Indicates discrete Maximum control input at all times; , , , , , , , , , , , , , , , , , , , , , , , , , and To represent an unknown scalar, This is the upper bound of the performance metric. 0 indicates that the system is running stably, 1 indicates that the system has failed, * indicates the transpose of the matrix at the corresponding position in the LMI, and 0 indicates a zero matrix of the appropriate dimension.

[0076] The controller gain is calculated by following the steps above and combined with the state transition matrix to determine whether the controller adopts conventional control or fault-tolerant control. This enables random switching between normal control strategy and fault-tolerant control strategy, allowing the system to cope with uncertainties and potential faults during operation in a probabilistic manner.

[0077] This algorithm optimizes the controller parameters in real time along the time sequence during the pressure holding process of injection molding. Based on these parameters, the optimal control law can be calculated. After being implemented in the pressure holding stage of the injection molding process, it can drive the system output to gradually converge to the expected set value.

[0078] Implementation Case:

[0079] The patent application proposes a robust model-based predictive fault-tolerant switching control method for the injection molding holding pressure process with recoverable faults. This method effectively eliminates the negative impacts of uncertainty, low time delay, external unknown disturbances, and recoverable faults on the holding pressure stage of the injection molding process. In the injection molding process, the smooth operation of the nozzle pipeline is crucial for successful holding pressure and is also one of the factors affecting equipment failure. Nozzle pipeline blockage is a dynamic process: in the early stages of a fault, continuous fluid impact within the system may dissipate the blockage, restoring function; if this process is not completed in time, the blockage will stabilize and worsen, eventually developing into irreversible complete blockage. Simultaneously, the existence of time delays causes a time lag between the output and input of the control system, thus affecting system stability. Furthermore, the system's robustness decreases, weakening its resistance to external disturbances. Moreover, as the equipment operates in harsh environments, its aging rate accelerates, increasing the failure rate.

[0080] After extensive experiments on a solid injection molding machine, the input-output model for the holding pressure stage of the injection molding process is obtained as follows:

[0081]

[0082] in, , , , , , , , , , , , , , , , .

[0083] In addition, the system failure factors are: , , The controller parameters are: , .

[0084] The following DTI index is introduced to evaluate the tracking performance of the system:

[0085]

[0086] The simulation focuses on the holding pressure stage of an injection molding process, which involves uncertainty, setpoint variations, unknown bounded external disturbances, and intermittent faults, to verify the feasibility of the controller described in this chapter. The controller parameters can be determined through extensive testing. For ease of observation, three different fault probabilities are compared in the simulation: 1) , ;2) , ;3) , .

[0087] The output response curves under three failure probabilities are compared as follows: Figure 2-4 As shown in the figures, the solid line represents the output response, and the dashed line represents the expected output value. Observing these three figures, the control scheme proposed in the patent application can effectively maintain system stability under three different fault probabilities and achieve rapid tracking of the expected target value by the output response. Experimental results show that the scheme has adaptive switching characteristics: when the fault probability is high... When the probability of failure is low, the system can quickly switch to fault-tolerant control mode to cope with sudden failures; while when the probability of failure is low... When switching to fault-tolerant mode, the controller switches relatively slowly to avoid unnecessary frequent switching. In the event of a fault, although the oscillation amplitude of the output response will increase due to the actuator failure, the system can still operate stably and track the expected output value through the designed fault-tolerant switching controller. Compared to traditional methods, this approach can handle faults promptly, allowing the system to converge and reach a stable state. However, during normal system operation, it can cause frequent and significant fluctuations in the output response, thus affecting the quality of output tracking. Figure 2-4 As can be seen, compared with the comparative methods, the method proposed in this chapter has a faster and smoother output response, and only switches to the fault-tolerant controller in the event of a fault. Therefore, it can improve the system's control efficiency, productivity, and product quality.

[0088] Switching signals under three fault probabilities, such as Figure 5-7 As shown. Figure 5-7 The diagram illustrates the signal points for controller switching under different actuator conditions. A number 0 indicates a fault-free, normal actuator operation, while a number 1 indicates a fault. As can be seen from the diagram, the time span for controller switching changes with variations in fault probability and mean dwell time. Before switching or after the actuator recovers, the system uses a conventional controller. When an actuator fails, the controller switches to the designed FTC (Flexible Transmitter Control).

[0089] Tracking performance under three failure probabilities, such as Figure 8-10 As shown in the figure, under the control of the method described in this chapter, the output tracking error is well controlled regardless of the probability of actuator failure. In contrast, traditional methods exhibit several significant peaks at both low and high failure probabilities. Compared to the comparative methods, the evaluation metrics of the method described in this chapter show less overall fluctuation. Therefore, long-term use of the proposed method can save resources, reduce energy consumption, and create higher economic value.

