Coordinated control method for flexible coupling dual permanent magnet synchronous motor based on incremental model predictive control

Abstract

The application discloses a flexible coupling double permanent magnet synchronous motor coordinated control method based on an incremental model predictive control, and belongs to the technical field of multi-motor coordinated control. In view of the technical problems that a flexible coupling double PMSM system is prone to different speed synchronization and uneven torque distribution under heavy load, and current / voltage constraints restrict performance and safety, the technical scheme of the application is as follows: a double PMSM cross-coupling mathematical model is established, and an incremental state space prediction model with constant disturbance suppression capability is constructed; in a model predictive control framework, speed and current synchronization errors are introduced into a cost function, current / voltage constraints are explicitly processed, optimal compensation voltage is solved through rolling optimization, and the compensation voltage is superimposed on a current loop output to drive a motor, so that double motor coordinated operation is realized. The method has high-precision speed tracking, torque balance and fast dynamic response, and strictly guarantees that current / voltage is within a safety constraint, and is suitable for flexible coupling multi-motor driving systems such as conveyor belts.

Description

Technical Field

[0001] This invention relates to the field of multi-motor coordinated control technology, and in particular to a coordinated control method for flexible coupled dual permanent magnet synchronous motors based on incremental model predictive control. Background Technology

[0002] In industrial applications with high inertia and heavy loads, such as textile machinery, large mining conveyors, and new energy electric vehicle drive systems, a single motor often struggles to meet the dual demands of high power output and high dynamic response. Therefore, a topology scheme employing multiple PMSMs (Permanent Magnet Synchronous Motors) working in tandem is frequently adopted. Especially in conveyor belt systems, multiple motors are typically mechanically coupled through flexible media such as conveyor belts and chains. The power transmission of these flexible-coupled dual PMSM systems relies on elastic elements. During operation, they are subject to both electrical coupling between motors and the combined effects of mechanical elastic deformation, load disturbances, and the dispersion of motor parameters, resulting in a control complexity far exceeding that of rigidly connected multi-motor systems.

[0003] The core operational pain points of such systems are concentrated in two aspects: First, the risk of synchronization mismatch: If there is a continuous deviation in the speed of the two motors, it will cause periodic fluctuations in the tension of the conveyor belt. At best, it will aggravate belt wear and cause slippage; at worst, it will cause belt breakage and shutdown when the load changes suddenly. Second, uneven torque distribution: Due to the influence of mechanical elastic hysteresis and asymmetrical load distribution, the actual output torque of the two motors is prone to difference. Long-term operation will cause single-machine overload, insulation aging, and significantly shorten the equipment life. In severe cases, it will directly burn out the motor and threaten the safety and stability of the system.

[0004] To address the aforementioned issues, existing dual-motor coordinated control technologies have developed several solutions: for example, integral sliding mode control based on disturbance observers achieves feedforward compensation by observing load disturbances, thereby improving synchronous disturbance rejection capability; adaptive control based on reinforcement learning can optimize dynamic response by fitting the nonlinear characteristics of the system through offline training. However, these methods generally suffer from a common deficiency in constraint handling capability: physical constraints such as current and voltage are usually only passively handled by a post-processed saturation limiting stage and are not incorporated into the core optimization framework of the controller—this means that when the system encounters extreme conditions such as load changes or start-stop shocks, instantaneous overcurrent and overvoltage may still occur, failing to fundamentally avoid safety risks.

[0005] Model predictive control (MDI), as an advanced control method capable of explicitly handling multivariable, multi-objective, and multi-constraint scenarios, has demonstrated its advantages in high-performance single-motor control. Through a rolling optimization mechanism, it can solve for the optimal control quantity that satisfies the constraints in each sampling period, balancing dynamic performance and safety boundaries. However, this method is not yet fully adapted to the unique characteristics of flexible dual-PMSM systems. On the one hand, existing MDI schemes often fail to consider the mechanical coupling characteristics of the two motors and do not simultaneously incorporate speed synchronization error and torque distribution error into the optimization objectives, making it difficult to achieve dual-motor coordination. On the other hand, there is a lack of targeted model design for suppressing oscillations caused by flexible loads and actively compensating for constant load disturbances.

