A sliding mode fault-tolerant control method for high-temperature forging dynamic three-dimensional measurement
By combining discrete singular perturbation Markov jump system and dynamic event triggering mechanism, a distributed cooperative control strategy was designed to solve the problems of fast convergence and robustness of high temperature forging dynamic three-dimensional measurement system under deception attack and actuator failure, and to achieve efficient network resource utilization and safe operation.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- QINGDAO UNIV OF TECH
- Filing Date
- 2026-03-12
- Publication Date
- 2026-06-05
AI Technical Summary
In the context of the Industrial Internet of Things (IIoT), the dynamic three-dimensional measurement system for high-temperature forging is susceptible to spoofing attacks and actuator failures. Furthermore, the limited wireless communication bandwidth resources make it difficult for existing control strategies to converge quickly and maintain high-performance tracking within a limited time. At the same time, the system cannot optimize network transmission load, resulting in insufficient system robustness and operational security.
A distributed cooperative control strategy is designed by adopting a discrete singular perturbation Markov jump system model and combining integral sliding surface and dynamic event triggering mechanism. By constructing a closed-loop system model and sliding mode control law, the system can achieve rapid convergence in a finite time and reduce the network transmission load from the sensor to the edge controller, thereby improving the robustness and security of the system.
In complex scenarios involving deception attacks and actuator failures, the system can quickly converge and maintain high-performance tracking within a limited time, significantly reducing network transmission load and improving the system's robustness and operational security.
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Abstract
Description
Technical Field
[0001] This invention relates to the fields of electrical engineering, control engineering, and industrial Internet of Things, specifically to a sliding mold fault-tolerant control method for dynamic three-dimensional measurement in high-temperature forging. Background Technology
[0002] The development of Industrial Internet of Things (IIoT) technology has driven the evolution of various control systems in the high-temperature forging industry from traditional centralized control to distributed edge intelligent architectures, which are widely used in smart factories, multi-objective collaborative production lines, and remote operation and maintenance. However, due to the openness of industrial wireless networks (such as 5G and WirelessHART), the control loop of the high-temperature forging dynamic three-dimensional measurement system is highly vulnerable to network attacks, such as spoofing attacks and denial-of-service attacks. These attacks can disrupt the normal operation of the system, leading to performance degradation or even system crashes.
[0003] In control theory, Markov jump systems are an important class of hybrid systems, effectively describing the stochastic switching of system structure or parameters caused by component failures, sudden environmental changes, etc. Singularly perturbated Markov jump systems further introduce the concept of time-scale separation, enabling more precise description of complex systems with fast and slow dynamic characteristics. To ensure the safe and stable operation of such complex systems in harsh environments, sliding mode control is often used due to its strong robustness to matching uncertainties and external disturbances. Meanwhile, to alleviate the problem of limited network bandwidth resources, event-triggered control strategies have been proposed. These strategies transmit data only when the system state meets specific conditions, rather than through traditional periodic transmission, thus effectively conserving network resources. Existing event-triggered mechanisms include static event triggering and dynamic event triggering.
[0004] Despite the progress made in the aforementioned aspects, existing technologies still have significant limitations in the practical application of dynamic three-dimensional measurement systems for high-temperature forging, especially in complex scenarios facing multiple constraints and threats. For example: First, there is insufficient modeling of random cybersecurity threats such as spoofing attacks. Existing methods fail to effectively utilize stochastic processes such as Bernoulli distribution to characterize the uncertainty of attacks, leading to overly conservative controller designs or insufficient security. Second, in terms of balancing resource efficiency and system performance, traditional event-triggered mechanisms struggle to adaptively adjust trigger thresholds under complex random attack environments, failing to achieve optimal utilization of industrial wireless network resources while ensuring stable operation of the measurement process. Furthermore, when the system is simultaneously affected by multiple uncertainties such as random spoofing attacks, actuator failures, external interference, and singular perturbation characteristics, existing methods lack robust control strategies that can guarantee rapid convergence of the system state within a finite time and maintain predetermined performance, making it difficult to meet the stringent requirements of high-temperature forging equipment for dynamic response in dynamic three-dimensional measurement of forgings. Summary of the Invention
[0005] To address the shortcomings of existing technologies, the technical problem this invention aims to solve is: in an industrial IoT environment, when a high-temperature forging dynamic three-dimensional measurement system is subjected to deception attacks on the control network, random degradation failures of the actuator, and limited industrial wireless communication bandwidth resources, how to design a distributed collaborative control strategy to enable the system to quickly converge to the set value within a limited time and maintain high-performance tracking, while significantly reducing the network transmission load from the sensor to the edge controller, and improving the robustness and operational safety of the system under harsh working conditions and network threats.
