Anti-disturbance event-triggered model predictive control method based on PID mechanism for input-affine nonlinear systems

Abstract

The application discloses a kind of PID mechanism-based anti-disturbance event-triggered model predictive control methods for input affine nonlinear system, and relates to the technical field of automation and process control.The method comprises: establishing input affine nonlinear system mathematical model and defining constraint;Design nonlinear disturbance observer to estimate external disturbance in real time, construct feedforward compensation control law;On the basis of disturbance compensation, design robust MPC, solve optimal control problem at trigger time to handle residual error;Construct dynamic event-triggered function based on PID proportion-integral-derivative adjustment idea, by comparing trigger function value and adaptive dynamic threshold, determine whether to trigger MPC to solve again.System total control input is the sum of feedforward compensation law and MPC optimal control law.The application guarantees control performance and anti-disturbance robustness, significantly reduces optimization solving frequency, saves calculation and communication resources, and is suitable for resource-limited networked control system.

Description

Technical Field

[0001] This invention relates to the field of automation and process control technology, and in particular to a disturbance rejection event-triggered model predictive control method based on PID mechanism for input affine nonlinear systems. Background Technology

[0002] Model Predictive Control (MPC), as an advanced process control strategy, has been widely applied and extensively studied in modern industrial processes due to its ability to explicitly handle the multivariable, nonlinear characteristics and input / output constraints of a system. Its basic principle is to solve an open-loop optimization problem in a finite-time domain online based on the system's dynamic model at each sampling time, and then apply the first element of the obtained optimal control sequence to the system.

[0003] However, the core of traditional MPC lies in the need to solve complex optimization problems online "at every moment," which often brings a huge computational burden, especially for nonlinear systems, where solving online optimization problems is even more time-consuming. In networked control systems with limited computing resources and communication bandwidth (such as wireless sensor networks and embedded control systems), this high-frequency online computation not only leads to severe computational latency but also causes communication network congestion, becoming a key bottleneck restricting the large-scale promotion of MPC technology in resource-sensitive applications.

[0004] To overcome this bottleneck, Event-Triggered Model Predictive Control (ET-MPC) was developed. The core idea of ​​ET-MPC is to introduce a "trigger mechanism" as a watchdog, which only triggers the solver and updates the control input when system state deviations, performance indicators, or external conditions exceed preset thresholds; otherwise, the control law from the previous time step is used. This approach can significantly reduce the frequency of solving optimization problems, thereby effectively saving computational and communication resources.

[0005] Despite the enormous potential shown by ET-MPC, most existing methods still suffer from the following shortcomings:

[0006] First, the static nature of the triggering mechanism is mismatched with the dynamic changes in the system. Most existing ET-MPC studies use static thresholds based on the state deviation norm as triggering conditions. These static thresholds cannot perceive the dynamic changing trends of system errors, leading to unnecessary resource waste when the system is in a steady state due to overly conservative thresholds; and when the system suffers severe disturbances, their slow response prevents timely updates to the control input, resulting in decreased control performance and even compromising the feasibility of system constraints.

[0007] Secondly, existing methods lack robustness for nonlinear systems, especially input affine nonlinear systems. Real-world industrial processes often exhibit complex nonlinear characteristics and are inevitably affected by external disturbances and unmodeled dynamics. For input affine nonlinear systems, these disturbances are amplified through coupling with the system state and control input via nonlinear equations, making traditional triggering mechanisms based on static thresholds highly susceptible to failure. When disturbances occur, they may cause a surge in triggering frequency, degrading ET-MPC to periodic control and losing its event-triggered advantage; or, due to untimely disturbance compensation, the system state may deviate significantly from the predicted trajectory within the trigger interval, compromising the algorithm's recursive feasibility and closed-loop stability.