[0006] In summary, there is an urgent need for an improved incremental model predictive control method for flexible coupled dual PMSM systems, which can simultaneously achieve high-precision speed tracking, torque balancing, and load disturbance suppression within a unified optimization framework. Furthermore, it should proactively and explicitly embed current and voltage safety constraints into the control logic, thereby addressing the performance and safety shortcomings of existing technologies. Summary of the Invention

[0007] The purpose of this invention is to overcome the problems in the background technology and provide a coordinated control method for a flexible coupled dual permanent magnet synchronous motor based on incremental model predictive control. This invention addresses the issues of asynchronous speed and uneven torque in a flexible coupled dual permanent magnet synchronous motor for conveyor belts under large inertial loads, where conventional control cannot actively constrain current and voltage. The invention first constructs a continuous state-space model of the system, including belt elasticity and cross-coupling integral terms. After Euler discretization, an incremental model is constructed by introducing the output error integral to suppress constant-value disturbances. A cost function is built that simultaneously includes speed and current synchronization errors, transforming the motor current and voltage limits into linear inequality constraints and incorporating them into rolling optimization. The optimal voltage increment sequence is selected for prediction / control time-domain solution. The first set of increment sequences is used as q-axis voltage compensation and superimposed on the current loop output, achieving high-precision speed tracking and torque balance, avoiding overcurrent and overvoltage throughout the entire process, and improving the synchronous stability and operational safety of the conveyor belt.

[0008] To achieve the above-mentioned objectives, the present invention employs the following technical solution: a coordinated control method for a flexible coupled dual permanent magnet synchronous motor based on incremental model predictive control, comprising the following steps:

[0009] S1. Based on the cross-coupled control structure, establish the state-space model of the flexible coupled dual PMSM system.

[0010] S2. Based on model predictive control theory, the state-space model described in step S1 is discretized using Euler and an incremental model is constructed.

[0011] S3. Select the appropriate control time domain and prediction time domain Establish an incremental prediction model for the system output.

[0012] S4. Design the cost function, whose output includes the system output reflecting the speed synchronization error and current synchronization error of the two motors.

[0013] S5. Transform the current and voltage constraints of the motor into linear inequality constraints on the control input and its increment.

[0014] S6. In each sampling period, based on the current state of the system, solve the optimization problem online with the cost function as the objective and the linear inequality as the constraint to obtain the optimal control increment sequence. Then, apply the first control increment sequence in the optimal control increment sequence to the system as the control increment sequence for the two motors. Coordination compensation amount of shaft control voltage.

[0015] Furthermore, in step S1, the state-space model of the constructed flexible coupled dual PMSM system is as follows:

[0016] ,

[0017] in, It is a state variable. , They are PMSM1 and PMSM2 respectively. shaft current, , These are the mechanical angular velocities of PMSM1 and PMSM2, respectively. , , , This is the cross-coupling feedback adjustment coefficient. , , For integration time variable, Represents the time variable Integral differential element, , The PI parameters for speed regulator 1 (ASR1) in PMSM1, , The PI parameters for speed regulator 2 (ASR2) in PMSM2, The system is given the tracking angular velocities of the two motors. , ; It is a control input. It is an external signal. , It is the load driven by the two PMSMs themselves; , , , , , , , , , , These are the stator resistors of PMSM1 and PMSM2, respectively. , They are PMSM1 and PMSM2 respectively. Shaft inductor, , These are the PI parameters of ACQR1 in PMSM1. , These are the PI parameters of ACQR2 in PMSM2. , These are the pole logarithms of PMSM1 and PMSM2, respectively. , These are the permanent magnet flux linkages of PMSM1 and PMSM2, respectively. , These are the moments of inertia of PMSM1 and PMSM2, respectively. It is the radius of the roller. It is the tension coefficient of the belt. , These are the damping coefficients of PMSM1 and PMSM2, respectively.

[0018] ,

[0019] ,

[0020] , , It is the weighting coefficient.