[0006] To address the aforementioned technical problems, this invention provides a sliding mold fault-tolerant control method for dynamic three-dimensional measurement in high-temperature forging, comprising the following steps:
[0007] S1. Construct a system model of a discrete singular perturbation Markov jump system, using an integral sliding mode surface and considering the controller in the approaching stage according to sliding mode control theory, taking into account the impact of actuator failure and deception attack on the system, and construct a closed-loop system model in the approaching state.
[0008] S2. Give the conditions for reachability under the sliding mode control law in S1, and prove them;
[0009] S3. Based on S1, the system in the approaching phase and the sliding phase is a random finite-time bounded system that satisfies the condition of having perturbations. Determine the conditions for robust stability and prove them.
[0010] S4. Based on the conditions in S3, derive the controller gain of the system to achieve effective control of the system.
[0011] Furthermore, in S1, a system model of a discrete singularly perturbed Markov jump system is constructed. Using an integral sliding mode surface and considering the controller in the approaching phase based on sliding mode control theory, the impact of actuator failure and deception attacks on the system is taken into account. The closed-loop system model in the approaching state is constructed using the following method:
[0012] S11. The system model of the discrete-time Markov jump system is:
[0013]
[0014] in Represents the state vector. An actuator input signal indicating a potential fault. For controlled output of the system, Belonging to External disturbances in space are input variables. , , and All are pre-defined constant matrices of appropriate dimensions. Matrices with a specific dimension. It is a singular perturbation matrix with rank strictly less than n. Variables Representing a finite set The mode transition probability matrix of the previous class of singularly perturbed Markov jump systems It can be obtained through the following equation:
[0015]
[0016] in, , , .
[0017] The formula for the dynamic event triggering mechanism can be expressed as:
[0018]
[0019] in This represents the constructed auxiliary dynamic variable, whose initial conditions are: and satisfy , . It can be expressed by the following formula:
[0020]
[0021] In this formula, and All are positive definite symmetric matrices, used as weighting matrices. Error function The definition is as follows:
[0022]
[0023] Constructed auxiliary dynamic variables The following relationship must be satisfied:
[0024]
[0025] The deception attack model is as follows:
[0026]
[0027] in , .
[0028] Conditional probability matrix Depend on The result is as follows. , , and For ease of writing, the formulas will be... Recorded as ,like , , , , , Recorded as , , , , , .
[0029] S12, the sliding surface function is:
[0030]
[0031] in, From 0 to Sliding mode control (SMC) law over a time interval (referred to as the approach phase):
[0032]
[0033] in, .
[0034] S13, The actuator fault model is:
[0035]
[0036] S14. Based on the above, the closed-loop system model can be derived:
[0037]
[0038] Furthermore, based on S1, S2 gives and proves the conditions for reachability under the sliding mode control law, using the following method:
[0039] S21, in parameters satisfy Under certain conditions, by employing a sliding mode control strategy, the trajectory of the initial discrete-time system will be within a predetermined finite interval. The interior is driven toward the sliding surface superior.
[0040] S22. The specific proof process is as follows:
[0041] First, from the smooth mold surface , deduced Choose the Lyapunov equation Calculations show that ,in , .
[0042] Thus prove The system is monotonically decreasing and its state is driven to the sliding surface; thus, by accumulating this inequality from 0 to... Combining the initial conditions, the explicit upper bound of the arrival time is obtained as follows: As long as you choose a sufficiently large ℓ This ensures that the system operates within a preset, finite time interval. It reaches and maintains s(k)=0.