[0008] Finally, existing research has gaps in the collaborative design of disturbance and event-triggered mechanisms. While combining a Disturbance Observer (DOB) with an MPC to form a Disturbance Observer-based MPC (DOB-MPC) has been shown to effectively improve system robustness by rapidly suppressing measurable / predictable disturbances through feedforward compensation, a lack of literature reports on how to design an intelligent triggering mechanism capable of sensitively sensing disturbance changes within an event-triggered framework, particularly in affine nonlinear systems, and systematically borrowing and transferring the dynamic adjustment concept of proportional-integral-derivative (PID) to construct trigger thresholds to achieve a better balance between "trigger accuracy" and "resource conservation." Existing schemes lack effective utilization of information such as disturbance estimation errors and uncompensated residuals, making the triggering mechanism unable to adapt to the system's current actual disturbance rejection capability. Summary of the Invention

[0009] To address this, this invention provides a disturbance-resistant event-triggered model predictive control method based on a PID mechanism for input affine nonlinear systems. This method solves the technical problem in the prior art where the event-triggered mechanism relies on static thresholds, cannot perceive the dynamic changes in system errors, and lacks adaptive compensation capabilities for disturbances, making it difficult to achieve both control performance and resource utilization efficiency in environments with limited computing resources.

[0010] To address the aforementioned technical problems, embodiments of the present invention provide a disturbance-resistant event-triggered model predictive control method based on a PID mechanism for input affine nonlinear systems. This method includes the following steps:

[0011] Step S1: Establish a mathematical model of the continuous-time input affine nonlinear system and define its state constraints and control input constraints;

[0012] Step S2: Design a nonlinear disturbance observer to estimate the external disturbances to the system in real time, and construct a feedforward compensation control law based on the estimated values ​​to suppress the impact of the disturbances.

[0013] Step S3: Based on the disturbance feedforward compensation, design a robust MPC to solve the optimal control problem in the finite time domain at the event trigger time, so as to handle the remaining error and uncertainty after compensation;

[0014] Step S4: Construct a dynamic event trigger function based on the PID mechanism. This function includes the proportional, integral, and derivative terms of the error. By comparing the calculated value of this trigger function with the dynamic threshold, determine whether to trigger the MPC optimization solver to resolve and update the control input.

[0015] The total control input of the system is the sum of the feedforward compensation control law and the optimal control law output by the MPC optimization solver.

[0016] Preferably, the mathematical model of the input affine nonlinear system in step S1 is:

[0017] ;

[0018] in, The derivative of the system state; Let be the system state vector. The number of state variables; To control the input vector, To control the number of input variables; Let be an externally unknown but bounded perturbation vector. The number of external disturbance variables; For drift term; The input mapping matrix; The disturbance mapping matrix is ​​given; the system state and control input satisfy hard constraints: ,in, and Let represent the state constraint set and the control constraint set containing the origin, respectively, both of which are compact convex sets.

[0019] Preferably, the design of the nonlinear disturbance observer in step S2 specifically involves:

[0020] Constructing intermediate auxiliary variables and nonlinear functions Let the observer dynamics be:

[0021] ;

[0022] ;

[0023] in, as an intermediate auxiliary variable The derivative; The observer gain matrix is... ; For drift term; The input mapping matrix; To control the input vector; The perturbation mapping matrix; This is the disturbance estimate; by selecting an appropriate... This makes the dynamic system of estimation error asymptotically stable and obtains an upper bound on the disturbance estimation error.

[0024] Preferably, in step S2, a feedforward compensation control law is constructed. For unmatched disturbances, orthogonal projection is used to decompose the disturbance into compensable parts. With the uncompensated portion :

[0025] ;

[0026] ;

[0027] in, The input mapping matrix; The pseudo-inverse of the input mapping matrix; The perturbation mapping matrix; It is an externally unknown but bounded perturbation vector; The orthogonal complement of the input mapping matrix. The pseudo-inverse of orthogonal complement; setting a compensation control law. and the residual disturbance after compensation The upper bound is denoted as ,in This is the upper bound of the residual perturbation. The representation is defined as follows: Indicates the supremacy. For time range, Let be the norm of the residual perturbation.

[0028] Preferably, in step S3, at each triggering time The robust MPC optimal control problem to be solved is:

[0029] ;

[0030] ;

[0031] ;

[0032] ;

[0033] ;

[0034] ;

[0035] in, This is the optimal control sequence. To predict time variables in the time domain, This is the current trigger time; For minimization operators; The cost function; This represents the current predicted state. The control trajectory needs to be optimized; To predict the state derivative; To predict the state trajectory; For drift term; The input mapping matrix; For predictive control input; To predict the state of the trajectory at the trigger moment; This represents the actual state of the system at the moment of triggering. For tightening the set of control constraints; It is a time-varying set of state constraints; For prediction in the time domain; For the terminal domain.