[0021] Furthermore, the specific content of step S2 is as follows:

[0022] The state-space model in step S1 is discretized using the forward Euler method. The discrete-time state-space model is as follows:

[0023] ,

[0024] in, , , , , This refers to the sampling time; all state variables of a dual PMSM system are measurable or estimable. Assuming a very short sampling period, the given speed and load of the motor remain constant between two adjacent sampling times, i.e. To suppress constant or slowly time-varying disturbances, the integral of the output error is introduced as an additional state into the prediction model, resulting in the incremental model:

[0025] ,

[0026] in, , , , , , .

[0027] Furthermore, the specific content of step S3 is as follows:

[0028] Select an appropriate control time domain and prediction time domain And satisfy The output prediction model of the system is established as follows:

[0029] ,

[0030] in,

[0031] ,

[0032] ,

[0033] ,

[0034] .

[0035] Furthermore, in step S4, the specific content of the design cost function is as follows:

[0036] The controller's control objective is to achieve zero synchronization error in the speed and current of the two motors. To reduce system vibration, maintain system smoothness, and minimize changes in control input, the cost function is designed as follows:

[0037] ,

[0038] in, It is a diagonal matrix. , It controls the dimension of the input. It is a control weighting factor. The larger the value, the smaller the expected change in the control input.

[0039] Furthermore, the specific details of step S5 are as follows:

[0040] PMSM1 shaft current and shaft voltage Since an equation exists, the problem of constraining the current can be transformed into a problem of constraining the voltage:

[0041] It is a continuous-time function discrete-time function, yes The discrete-time function is used to ensure that the motor does not overcurrent. The shaft current must not exceed the current limit, i.e. , ,in, It is the first Control input voltage at each sampling time To control the lower limit of the allowable range of input voltage, To control the upper limit of the allowable range of input voltage, It controls the lower limit of the input voltage increment constraint. It controls the upper limit of the input voltage increment constraint. , , and The value needs to be determined based on hardware performance and engineering application requirements. ,

[0042] ,

[0043] ,

[0044] ,

[0045] Select The constraints for the two motors are: ,in, It controls the increment sequence. It is the first The control input voltage increment sequence of the dual PMSM at each sampling time. It is the first The control input voltage increment of PMSM1 at each sampling time No. The control input voltage increment of PMSM2 at each sampling time; It is the first The control input voltage increment sequence of the dual PMSM at each sampling time. It is the first The control input voltage increment of PMSM1 at each sampling time No. The control input voltage increment of PMSM2 at each sampling time; It is the first The control input voltage increment sequence of the dual PMSM at each sampling time. It is the first The control input voltage increment of PMSM1 at each sampling time No. The control input voltage increment of PMSM2 at each sampling time;

[0046] , ,in, It is the first The control input voltage of PMSM1 at each sampling time No. The control input voltage of PMSM2 at each sampling time.

[0047] In step S6, the specific details of the coordinated compensation amount of the q-axis control voltage of the two motors are as follows:

[0048] The cost function is obtained by combining the output prediction model from step S3 with the cost function from step S4. :

[0049] ,

[0050] in, Let the cost function be the model predictive control optimization problem. , The goal is to find the optimal control input that makes the cost function... Minimum, that is:

[0051]

[0052] in, This indicates finding the minimum value of the substitution function. The optimal control increment sequence for the control input is given by the following constraints: , It is the optimal control increment sequence that satisfies the constraints and minimizes the cost function. For PMSM1 in the The optimal voltage increment at each sampling time. For PMSM2 in the The optimal voltage increment at each sampling time. For PMSM1 in the The optimal voltage increment at each sampling time. For PMSM2 in the The optimal voltage increment at each sampling time; based on the design concept of model predictive control, the first optimal control increment... That is, the coordinated compensation amount of the q-axis control voltage of the two motors is applied to the system. At the next moment, the system will update the variables and then repeatedly solve the optimal coordinated compensation amount of the q-axis control voltage online.

[0053] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0054] 1. Achieve integrated coordinated control of speed and torque synchronization: By incorporating speed synchronization error and current (torque) synchronization error into the cost function, the two core objectives of speed tracking and torque balance are handled simultaneously within an optimization framework, thereby improving the overall coordination performance of the system.

[0055] 2. Improving system safety by directly embedding current and voltage constraints into the optimization process: This invention establishes a mapping relationship between current and control voltage, converting physical constraints such as current and voltage into control input constraints, and uniformly incorporating them into the rolling optimization process of model predictive control. This proactively ensures that the system does not violate safety boundaries in any dynamic process, fundamentally avoiding the risks of overcurrent and overvoltage, and improving the operational safety and reliability of the system.

