Double-motor system model predictive speed control device and method based on cogging dead-zone model

Abstract

The application provides a double-motor predictive speed control device and method based on a cogging dead zone model, and relates to a heliostat multi-servo driving system. For the speed control of the double-motor system, an improved dead zone model (cogging dead zone model) is used to model the cogging, a dynamic model of the double-motor system is established based on the model, a model predictive speed controller and a control system based on the dead zone model are designed according to the dynamic model, the feedback correction link is used to correct the prediction result, the influence of the transmission cogging in the heliostat multi-servo system can be reduced, and the fast, stable and non-overshoot speed regulation effect is realized.

Description

Technical Field

[0001] This invention relates to the field of heliostat multi-servo drive system technology, and in particular to a model predictive speed control device and method for a dual-motor system based on a backlash dead zone model. Background Technology

[0002] With the development of social productivity and the continuous improvement of people's living standards, our demand for energy is constantly increasing. Currently, most energy is derived from fossil fuels, but the excessive use of fossil fuels has caused increasingly serious environmental pollution, climate change, and increased natural disasters. Humanity is also gradually realizing the energy crisis brought about by the gradual depletion of non-renewable fossil fuels. Therefore, the development and utilization of renewable energy is one of the key priorities for global development.

[0003] Among numerous renewable energy sources, solar energy has become one of the ideal energy sources for future society due to its advantages such as large reserves, wide distribution without geographical limitations, safe and harmless use, and long-term development and use. It occupies an important position in future energy strategies.

[0004] As a crucial component of tower solar thermal power plants, heliostats concentrate and reflect sunlight onto the receiver at the top of the collector tower by adjusting its pitch and azimuth angles. This heats molten salt in the pipes, which then exchanges heat with the working fluid in the turbine to produce high-temperature steam, driving the turbine to generate electricity. Therefore, accurately tracking the angle of sunlight is the primary task of the heliostat. Its motion accuracy directly affects solar energy collection, thus impacting the power plant's solar energy utilization rate and ultimately its power generation efficiency. This places high demands on the motion control precision of the heliostat.

[0005] Compared to single-servo drives, multi-servo drive systems can be driven by multiple low-power motors to improve control accuracy, and can lock the load by applying bias torque to achieve precise position control. In addition, heliostats generally have large weight and inertia, and are also greatly affected by wind, exhibiting characteristics of large inertia and large disturbances. Using a multi-servo drive system can output high torque, improving the overall driving capability and overload capacity of the system.

[0006] However, since multi-servo drive systems often employ gear transmission, backlash occurs. Backlash refers to the nonlinear phenomenon caused by positional errors due to clearance in the gear transmission mechanism, primarily occurring during the commutation of the drive motor. Due to backlash, a backlash phenomenon occurs when the system's driving torque changes direction, meaning the driving torque cannot be transmitted to the driven part, causing temporary uncontrollability of the driven part. This backlash leads to a deviation between the input and output ends, increasing the system's output error and significantly negatively impacting the control accuracy of the multi-servo drive system, thus hindering precise control of the heliostat angle.

[0007] Therefore, in order to minimize the impact of transmission backlash in the heliostat multi-servo drive system and achieve precise control of the heliostat angle, the dual-motor system can be adjusted or controlled in terms of both speed and position.

[0008] Based on this, the present invention proposes a model prediction speed control device and method for a dual-motor system based on a backlash dead zone model, which reduces or even eliminates the influence of transmission backlash in the multi-servo drive system of a heliostat from the perspective of speed regulation, so as to achieve precise control of the angle of the heliostat. Summary of the Invention

[0009] The purpose of this invention is to provide a model prediction speed control device and method for a dual-motor system based on a backlash dead zone model, which reduces the influence of transmission backlash in the multi-servo drive system of a heliostat from the perspective of speed regulation, so as to achieve precise control of the heliostat angle.

[0010] To achieve the above objectives, the present invention provides the following technical solution:

[0011] The present invention provides a model predictive speed control device for a dual-motor system based on a backlash dead zone model, which is based on a dual-motor system with a backlash element; the device is a model predictive speed control for a dual-motor system based on a backlash dead zone model, including a dynamic model of the dual-motor system based on a backlash dead zone model and a model predictive speed controller.