[0036] Preferably, the dynamic event triggering function based on the PID mechanism in step S4 is defined as follows:

[0037] ;

[0038] in, For the trigger function value; The error between the actual state and the predicted state of the system; , , These are the proportional, integral, and differential weighting coefficients, respectively. Based on terminal cost matrix The weighted norm; To predict time variables in the time domain; This is the current trigger time.

[0039] Preferably, the dynamic event triggering condition in step S4 is:

[0040] Compare trigger function values With dynamic threshold ,when When the trigger condition is met, the trigger time is recorded. And update the control input; otherwise, keep the control input unchanged from the previous trigger moment, where For dynamic thresholds;

[0041] Next actual triggering time Pick With forced triggering time The minimum value, i.e. ,in To perform the minimum value operation, For prediction in the time domain.

[0042] Preferably, the dynamic threshold Based on the upper bound of residual disturbance Prediction time domain and adaptive PID parameter setting:

[0043] ;

[0044] in, To the upper bound of residual disturbance Related constants, and These are design parameters related to the system's Lipschitz constant and shrinkage rate.

[0045] Preferably, the system's total control input The optimal control law obtained by robust MPC optimization Feedforward compensation control law provided by the disturbance observer Superimposed composition:

[0046] ;

[0047] in, It is only updated at the moment the event is triggered, and remains unchanged during the trigger interval; It is continuously updated based on the real-time estimates from the interference observer.

[0048] This invention also provides a computer storage medium storing a computer software product, the computer software product including several instructions for causing a computer device to execute the above-described disturbance rejection event triggered model predictive control method based on PID mechanism for input affine nonlinear systems.

[0049] As can be seen from the above technical solutions, this invention application has the following beneficial effects:

[0050] (1) Significantly reduces computational and communication burden, achieving "on-demand triggering" resource optimization. This invention replaces the static threshold mechanism in traditional event-triggered control (ET-MPC) by constructing a dynamic event triggering function based on the PID proportional-integral-derivative control concept. This function uses the proportional term to sense the current error amplitude in real time, the integral term to remember historical accumulated errors to prevent steady-state drift, and the derivative term to monitor the error change rate to capture the sudden change trend of disturbances. Only when the system dynamics truly require intervention (i.e., the PID triggering function value exceeds the dynamic threshold) is the MPC optimization solver activated to update the control law. This mechanism fundamentally breaks the resource waste mode of "timed update" in traditional periodic control, and minimizes the solution frequency of optimization problems while ensuring control performance, thereby significantly saving computational resources and communication bandwidth in constrained network environments.

[0051] (2) Effectively improves the robustness of nonlinear systems against disturbances and achieves active suppression of matched / unmatched disturbances. Addressing the problem that external disturbances in input affine nonlinear systems are easily amplified by nonlinear coupling, this invention constructs a dual-channel disturbance rejection architecture of "feedforward compensation + feedback stabilization". First, the disturbance is reconstructed in real time by a nonlinear disturbance observer (DOB), and based on orthogonal projection decomposition technology, the disturbance is accurately divided into a compensable part and an uncompensated part. Then, a feedforward compensation law is constructed to quickly suppress the compensable part. Based on this, a robust MPC controller is designed to handle observer estimation errors and uncompensated residual disturbances, and system stability is ensured through constraint tightening and terminal domain design. This collaborative design enables the system to maintain good control accuracy and robust stability even when facing strong nonlinearity, large disturbances, and unmodeled dynamics.