[0056] 3. Effective suppression of constant (slow time-varying) load disturbances: This invention establishes an incremental state-space model that includes the integral term of the output error, and introduces state increment and control increment into the prediction model to achieve active suppression of constant (slow time-varying) loads.

[0057] 4. Based on the flexible coupling characteristics of conveyor belts, this invention establishes a cross-coupling prediction model for dual motors and uses model predictive control to solve for the optimal voltage compensation of the dual motors in real time, achieving coordinated control and torque balance between the two motors. Under sudden load changes, it can quickly restore synchronization, reduce conveyor belt tension fluctuations, and effectively suppress faults such as slippage, belt deviation, and belt breakage, thereby improving the dynamic performance, operational stability, and safety reliability of the flexible conveyor system. Attached Figure Description

[0058] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used together with the embodiments of the invention to explain the invention and do not constitute a limitation thereof.

[0059] Figure 1 This is a framework diagram for implementing the method of the present invention.

[0060] Figure 2 This is a dynamic response diagram of the speed synchronization of two motors in a flexible dual PMSM system under physical constraints, provided by an embodiment of the present invention, under a cross-coupled control structure and model predictive control method.

[0061] Figure 3 This invention provides a flexible dual PMSM system with physical constraints, based on a cross-coupled control structure and model predictive control method. Dynamic response diagram of shaft current synchronization.

[0062] Figure 4 This invention provides a flexible dual PMSM system with a cross-coupled control structure and model predictive control method under conditions without physical constraints. Dynamic response diagram of shaft current synchronization.

[0063] Figure 5 This is a dynamic response diagram of a flexible dual PMSM system under physical constraints, provided by an embodiment of the present invention, which uses a cross-coupled control structure and a model predictive control method to control the input voltage.

[0064] Figure 6 This is a dynamic response diagram of a flexible dual PMSM system under cross-coupled control structure and model predictive control method provided in an embodiment of the present invention, showing the control input voltage under no physical constraints. Detailed Implementation

[0065] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. Of course, the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0066] like Figure 1 As shown, this embodiment provides a coordinated control method for a flexible coupled dual permanent magnet synchronous motor based on incremental model predictive control, including the following steps:

[0067] Step 1: Based on the coupling characteristics of the flexible coupled dual PMSM system, model the flexible coupled dual PMSM system as a state-space model:

[0068] ,

[0069] in, It is a state variable. , They are PMSM1 and PMSM2 respectively. shaft current, , These are the mechanical angular velocities of PMSM1 and PMSM2, respectively. , , , This is the cross-coupling feedback adjustment coefficient. , , For integration time variable, Represents the time variable Integral differential element, , The PI parameters for speed regulator 1 (ASR1) in PMSM1, , The PI parameters for speed regulator 2 (ASR2) in PMSM2, The system is given the tracking angular velocities of the two motors. , ; It is a control input. It is an external signal. , It is the load driven by the two PMSMs themselves; , , , , , , , , , , These are the stator resistors of PMSM1 and PMSM2. , It is PMSM1, PMSM2 Shaft inductor, , These are the PI parameters of ACQR1 in PMSM1. , These are the PI parameters of ACQR2 in PMSM2. , These are the pole logarithms of PMSM1 and PMSM2. , It is the permanent magnet flux linkage of PMSM1 and PMSM2. , These are the moments of inertia of PMSM1 and PMSM2. It is the radius of the roller. It is the tension coefficient of the belt. , These are the damping coefficients of PMSM1 and PMSM2; , , , , It is the weighting coefficient.

[0070] Step 2: Discretize the continuous-time state-space model constructed in Step 1 using model predictive control theory, and construct an incremental model. The specific process is as follows:

[0071] The state-space model in step S1 is discretized using the forward Euler method. The discrete-time state-space model is as follows:

[0072] ,

[0073] in, , , , , This refers to the sampling time. All state variables of a dual PMSM system are measurable or estimable. Assuming a very short sampling period, the given speed and load of the motor remain constant between two adjacent sampling times, i.e. To suppress constant or slowly time-varying disturbances, the integral of the output error is introduced as an additional state into the prediction model, resulting in the incremental model:

[0074] ,

[0075] in, , , , , , .