[0043] Furthermore, S3, based on S1, presents the approach phase and the sliding phase of the system as a random finite-time bounded system that satisfies the condition of perturbation. The robust stability condition is proven using the following method:
[0044] S31. For a given constant , , ( (), ) and matrix If positive numbers exist and ,matrix , = , = , = , = , = , , , and those with corresponding dimensions , , If the following conditions are met, then during the approach phase... Within, a closed-loop system is considered to be about ( , ,0, Q) is random, finite-time bounded:
[0045]
[0046]
[0047]
[0048]
[0049]
[0050]
[0051] in,
[0052] ,
[0053] ,
[0054] ,
[0055] ,
[0056] ,
[0057] ,
[0058] ,
[0059] ,
[0060] , (18)
[0061] ,
[0062] ,
[0063] , ,
[0064] ,
[0065] ,
[0066] ,
[0067] ,
[0068] ,
[0069] ,
[0070] ,
[0071] .
[0072] S32. The proof is as follows:
[0073] Choose the following Lyapunov equation:
[0074]
[0075] in, .
[0076] First, calculate the expected difference of each component along the system trajectory. Jensen's inequality is used to define the double summation term and the free weight matrix. , Handle time-delay dependencies and combine them with dynamic event triggering conditions. Substitute the event triggering inequality This integrates various elements into The form; then guaranteed by LMI conditions. And satisfy Using sliding mode control law boundary Constrain the control input and iterate the inequality from the initial time to... By combining the matrix upper and lower bound estimates with the initial condition assumptions, the final derivation is that the state satisfies... This proves that the system is in the approaching phase. Internal matters The singular perturbation is bounded by finite time.
[0077] S33, when At that time, the system state reaches and remains on the sliding surface. Utilizing... Given the given conditions, the equivalent control law can be derived:
[0078]
[0079] Will Substituting into system (11), we can obtain the closed-loop system:
[0080]
[0081] The sliding phase system is random, finite-time bounded, and satisfies the condition that there exists a perturbation. The conditions and proof process for robust stability are similar to those for the approaching phase, so they will not be repeated here.
[0082] Furthermore, based on the conditions in S3, the controller gain of the system is derived in S4 to achieve effective control of the system, using the following method:
[0083] S4. Derive the controller gain of the system to achieve effective control of the system:
[0084] By employing variable substitution and matrix inequality relaxation techniques, the bilinear matrix inequalities in S3, which are difficult to solve directly, are transformed into computable linear matrix inequalities (LMIs). Specifically, this is achieved by defining... , , , , , , , , , , , , Auxiliary variables, and actuator failure uncertainty. Decoupling The linear form, while utilizing inequalities Relaxing the nonconvex terms ultimately yields information about the new variable. , , Standard LMIs such as MATLAB can be used to directly solve for controller gain and event trigger weights, enabling the collaborative design of asynchronous controllers and dynamic event triggering strategies. Attached Figure Description
[0085] Figure 1 This is a block diagram of a closed-loop system.
[0086] Figure 2 This represents the probability of a deception attack occurring.
[0087] Figure 3 Transition probability and conditional probability ;
[0088] Figure 4 For state trajectory;
[0089] Figure 5 For the moment and interval of release;
[0090] Figure 6 It is a sliding surface function;
[0091] Figure 7 For sliding mode control rate;
[0092] Figure 8 It assists in the process of dynamic variable changes. Detailed Implementation
[0093] To address the complex operating conditions of high-temperature forging industrial IoT systems, which are vulnerable to control network spoofing attacks, actuator random degradation failures, and limited industrial wireless communication bandwidth, an asynchronous method combining probabilistic dynamic event triggering strategy and finite-time sliding mode control (SMC) is proposed. Controller design scheme: To alleviate network congestion under limited bandwidth, a probabilistic dynamic event triggering strategy is adopted to reduce data transmission; spoofing attacks following Bernoulli distribution and actuator failures introducing model uncertainty are incorporated into system modeling; a suitable sliding mode surface is constructed and an SMC law is designed; by analyzing the finite-time boundedness condition of the closed-loop system (considering the influence of SMC and weight matrix), linear matrix inequalities (LMIs) are used to achieve the collaborative design of asynchronous controller and event triggering weight matrix; finally, the effectiveness and practicality of the method are verified by an example.