[0012] The dual-motor system dynamics model based on the backlash dead zone model is based on drive motor one and drive motor two driving the load. Drive motor one and drive motor two transmit torque to the load through drive gear one, drive gear two, and load gear, respectively. There is backlash between drive gear one and drive gear two and load gear, which is used to establish a backlash dead zone model. The backlash dead zone model is used to describe the torque transmission between the two gears when the system passes through the backlash. When the gears are meshed, a spring-damped model is used to describe the torque transmission; when they are not meshed, a first-order spring model is used to describe the torque transmission.

[0013] The model predictive speed controller includes load position estimation, state prediction model, rolling optimization, and feedback correction. The reference speed is input to the model predictive speed control device, and the torque of the two drive motors is obtained through rolling optimization. The position of the load is estimated, and the estimated load speed is obtained through differentiation. The estimated load speed is compared with the output of the prediction model for feedback correction, and finally the output load speed is obtained.

[0014] The present invention provides a preferred embodiment in the first aspect, wherein the load position estimation is performed by using a hysteresis model to estimate the load position, two estimated load positions are obtained based on the outputs of two drive motors, the average of the two estimated values ​​is taken as the estimated load position, and the system estimated state including position and velocity is obtained based on the differential relationship between position and velocity.

[0015] In a first aspect, the present invention provides a preferred embodiment in which the state prediction model employs a control flow with one-time lag compensation: at time k, the optimal input calculated in the previous time step is input. And read the current system state x. k Then, the state prediction model and the current state x are used. k Predict the system state at the next moment. Then use the predicted Calculate the optimal input at time k+1 And it acts on the dual-motor system at time k+1.

[0016] In a second aspect, the present invention provides a model predictive speed control method for a dual-motor system based on a backlash dead zone model, comprising the following steps:

[0017] (1) Under the current control cycle, given the reference speed input, obtain the rotor positions of the two drive motors;

[0018] (2) Obtain the estimated load position based on the rotor positions of the two drive motors;

[0019] (3) The estimated load position is obtained by differentiation to obtain the estimated load speed;

[0020] (4) Based on the current input torque and load, estimate the speed and obtain the predicted output speed through the prediction model;

[0021] (5) Compare the predicted output speed with the estimated load speed to calculate the prediction error;

[0022] (6) Compensate the error feedback to the reference speed input for the next control cycle;

[0023] (7) The predicted output is used as the current state of the system to solve the optimization problem, and the optimal input torque of the dual motor system in the next control cycle is obtained to achieve one-step lag compensation;

[0024] (8) Obtain the optimal input torque of the two drive motors and apply it to the next control cycle.

[0025] In a second aspect, the present invention provides a preferred solution in which, in step (7), the optimal input torque of the dual-motor system is obtained by solving an optimization problem with torque constraints that optimizes tracking performance and minimizes torque jitter. A cost function composed of the L2 norm of the output error and the L2 norm of the input increment is selected. The tracking performance is optimized and the torque jitter is minimized by adjusting the weight matrix of the tracking error and the weight matrix of the input increment. Furthermore, before step (1), a step is included: the weight matrix of the tracking error and the weight matrix of the input increment are initialized before the start of the first control cycle and remain unchanged in each control cycle.

[0026] Compared with existing technologies, the above technical solution has the following beneficial technical effects:

[0027] (1) For the speed control of dual-motor system, the present invention proposes an improved dead zone model (backlash dead zone model) to model the backlash, and establishes a dynamic model of dual-motor system based on the model. Based on the dynamic model, a model prediction speed controller and control system based on the dead zone model are designed. The prediction results are corrected by the feedback correction link, which can reduce the influence of transmission backlash in the heliostat multi-servo system and achieve a fast, stable and overshoot-free speed regulation effect.