[0076] Step 3: Using model predictive control theory, construct the incremental model from Step 2 into an incremental predictive model. The specific steps are as follows:

[0077] Select an appropriate control time domain and prediction time domain And satisfy The output prediction model of the system is established as follows:

[0078]

[0079] in,

[0080] , , , .

[0081] Step 4: Design the cost function. The specific design steps are as follows:

[0082] The controller's control objective is to achieve zero synchronization error in the speed and current of the two motors. To reduce system vibration, maintain system smoothness, and minimize changes in control input, the cost function is designed as follows:

[0083] ,

[0084] in, It is a diagonal matrix. , It controls the dimension of the input. It is a control weighting factor. The larger the value, the smaller the expected change in the control input.

[0085] Step 5: Based on the physical constraints, construct linear inequality constraints. Specific steps include:

[0086] PMSM1 shaft current and shaft voltage Since an equation exists, the problem of constraining the current can be transformed into a problem of constraining the voltage:

[0087] It is a continuous-time function discrete-time function, yes The discrete-time function. To ensure the motor does not overcurrent, The shaft current must not exceed the current limit, i.e. , ,in, It is the first Control input voltage at each sampling time To control the lower limit of the allowable range of input voltage, To control the upper limit of the allowable range of input voltage, It controls the lower limit of the input voltage increment constraint. It controls the upper limit of the input voltage increment constraint. , , and The value needs to be determined based on hardware performance and engineering application requirements. , , , Select The constraints for the two motors are:

[0088] ,in, It controls the increment sequence. It is the first The control input voltage increment sequence of the dual PMSM at each sampling time. It is the first The control input voltage increment of PMSM1 at each sampling time No. The control input voltage increment of PMSM2 at each sampling time; It is the first The control input voltage increment sequence of the dual PMSM at each sampling time. It is the first The control input voltage increment of PMSM1 at each sampling time No. The control input voltage increment of PMSM2 at each sampling time; It is the first The control input voltage increment sequence of the dual PMSM at each sampling time. It is the first The control input voltage increment of PMSM1 at each sampling time No. The control input voltage increment of PMSM2 at each sampling time; , ,in, It is the first The control input voltage of PMSM1 at each sampling time No. The control input voltage of PMSM2 at each sampling time.

[0089] Step 6: Solve The optimal control voltage coordination compensation for the shaft includes the following steps:

[0090] The cost function is obtained by combining the output prediction model from step 3 with the cost function from step 4. :

[0091] ,

[0092] in, Let the cost function be the model predictive control optimization problem. , The goal is to find the optimal control input that makes the cost function... Minimum, that is:

[0093] ,

[0094] in, This indicates finding the minimum value of the substitution function. This indicates that the following constraints are satisfied. The optimal control increment sequence for the control input is... , It is the optimal control increment sequence that satisfies the constraints and minimizes the cost function. For PMSM1 in the The optimal voltage increment at each sampling time. For PMSM2 in the The optimal voltage increment at each sampling time. For PMSM1 in the The optimal voltage increment at each sampling time. For PMSM2 in the The optimal voltage increment at each sampling time, based on the design principle of model predictive control, yields the first optimal control increment sequence. That is, the coordinated compensation amount of the q-axis control voltage of the two motors is applied to the system. At the next moment, the system will update the variables and then repeatedly solve the optimal coordinated compensation amount of the q-axis control voltage online.

[0095] In this embodiment, to evaluate the performance advantages of the control method proposed in this invention, two sets of comparative simulations were set up: the constrained model predictive control method proposed in this invention was compared with the linear quadratic optimal control method alone, and the results are as follows. Figures 2-6 As shown.