[0094] S1. Construct a system model of the discrete singularly perturbed Markov jump system. Utilize the integral sliding mode surface and consider the controller in the approaching phase based on sliding mode control theory. Consider the impact of actuator failure and deception attacks on the system to obtain the closed-loop system model in the approaching state.
[0095] The system model of the discrete-time Markov jump system is as follows:
[0096]
[0097] in Represents the state vector. An actuator input signal indicating a potential fault. For controlled output of the system, Belonging to External disturbances in space are input variables. , , and All are pre-defined constant matrices of appropriate dimensions. Matrices with a specific dimension. It is a singular perturbation matrix with rank strictly less than n. Variables Representing a finite set The mode transition probability matrix of the previous class of singularly perturbed Markov jump systems It can be obtained through the following equation:
[0098]
[0099] in, , , .
[0100] The formula for the dynamic event triggering mechanism can be expressed as:
[0101]
[0102] in This represents the constructed auxiliary dynamic variable, whose initial conditions are: and satisfy , . It can be expressed by the following formula:
[0103]
[0104] In this formula, and All are positive definite symmetric matrices, used as weighting matrices. Error function The definition is as follows:
[0105]
[0106] Constructed auxiliary dynamic variables The following relationship must be satisfied:
[0107]
[0108] The deception attack model is as follows:
[0109]
[0110] in , .
[0111] Conditional probability matrix Depend on The result is as follows. , , and For ease of writing, the formulas will be... Recorded as ,like , , , , , Recorded as , , , , , .
[0112] The sliding surface function is:
[0113]
[0114] in, From 0 to Sliding mode control (SMC) law over a time interval (referred to as the approach phase):
[0115]
[0116] in, .
[0117] The actuator failure model is as follows:
[0118]
[0119] Based on the above, a closed-loop system model can be derived:
[0120]
[0121] S2. Give the conditions for reachability under the sliding mode control law in S1, and prove them.
[0122] In parameters satisfy Under certain conditions, by employing a sliding mode control strategy, the trajectory of the initial discrete-time system will be within a predetermined finite interval. The interior is driven toward the sliding surface superior.
[0123] The specific proof process is as follows:
[0124] First, from the smooth mold surface , deduced Choose the Lyapunov equation Calculations show that ,in , .
[0125] Thus prove The system is monotonically decreasing and its state is driven to the sliding surface; thus, by accumulating this inequality from 0 to... Combining the initial conditions, the explicit upper bound of the arrival time is obtained as follows: As long as you choose a sufficiently large ℓ This ensures that the system operates within a preset, finite time interval. It reaches and maintains s(k)=0.
[0126] S3. Based on S1, the system in the approaching and sliding phases is given a random finite-time bounded state that satisfies the condition under perturbation. Determine the robust and stable conditions and prove them.
[0127] For a given constant , , ( (), ) and matrix If positive numbers exist and ,matrix , = , = , = , = , = , , , and those with corresponding dimensions , , If the following conditions are met, then during the approach phase... Within, a closed-loop system is considered to be about ( , ,0, Q) is random, finite-time bounded:
[0128]
[0129]
[0130]
[0131]
[0132]
[0133]
[0134] in,
[0135] ,
[0136] ,
[0137] ,
[0138] ,
[0139] ,
[0140] ,
[0141] ,
[0142] ,
[0143] , (18)
[0144] ,
[0145] ,
[0146] , ,
[0147] ,
[0148] ,
[0149] ,
[0150] ,
[0151] ,
[0152] ,
[0153] ,
[0154] .
[0155] The proof is as follows:
[0156] Choose the following Lyapunov equation:
[0157]
[0158] in, .
[0159] First, calculate the expected difference of each component along the system trajectory. Jensen's inequality is used to define the double summation term and the free weight matrix. , Handle time-delay dependencies and combine them with dynamic event triggering conditions. Substitute the event triggering inequality This integrates various elements into The form; then guaranteed by LMI conditions. And satisfy Using sliding mode control law boundary Constrain the control input and iterate the inequality from the initial time to... By combining the matrix upper and lower bound estimates with the initial condition assumptions, the final derivation is that the state satisfies... This proves that the system is in the approaching phase. Internal matters The singular perturbation is bounded by finite time.