[0052] (3) The system achieves adaptive matching between the triggering mechanism and the anti-disturbance capability, ensuring recursive feasibility and closed-loop stability. This invention breaks the traditional separation between event triggering mechanism design and controller design, establishing a theoretical closed loop from "disturbance suppression capability" to "triggering decision logic." Dynamic threshold The setting is directly related to the upper bound of residual perturbation determined by DOB and robust MPC. (Right now ), system Lipschitz constant and terminal shrinkage rate Key performance indicators, etc. Simultaneously, by introducing a forced trigger timing... As a fallback mechanism, it ensures that even if the system remains stable for a long period, the control law will not be updated beyond a prediction time domain. This design allows the "sensitivity" of event triggering to dynamically match the actual "disturbance resistance" of the system, theoretically guaranteeing the recursive feasibility of the algorithm and the global stability of the closed-loop system. Attached Figure Description

[0053] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly described below. Referring to the drawings will make the features and advantages of the present invention clearer. The drawings are illustrative and should not be construed as limiting the present invention in any way. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. Wherein:

[0054] Figure 1 This is a flowchart of a disturbance rejection event-triggered model predictive control method based on PID mechanism for input affine nonlinear systems provided by the present invention;

[0055] Figure 2 This is the overall system control architecture diagram. Detailed Implementation

[0056] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0057] Example 1:

[0058] To address the technical problem in existing technologies where event triggering mechanisms rely on static thresholds, cannot perceive dynamic changes in system errors, and lack adaptive compensation capabilities for disturbances, resulting in a difficulty in achieving both control performance and resource utilization efficiency in environments with limited computing resources.

[0059] like Figure 1 As shown, the method of the present invention includes the following steps S1 to S4. Figure 2 The overall system control architecture of the present invention is shown, which includes a communication network, an input affine nonlinear system, a PID type event-triggered sampling module, and a dual-channel control architecture including a robust MPC module and a DOB module.

[0060] Step S1: Establish a mathematical model of the continuous-time input affine nonlinear system and define its state constraints and control input constraints.

[0061] Specifically, consider a class of continuous-time input affine nonlinear systems, whose mathematical model is described as follows:

[0062] ;

[0063] in, The derivative of the system state; Let be the system state vector. The number of state variables; To control the input vector, To control the number of input variables; Let be an externally unknown but bounded perturbation vector. The number of external disturbance variables; The drift term describes the free evolution dynamics of the system under no control input and no external disturbance. The input mapping matrix describes the control input. How it affects the rate of change of system state; Let be the disturbance mapping matrix, describing the external disturbance. How it affects the rate of change of system state;

[0064] The above function , , All of them are smooth nonlinear functions defined on the state space.

[0065] The system state and control inputs must meet the following hard constraints:

[0066] ;

[0067] in, and Let represent the set of state constraints and the set of control constraints containing the origin, respectively, both of which are compact convex sets. Perturbation mapping matrix. It is uniformly bounded within the constraint set.

[0068] Step S2: Design a nonlinear disturbance observer to estimate the external disturbances to the system in real time, and construct a feedforward compensation control law based on the estimated values ​​to suppress the impact of the disturbances.

[0069] Specifically, to reconstruct and estimate matched or partially mismatched disturbances in the system in real time, the following nonlinear disturbance observer is designed. First, intermediate auxiliary variables are constructed. and nonlinear functions Let the observer dynamics be:

[0070] ;

[0071] ;

[0072] in, as an intermediate auxiliary variable The derivative; These are intermediate auxiliary variables used to avoid directly using the derivative of the perturbation in the observer equation; The observer gain matrix is ​​defined as follows: That is, nonlinear functions State Jacobian matrix; For drift term; The input mapping matrix; To control the input vector; The perturbation mapping matrix; For the nonlinear equations that need to be designed; The disturbance estimate is the output of the observer.

[0073] By selecting a suitable nonlinear function and its corresponding gain matrix This makes the dynamic system of the estimation error asymptotically stable. Let For state An irrelevant constant Herwitz matrix provides an upper bound for the perturbation estimate and its estimation error.

[0074] In obtaining disturbance estimates Subsequently, to suppress the impact of disturbances on the system, a feedforward compensation control law is constructed. The total control input of the system is designed as a performance-optimized control law. With compensation control rate sum:

[0075] ;

[0076] If the disturbance is a matched disturbance, the control input can achieve complete compensation. However, when an unmatched disturbance exists, the control input cannot achieve complete compensation. For unmatched disturbances, orthogonal projection is used to decompose the disturbance into a compensable part. and the portion that could not be compensated The system can now be described as follows:

[0077] ;

[0078] ;

[0079] ;

[0080] in, The pseudo-inverse of the input mapping matrix; The orthogonal complement of the input mapping matrix; It is a pseudo-inverse of the orthogonal complement.