[0096] Figure 2 The speed response diagrams of the two motors under model predictive control were plotted. The results show that the system starts smoothly with no significant overshoot. Both motors quickly reach steady state within approximately 0.8 seconds and accurately track the given speed, demonstrating good speed tracking capability. When a sudden load is applied to motor 1, the speeds of both motors decrease synchronously and instantaneously due to the increased load. A brief speed deviation occurs between the two motors due to load asymmetry. However, under the coordinated action of the controller, this speed deviation is rapidly eliminated within approximately 25 milliseconds, the system resynchronizes speed, and achieves speed tracking within approximately 0.7 seconds. When a sudden load is applied to motor 2, a similar rapid recovery process is observed. This strongly demonstrates that the control strategy proposed in this paper has significant speed synchronization and rapid dynamic adjustment capabilities.

[0097] Figure 3 and Figure 4 The flexible connection dual PMSM system under the two methods is plotted separately. The dynamic response diagram of shaft current synchronization shows that the two motors exhibit stable performance under steady-state conditions and before load abrupt changes. The shaft currents are basically the same, indicating that the system has achieved precise torque balance. When Motor 1 suddenly increased by 0.4 When the load is high, its The q-axis current immediately increases to generate more torque to overcome the load, resulting in a difference in current between the two motors. After approximately 20 milliseconds, the q-axis currents of the two motors adjust to be approximately equal. A sudden increase of 0.1 is applied to motor 2. When the load is large, its current regulation and synchronization process is more efficient than that of a normal load. Faster response and less fluctuation. This demonstrates that the controller can adaptively adjust the control force according to the magnitude of the disturbance. (Comparison) Figure 3 and Figure 4 It can be clearly seen that the model predictive control optimization problem designed successfully limits the operating current to a safe limit by explicitly introducing current constraints, thus avoiding potential overcurrent risks.

[0098] Figure 5 and Figure 6Dynamic response diagrams of the control input voltage of the flexible-connected dual PMSM system were plotted under two different methods. The results show that the compensation voltage obtained by using only the linear quadratic optimal control method produces a severe spike during load abrupt changes, which is dangerous and impractical in real-world systems, easily leading to motor overcurrent and magnetic saturation. However, by using the constrained incremental model predictive control method of this invention, the compensation voltage at all times is strictly limited within the constraints. This intuitively and conclusively demonstrates that the control strategy presented in this paper can strictly limit the system operation within a safe region, ensuring system safety.

[0099] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A coordinated control method for a flexible coupled dual permanent magnet synchronous motor based on incremental model predictive control, characterized in that, Includes the following steps: S1. Based on the cross-coupled control structure, establish the state-space model of the flexible coupled dual PMSM system; S2. Based on model predictive control theory, the state-space model described in step S1 is discretized using Euler and an incremental model is constructed. S3. Select the appropriate control time domain and prediction time domain Establish an incremental prediction model for the system output; S4. Design the cost function, whose output includes the system output reflecting the speed synchronization error and current synchronization error of the two motors; S5. Transform the current and voltage constraints of the motor into linear inequality constraints on the control input and its increment. S6. In each sampling period, based on the current state of the system, solve the optimization problem online with the cost function as the objective and the linear inequality as the constraint to obtain the optimal control increment sequence. Then, apply the first control increment sequence in the optimal control increment sequence to the system as the control increment sequence for the two motors. Coordination compensation amount of shaft control voltage.

2. The coordinated control method for flexible coupled dual permanent magnet synchronous motors based on incremental model predictive control as described in claim 1, characterized in that, In step S1, the state-space model of the constructed flexible coupled dual PMSM system is as follows: ， in, It is a state variable. , They are PMSM1 and PMSM2 respectively. shaft current, , These are the mechanical angular velocities of PMSM1 and PMSM2, respectively. , , , This is the cross-coupling feedback adjustment coefficient. , , For integration time variable, Represents the time variable Integral differential element, , The PI parameters for speed regulator 1 in PMSM1, , The PI parameters for speed regulator 2 in PMSM2, The system is given the tracking angular velocities of the two motors. , ; It is a control input. It is an external signal. , It is the load driven by the two PMSMs themselves; , , , , , , , , , , These are the stator resistors of PMSM1 and PMSM2, respectively. , They are PMSM1 and PMSM2 respectively. Shaft inductor, , These are the PI parameters of ACQR1 in PMSM1. , These are the PI parameters of ACQR2 in PMSM2. , These are the pole logarithms of PMSM1 and PMSM2, respectively. , These are the permanent magnet flux linkages of PMSM1 and PMSM2, respectively. , These are the moments of inertia of PMSM1 and PMSM2, respectively. It is the radius of the roller. It is the tension coefficient of the belt. , These are the damping coefficients of PMSM1 and PMSM2, respectively. ， ， , , It is the weighting coefficient.