[0160] when At that time, the system state reaches and remains on the sliding surface. Utilizing... Given the given conditions, the equivalent control law can be derived:
[0161]
[0162] Will Substituting into system (11), we can obtain the closed-loop system:
[0163]
[0164] The sliding phase system is random, finite-time bounded, and satisfies the condition that there exists a perturbation. The conditions and proof process for robust stability are similar to those for the approaching phase, so they will not be repeated here.
[0165] S4. Based on the conditions in S3, derive the controller gain of the system to achieve effective control of the system.
[0166] By employing variable substitution and matrix inequality relaxation techniques, the bilinear matrix inequalities in S3, which are difficult to solve directly, are transformed into computable linear matrix inequalities (LMIs). Specifically, this is achieved by defining... , , , , , , , , , , , , Auxiliary variables, and actuator failure uncertainty. Decoupling The linear form, while utilizing inequalities Relaxing the nonconvex terms ultimately yields information about the new variable. , , Standard LMIs, etc.
[0167] Example: An example is used to verify the effectiveness of the proposed method. In the simulation, consider that the system has two Markov transition modes, and the transition probability of the Markov process is... The conditional transition probability is The remaining parameters are as follows: , , , , , , , , , , , , , , , , , , , , .
[0168] The controller gain was obtained through simulation using MATLAB: , In addition, we obtained , , , , , , Data such as...
[0169] Simulation was obtained simultaneously. Figures 1-7 Together, they depicted the entire process of the proposed asynchronous sliding mode control strategy under deception attacks and actuator failures:
[0170] Figure 1 Provide a closed-loop system block diagram to illustrate the asynchronous signal interactions and attack / interference paths between the event triggers, actuator network, and controller; Figure 2 middle This indicates that the attack exhibits a Bernoulli-like random switching characteristic, with the peak time corresponding to the highest risk of data injection; Figure 3 Display system mode transition probability Observational conditional probability of the controller Real-time matching provides a basis for the asynchronous law; Figure 4 This shows that the state trajectory converges and remains bounded in a finite time, verifying its stability; Figure 5 The sparse distribution of trigger and release times indicates that the probabilistic dynamic event mechanism significantly saves bandwidth. Figure 6 Sliding surface Rapidly approaches zero, confirming arrival within a finite time; Figure 7 Control quantity The system first drives the device at a large amplitude and then switches to a small amplitude dithering mode to achieve robust control. Figure 8 Auxiliary variables As the trigger-decay cycle changes, with Figure 7 The release rhythm corresponds one-to-one, fully demonstrating the safe, energy-saving, and reliable operation of the closed-loop system under conditions of both attack and failure.
Claims
1. A sliding mode fault-tolerant control method for dynamic three-dimensional measurement in high-temperature forging, characterized in that, Includes the following steps: S1. Construct a discrete-time singular perturbation Markov jump system model for a high-temperature forging measurement system, design an integral sliding surface, design a reaching stage controller based on sliding mode control theory, and consider the impact of actuator failure and deception attack on the system to construct a closed-loop system model in the reaching state. S2. Give sufficient conditions for the reachability of the system under the sliding mode control law in S1, and provide a proof. S3. Building upon S1, provide a system that is random, finite-time bounded and satisfies the condition of having perturbations during both the approach and sliding phases. Determine the sufficient conditions for robust stability and provide a proof; S4. Based on the conditions in S3, derive the controller gain of the system to achieve effective control of the system.