[0081] Set the disturbance compensation input as follows:

[0082] ;

[0083] Substituting the above compensation law into the original system, we can obtain the dynamics of the compensated system:

[0084] ;

[0085] in, The expression for the residual disturbance after compensation is as follows:

[0086] ;

[0087] here Let be the disturbance estimation error. The upper bound of the residual disturbance is defined as:

[0088] ;

[0089] in This is the upper bound of the residual perturbation. The representation is defined as follows: Indicates the supremacy. For time range, Let be the norm of the residual perturbation.

[0090] This upper bound will play a crucial role in subsequent robust MPC design and event triggering threshold calculation.

[0091] Step S3: Based on the disturbance feedforward compensation, design a robust model predictive controller (MPC) to solve the optimal control problem in the finite time domain at the event trigger time, so as to handle the remaining error and uncertainty after compensation.

[0092] Specifically, based on disturbance feedforward compensation, a robust MPC controller is designed to address residual uncertainties such as observer estimation error, unmodeled dynamics, and uncompensated disturbances. At each trigger time... Solve the following optimal control problem (OCP):

[0093] ;

[0094] The constraints are satisfied:

[0095] ;

[0096] ;

[0097] ;

[0098] ;

[0099] ;

[0100] ;

[0101] ;

[0102] ;

[0103] ;

[0104] ;

[0105] in, This is the optimal control sequence. To predict time variables in the time domain, This is the current trigger time; For minimization operators; Let cost function be For the stage cost function, For the terminal cost function; This represents the current predicted state. The control trajectory needs to be optimized; To predict the state derivative; To predict the state trajectory; For drift term; The input mapping matrix; For predictive control input; To predict the state of the trajectory at the trigger moment; This represents the actual state of the system at the moment of triggering. For tightening the set of control constraints; It is a time-varying set of state constraints; For prediction in the time domain; For the terminal domain, defined as .

[0106] By solving this optimization problem, the robust MPC optimal control law is obtained. It is used to eliminate residual tracking errors.

[0107] Step S4: Construct a dynamic event trigger function based on the PID mechanism. This function includes the proportional, integral, and derivative terms of the error. By comparing the calculated value of this trigger function with the dynamic threshold, determine whether to trigger the MPC optimization solver to resolve and update the control input. The total control input of the system is the sum of the feedforward compensation control law and the optimal control law output by the MPC optimization solver.

[0108] Specifically, to overcome the limitations of traditional static thresholds, this invention systematically embeds the PID proportional-integral-derivative control concept into the event triggering condition design. The dynamic event triggering function based on the PID mechanism is defined as follows:

[0109] ;

[0110] in, For the trigger function value; The error between the actual state and the predicted state of the system; , , These are the proportional, integral, and differential weighting coefficients, respectively. Based on terminal cost matrix The weighted norm; To predict time variables in the time domain; This is the current trigger time.

[0111] The physical meaning of this trigger function is:

[0112] The proportional term responds to the current error magnitude, ensuring timely triggering when the error is large.

[0113] The integral term stores the accumulated error during periods when the event was not triggered, preventing steady-state drift.

[0114] The rate of change of the differential term is monitored to ensure that sampling can be triggered quickly in the early stages of disturbances.

[0115] The event triggering conditions are defined as follows:

[0116] ;

[0117] That is, when the function value is triggered First time reaching or exceeding the dynamic threshold Record that moment as If the control input is not updated, the optimization solver will be triggered to update the control input; otherwise, the control input at the previous trigger time will remain unchanged.

[0118] To ensure recursion feasibility, a forced triggering mechanism is introduced, specifying the next actual triggering time. Take the minimum value between the PID conditional trigger time and the forced trigger time:

[0119] ;

[0120] in To perform the minimum value operation, For the predictive time domain, this design ensures that even under long-term stable conditions where PID conditions are not triggered, the control will not fail to update beyond a predictive time domain.