3. The coordinated control method for flexible coupled dual permanent magnet synchronous motors based on incremental model predictive control according to claim 2, characterized in that, The specific content of step S2 is as follows: The state-space model in step S1 is discretized using the forward Euler method. The discrete-time state-space model is as follows: ， in, , , , , This refers to the sampling time; assuming the sampling period is very short, the given speed and load of the motor remain constant between two adjacent sampling moments, i.e. To suppress constant or slowly time-varying disturbances, the integral of the output error is introduced as an additional state into the prediction model, resulting in the incremental model: ， in, , , , , , .

4. The coordinated control method for flexible coupled dual permanent magnet synchronous motors based on incremental model predictive control according to claim 3, characterized in that, The specific content of step S3 is as follows: Select an appropriate control time domain and prediction time domain And satisfy The output prediction model of the system is established as follows: ， in, ， ， ， 。 5. The coordinated control method for flexible coupled dual permanent magnet synchronous motors based on incremental model predictive control according to claim 4, characterized in that, In step S4, the specific content of the design cost function is as follows: The controller's control objective is to achieve zero synchronization error in the speed and current of the two motors. The cost function is designed as follows: ， in, It is a diagonal matrix. , It controls the dimension of the input. It is a control weighting factor. The larger the value, the smaller the expected change in the control input.

6. The coordinated control method for flexible coupled dual permanent magnet synchronous motors based on incremental model predictive control according to claim 5, characterized in that, The specific details of step S5 are as follows: PMSM1 shaft current and shaft voltage Since an equation exists, the problem of constraining the current can be transformed into a problem of constraining the voltage: It is a continuous-time function Discrete-time function, yes Discrete-time function, The shaft current must not exceed the current limit, i.e. , ,in, It is the first Control input voltage at each sampling time To control the lower limit of the allowable range of input voltage, To control the upper limit of the allowable range of input voltage, It controls the lower limit of the input voltage increment constraint. It controls the upper limit of the input voltage increment constraint. , , , ， ， ， Select The constraints for the two motors are: ,in, It controls the increment sequence. It is the first The control input voltage increment sequence of the dual PMSM at each sampling time. It is the first The control input voltage increment of PMSM1 at each sampling time No. The control input voltage increment of PMSM2 at each sampling time; It is the first The control input voltage increment sequence of the dual PMSM at each sampling time. It is the first The control input voltage increment of PMSM1 at each sampling time No. The control input voltage increment of PMSM2 at each sampling time; It is the first The control input voltage increment sequence of the dual PMSM at each sampling time. It is the first The control input voltage increment of PMSM1 at each sampling time No. The control input voltage increment of PMSM2 at each sampling time; , ,in, It is the first The control input voltage of PMSM1 at each sampling time. No. The control input voltage of PMSM2 at each sampling time.

7. The coordinated control method for flexible coupled dual permanent magnet synchronous motors based on incremental model predictive control according to claim 6, characterized in that, In step S6, the specific details of the coordinated compensation amount of the q-axis control voltage of the two motors are as follows: The cost function is obtained by combining the output prediction model from step S3 with the cost function from step S4. : ， in, Let the cost function be the model predictive control optimization problem. , The goal is to find the optimal control input that makes the cost function... Minimum, that is: in, This indicates finding the minimum value of the substitution function. The optimal control increment sequence for the control input is given by the following constraints: , It is the optimal control increment sequence that satisfies the constraints and minimizes the cost function. For PMSM1 in the The optimal voltage increment at each sampling time. For PMSM2 in the The optimal voltage increment at each sampling time. For PMSM1 in the The optimal voltage increment at each sampling time. For PMSM2 in the The optimal voltage increment at each sampling time; the first optimal control increment sequence That is, the coordinated compensation amount of the q-axis control voltage of the two motors is applied to the system. At the next moment, the system will update the variables and then repeatedly solve the optimal coordinated compensation amount of the q-axis control voltage online.

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