2. The sliding mold fault-tolerant control method for dynamic three-dimensional measurement in high-temperature forging according to claim 1, characterized in that, In step S1, a discrete-time singular perturbation Markov jump system model is constructed. Using the integral sliding surface, a controller considering the approaching stage is designed based on sliding mode control theory. In conjunction with the influence of actuator failure on the system, a closed-loop system model in the approaching state is obtained. S11. The system model of the discrete-time Markov jump system is: in Represents the state vector. An actuator input signal indicating a potential fault. For controlled output of the system, Belonging to External disturbances in space are input variables. , , and All are pre-defined constant matrices of appropriate dimensions. Matrices with a specific dimension. It is a singular perturbation matrix with rank strictly less than n. Variables Representing a finite set The mode transition probability matrix of the previous class of singularly perturbed Markov jump systems It can be obtained through the following equation: in, , , . The formula for the dynamic event triggering mechanism can be expressed as: in This represents the constructed auxiliary dynamic variable, whose initial conditions are: and satisfy , . It can be expressed by the following formula: In this formula, and All are positive definite symmetric matrices, used as weighting matrices. Error function The definition is as follows: Constructed auxiliary dynamic variables The following relationship must be satisfied: The deception attack model is as follows: in , . Conditional probability matrix Depend on The result is as follows. , , and For ease of writing, the formulas will be... Recorded as ,like , , , , , Recorded as , , , , , . S12, the sliding surface function is: in, From 0 to Sliding mode control (SMC) law over a time interval (referred to as the approach phase): in, . S13, The actuator fault model is: S14. Based on the above, the closed-loop system model can be derived:
3. The sliding mold fault-tolerant control method for dynamic three-dimensional measurement in high-temperature forging according to claim 1, characterized in that, Give the conditions for reachability of S1 under the sliding mode control law, and prove them: S21, in parameters satisfy Under certain conditions, by employing a sliding mode control strategy, the trajectory of the initial discrete-time system will be within a predetermined finite interval. The interior is driven toward the sliding surface superior. S22. The specific proof process is as follows: First, from the smooth mold surface , deduced Choose the Lyapunov equation Calculations show that ,in , . Thus prove The system is monotonically decreasing and its state is driven to the sliding surface; thus, by accumulating this inequality from 0 to... Combining the initial conditions, the explicit upper bound of the arrival time is obtained as follows: As long as you choose a sufficiently large ℓ This ensures that the system operates within a preset, finite time interval. It reaches and maintains s(k)=0.
4. The sliding mold fault-tolerant control method for dynamic three-dimensional measurement in high-temperature forging according to claim 1, characterized in that, Based on S1, we present the approach phase and the sliding phase of the system as a random finite-time bounded system, satisfying the condition under perturbation. Determine the robust and stable conditions and prove them: S31. For a given constant , , ( (), ) and matrix If positive numbers exist and ,matrix , = , = , = , = , = , , , and those with corresponding dimensions , , If the following conditions are met, then during the approach phase... Within, a closed-loop system is considered to be about ( , ,0, Q) is random, finite-time bounded: in, ， ， ， ， ， ， ， ， ， （18） ， ， ， ， ， ， ， ， ， ， ， 。 S32. The proof is as follows: Choose the following Lyapunov equation: in, . First, calculate the expected difference of each component along the system trajectory. Jensen's inequality is used to define the double summation term and the free weight matrix. , Handle time-delay dependencies and combine them with dynamic event triggering conditions. Substitute the event triggering inequality This integrates various elements into The form; then guaranteed by LMI conditions. And satisfy Using sliding mode control law boundary Constrain the control input and iterate the inequality from the initial time to... By combining the matrix upper and lower bound estimates with the initial condition assumptions, the final derivation is that the state satisfies... This proves that the system is in the approaching phase. Internal matters The singular perturbation is bounded by finite time. S33, when At that time, the system state reaches and remains on the sliding surface. Utilizing... Given the given conditions, the equivalent control law can be derived: Will Substituting into system (11), we can obtain the closed-loop system: The sliding phase system is random, finite-time bounded, and satisfies the condition that there exists a perturbation. The conditions and proof process for robust stability are similar to those for the approaching phase, so they will not be repeated here.
5. The sliding mold fault-tolerant control method for dynamic three-dimensional measurement in high-temperature forging according to claim 1, characterized in that, Based on the conditions in S3, the controller gain of the system is derived to achieve effective control of the system: By employing variable substitution and matrix inequality relaxation techniques, the bilinear matrix inequalities in S3, which are difficult to solve directly, are transformed into computable linear matrix inequalities (LMIs). Specifically, this is achieved by defining... , , , , , , , , , , , , Auxiliary variables, and actuator failure uncertainty. Decoupling The linear form, while utilizing inequalities Relaxing the nonconvex terms ultimately yields information about the new variable. , , Standard LMIs such as MATLAB can be used to directly solve for controller gain and event trigger weights, enabling the collaborative design of asynchronous controllers and dynamic event triggering strategies.