[0121] Dynamic threshold Based on the upper bound of residual disturbance Prediction time domain and adaptive PID parameter setting:

[0122] ;

[0123] in, To the upper bound of residual disturbance Related constants, and These are design parameters related to the system's Lipschitz constant and shrinkage rate.

[0124] This threshold design achieves an organic unity between the PID triggering mechanism and the robust MPC theoretical analysis results, enabling the triggering conditions to adapt to the system's anti-disturbance capability, dynamic characteristics, and prediction time domain length.

[0125] Furthermore, the system's overall control input The optimal control law obtained by robust MPC optimization Feedforward compensation control law provided by the disturbance observer Superimposed composition:

[0126] ;

[0127] in, It is only updated at the moment the event is triggered, and remains unchanged during the trigger interval; It is continuously updated based on the real-time estimates from the interference observer.

[0128] As can be seen from the above technical solutions, the present invention has the following beneficial effects:

[0129] 1. Reduce computational burden: Through the PID dynamic event triggering mechanism, MPC optimization is triggered only when necessary, which greatly reduces the frequency of optimization problem solving and saves computational and communication resources;

[0130] 2. Enhanced robustness against disturbances: By estimating and compensating for disturbances in real time through a nonlinear disturbance observer, and combining this with robust MPC to handle residual errors, the system's ability to suppress matched / unmatched disturbances is significantly enhanced.

[0131] 3. Adaptive triggering decision: The PID control concept is introduced into the triggering mechanism, enabling the triggering conditions to sense the magnitude, accumulation and rate of change of the error. The dynamic threshold is adaptively adjusted according to the system characteristics, achieving an optimal balance between "on-demand triggering" and "resource conservation".

[0132] 4. Ensure recursion feasibility: through a forced triggering mechanism. The design incorporates tightened constraints to ensure that the system can still satisfy the original constraints and maintain closed-loop stability under the event-triggered framework.

[0133] 5. Theoretical Completeness: The design of disturbance observers, robust MPC design, and PID event triggering mechanisms are systematically integrated, starting from the upper bound of residual disturbances. To dynamic threshold The design forms a complete theoretical closed loop.

[0134] Example 2:

[0135] This invention provides a computer storage medium storing a computer software product, which includes several instructions to cause a computer device to execute the aforementioned disturbance rejection event-triggered model predictive control method based on PID mechanism for input-oriented affine nonlinear systems.

[0136] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0137] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0138] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The functions specified in one or more boxes. These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable apparatus for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0139] Obviously, the above embodiments are merely illustrative examples for clear explanation and are not intended to limit the implementation. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is neither necessary nor possible to exhaustively list all possible implementations here. However, obvious variations or modifications derived therefrom are still within the scope of protection of this invention.

Claims

1. A disturbance-resistant event-triggered model predictive control method based on PID mechanism for input affine nonlinear systems, characterized in that, Includes the following steps: Step S1: Establish a mathematical model of the continuous-time input affine nonlinear system and define its state constraints and control input constraints; Step S2: Design a nonlinear disturbance observer to estimate the external disturbances to the system in real time, and construct a feedforward compensation control law based on the estimated values ​​to suppress the impact of the disturbances. Step S3: Based on the disturbance feedforward compensation, design a robust MPC to solve the optimal control problem in the finite time domain at the event trigger time, so as to handle the remaining error and uncertainty after compensation; Step S4: Construct a dynamic event trigger function based on the PID mechanism. This function includes the proportional, integral, and derivative terms of the error. By comparing the calculated value of this trigger function with the dynamic threshold, determine whether to trigger the MPC optimization solver to resolve and update the control input. The total control input of the system is the sum of the feedforward compensation control law and the optimal control law output by the MPC optimization solver.

2. The disturbance-resistant event-triggered model predictive control method based on PID mechanism for input affine nonlinear systems according to claim 1, characterized in that, The mathematical model of the input affine nonlinear system in step S1 is: ； in, The derivative of the system state; Let be the system state vector. The number of state variables; To control the input vector, To control the number of input variables; Let be an externally unknown but bounded perturbation vector. The number of external disturbance variables; For drift term; The input mapping matrix; The disturbance mapping matrix is ​​given; the system state and control input satisfy hard constraints: ,in, and Let represent the state constraint set and the control constraint set containing the origin, respectively, both of which are compact convex sets.