[0090] In summary, the robust model prediction fault-tolerant switching control method for the injection molding holding pressure process proposed in the patent application is feasible and effective. Firstly, by introducing a probabilistic switching strategy, this design achieves a paradigm shift in control strategy from the traditional "deterministic response" to "probabilistic proactive adaptation." The controller no longer passively waits for faults to occur but makes forward-looking decisions based on the fault probability model, achieving random and smooth switching between different control modes. This method endows the control system with a higher level of intelligence, enabling it to bridge the gap between normal operation and complete fault tolerance in a probabilistic manner, thereby optimizing its dynamic performance while ensuring system stability. Furthermore, compared to the Lyapunov-Krasovskii method for solving the low-latency problem, the dimension of the V function in the Lyapunov-Razumikhin method is directly related to the time delay. This makes LRF, with its significantly lower computational cost and lower conservatism under small time delays, superior. Finally, simulation experiments were conducted using the injection molding process as an example, and the results were compared with traditional iterative learning control methods, confirming the effectiveness of this method. Therefore, the method provided in the patent application has significant application value and development prospects.

Claims

1. A robust model-based predictive fault-tolerant switching control method for the injection molding holding pressure process with fault recoverability, characterized in that, The specific steps are as follows: Step 1: Construct a mathematical model of the injection molding holding pressure process with fault recovery capabilities; To address the bounded and random characteristics of intermittent actuator failures, a conditional probability model can be established based on historical system operating data to characterize its statistical evolution. and Define the system in Under the condition of always being in a fault-free state, it runs until The conditional probabilities of being in a fault state or a stable state at time 1, respectively, are represented by their respective probability values ​​using... and express; and Define the system in Under the condition that the current time is already in a fault state, it runs until The conditional probability of remaining in a faulty state or recovering to a stable state at any given time is represented by the following probability values: and express; Indicates the current state of the system It runs stably at all times. Indicates the current Faults occur frequently. It is a random variable that follows a Bernoulli random distribution. Represents conditional probability; In the controller design process, parameters are usually required. and However, in actual production conditions, accurately obtaining the values ​​of these two parameters is often very difficult. Therefore, we introduce the following form to represent the uncertainty of the parameters: and , and They are respectively and The estimated value, and Indicates the uncertain part. and These represent the boundaries of the uncertain part of the probability, respectively. By introducing state increments and output tracking errors, the mathematical model of the injection molding holding pressure process with fault recovery is expressed as follows: in, Indicates the direction of time. Representing discrete time Next Switching signals within a time period and These represent system operation without faults and faults, respectively. and They represent discrete and The system state at any given moment. , and They represent discrete Real-time control inputs, external unknown interferences, and system outputs. For discrete The matrix of an uncertain system at time t, and satisfying , Let be the uncertainty matrix of the system, and , For discrete Uncertain system matrix at time , It is an uncertainty matrix that satisfies , For an identity matrix of the corresponding dimension, Let these represent the system matrix, output matrix, and input matrix of appropriate dimensions, respectively. Represents a known matrix with appropriate dimensions. Represents the interference matrix. This represents the system's tracking error expression. The coefficient matrix represents the expression for the tracking error of the system. It is a thing with upper and lower boundaries Failure factors, and Given a matrix, and , For ease of design, the failure factor is expressed as: , , Indicates discrete The system output tracking error at any given time; Step 2: Design a robust model-predicted fault-tolerant switching controller; Based on the mathematical model of the injection molding holding pressure process in equation (1), the following fault-tolerant switching controller is designed: in, , It is the controller gain; Based on the fault-tolerant switching controller designed according to equation (2), the following closed-loop system model can be obtained: in, , ； Step 3: Obtain the real-time control law gain, compensation coefficient, and switching coefficient of the system by solving the sufficient conditions of the robust positive definite invariant set and the terminal constraint set; in, These are intermediate variables in the solution process. and Represents an unknown positive definite matrix. and These represent the state weighting matrix and the tracking weighting matrix, respectively. Indicates discrete Maximum control input at all times; , , , , , , , , , , , , , , , , , , , , , , , , , and To represent an unknown scalar, This is the upper bound of the performance metric. 0 indicates that the system is running stably, 1 indicates that the system has failed, * indicates the transpose of the matrix at the corresponding position in the LMI, and 0 indicates a zero matrix of the appropriate dimension. The controller gain is calculated by following the steps above and combined with the state transition matrix to determine whether the controller adopts conventional control or fault-tolerant control. This enables random switching between normal control strategy and fault-tolerant control strategy, allowing the system to cope with uncertainties and potential faults during operation in a probabilistic manner. This algorithm optimizes the controller parameters in real time along the time sequence during the pressure holding process of injection molding. Based on these parameters, the optimal control law can be calculated. After being implemented in the pressure holding stage of the injection molding process, it can drive the system output to gradually converge to the expected set value.

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