3. The disturbance-resistant event-triggered model predictive control method based on PID mechanism for input affine nonlinear systems according to claim 1, characterized in that, The design of the nonlinear disturbance observer in step S2 is specifically as follows: Constructing intermediate auxiliary variables and nonlinear functions Let the observer dynamics be: ； ； in, as an intermediate auxiliary variable The derivative; The observer gain matrix is... ; For drift term; The input mapping matrix; To control the input vector; The perturbation mapping matrix; This is the disturbance estimate; by selecting an appropriate... This makes the dynamic system of estimation error asymptotically stable and obtains an upper bound on the disturbance estimation error.

4. The disturbance-resistant event-triggered model predictive control method based on PID mechanism for input affine nonlinear systems according to claim 3, characterized in that, In step S2, a feedforward compensation control law is constructed. For unmatched disturbances, orthogonal projection is used to decompose the disturbance into compensable parts. With the uncompensated portion : ； ； in, The input mapping matrix; The pseudo-inverse of the input mapping matrix; The perturbation mapping matrix; It is an externally unknown but bounded perturbation vector; The orthogonal complement of the input mapping matrix. The pseudo-inverse of orthogonal complement; setting a compensation control law. and the residual disturbance after compensation The upper bound is denoted as ,in This is the upper bound of the residual perturbation. The representation is defined as follows: Indicates the supremacy. For time range, Let be the norm of the residual perturbation.

5. The disturbance-resistant event-triggered model predictive control method based on PID mechanism for input affine nonlinear systems according to claim 1, characterized in that, In step S3, at each triggering time The robust MPC optimal control problem to be solved is: ； ； ； ； ； ； in, This is the optimal control sequence. To predict time variables in the time domain, This is the current trigger time; For minimization operators; The cost function; This represents the current predicted state. The control trajectory needs to be optimized; To predict the state derivative; To predict the state trajectory; For drift term; The input mapping matrix; For predictive control input; To predict the state of the trajectory at the trigger moment; This represents the actual state of the system at the moment of triggering. For tightening the set of control constraints; It is a time-varying set of state constraints; For prediction in the time domain; For the terminal domain.

6. The disturbance-resistant event-triggered model predictive control method based on PID mechanism for input affine nonlinear systems according to claim 1, characterized in that, The dynamic event triggering function based on the PID mechanism in step S4 is defined as follows: ； in, For the trigger function value; The error between the actual state and the predicted state of the system; , , These are the proportional, integral, and differential weighting coefficients, respectively. Based on terminal cost matrix The weighted norm; To predict time variables in the time domain; This is the current trigger time.

7. The disturbance-resistant event-triggered model predictive control method based on PID mechanism for input affine nonlinear systems according to claim 6, characterized in that, The dynamic event triggering condition in step S4 is: Compare trigger function values With dynamic threshold ,when When the trigger condition is met, the trigger time is recorded. And update the control input; otherwise, keep the control input unchanged from the previous trigger moment, where For dynamic thresholds; Next actual triggering time Pick With forced triggering time The minimum value, i.e. ,in To perform the minimum value operation, For prediction in the time domain.

8. The disturbance-resistant event-triggered model predictive control method based on PID mechanism for input affine nonlinear systems according to claim 7, characterized in that, The dynamic threshold Based on the upper bound of residual disturbance Prediction time domain and adaptive PID parameter setting: ； in, To the upper bound of residual disturbance Related constants, and These are design parameters related to the system's Lipschitz constant and shrinkage rate.

9. The disturbance-resistant event-triggered model predictive control method based on PID mechanism for input affine nonlinear systems according to claim 1, characterized in that, System main control input The optimal control law obtained by robust MPC optimization Feedforward compensation control law provided by the disturbance observer Superimposed composition: ； in, It is only updated at the moment the event is triggered, and remains unchanged during the trigger interval; It is continuously updated based on the real-time estimates from the interference observer.

10. A computer storage medium, characterized in that, The computer storage medium stores a computer software product, which includes several instructions to cause a computer device to execute the disturbance rejection event-triggered model predictive control method based on PID mechanism for input affine nonlinear systems as described in any one of claims 1 to 9.

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