[0028] (2) This invention uses model predictive control for controller design. Compared with traditional PID control schemes, it can balance fastness and overshoot control performance, achieving both fast speed and no overshoot; and it has good dynamic response characteristics, balancing steady-state response and dynamic response performance. Since the application scenario of this controller is gear transmission, in order to reduce gear wear, it is desirable that the tracking response does not change abruptly, while also wanting a fast response. Therefore, it is expected that the tracking curve will show a trend of slow start-up and termination, and fast speed in the middle (e.g. Figure 9 (See illustration). PID is an error-based control scheme that, while pursuing steady-state response, cannot simultaneously meet the aforementioned dynamic response requirements; while model predictive control can achieve this goal through the constraint element in the solution of constrained optimization problems, thus model predictive control is more suitable for gear transmission applications.

[0029] (3) This invention designs a controller with a backlash elimination strategy, which is insensitive to the backlash size and increases the robustness of the control system compared with traditional controllers. Traditional control strategies are based on backlash width compensation control, so the backlash width needs to be obtained. However, inaccurate backlash width will have a significant impact on the performance of the controller. The backlash width can be obtained based on sensors, but inconvenient sensor installation and maintenance, unsuitable sensor size, etc., can lead to incoordination or even damage to the mechanical structure. The method of obtaining the backlash width based on the observer has many problems such as poor observer tracking effect. Therefore, the compensation strategy based on gear backlash width is not easy to implement in practical applications. This invention solves this problem well by using a controller with a backlash elimination strategy. Attached Figure Description

[0030] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0031] Figure 1 This is a schematic diagram of the structure of a dual-motor system in a dual-motor system model prediction speed control device based on a backlash dead zone model, provided in a specific embodiment of the present invention.

[0032] Figure 2 A block diagram of a dual-motor system in a dual-motor system model prediction speed control device based on a backlash dead zone model, provided as a specific embodiment of the present invention;

[0033] Figure 3 A schematic diagram of backlash in a dual-motor system model prediction speed control device based on a backlash dead zone model, provided as a specific embodiment of the present invention;

[0034] Figure 4 A system block diagram of a dual-motor system model predictive speed control device based on a backlash dead zone model, provided as a specific embodiment of the present invention;

[0035] Figure 5 This is an illustration of the time domain and control time domain of the speed control prediction for a dual-motor system based on a backlash dead zone model, provided in a specific embodiment of the present invention.

[0036] Figure 6 The control flowchart of a dual-motor system model prediction speed control device based on a backlash dead zone model provided in a specific embodiment of the present invention does not consider one-step lag compensation.

[0037] Figure 7 The control flowchart of a dual-motor system model prediction speed control device with one-step lag compensation based on a backlash dead zone model provided in a specific embodiment of the present invention is shown.

[0038] Figure 8 The flowchart of the model predictive speed control of a dual-motor system based on a backlash dead zone model is provided in a specific embodiment of the present invention.

[0039] Figure 9The image shows a comparison of the expected tracking curves of a model predictive controller designed using model predictive control and a traditional PID control scheme in a model predictive controller for eliminating transmission backlash in a multi-servo drive system for a heliostat, as provided in a specific embodiment of the present invention.

[0040] Figure 10 This is a schematic diagram of a spring damping model in a multi-servo drive system for heliostats, provided as a specific embodiment of the present invention.

[0041] The attached figures are labeled as follows:

[0042] Drive gear 11, drive gear 212, load gear 13;

[0043] Drive motor 1 21, drive motor 2 22, load motor 23. Detailed Implementation

[0044] 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, and 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.

[0045] Please refer to Figure 1 This embodiment is a model prediction speed control device for a dual-motor system based on a backlash dead zone model. The dual-motor system includes three gears: a drive gear one, a load gear, and a drive gear two that mesh sequentially. Drive motor one and drive motor two are used to rotate drive gear one and drive gear two, respectively.

[0046] The dual-motor system model prediction speed control device based on the backlash dead zone model in this embodiment is a dual-motor system model prediction speed control based on the backlash dead zone model, including a dual-motor system dynamic model based on the backlash dead zone model and a model prediction speed controller.

[0047] (I) Dynamic model of a dual-motor system based on the backlash dead zone model (improved dead zone model)

[0048] Please refer to Figure 1 The dual-motor system model established in this embodiment is driven by two drive motors (drive motor one and drive motor two) to drive the load. The torque is transmitted between the drive motor and the load through gears (drive gear one, drive gear two, and load gear), and the backlash nonlinearity between the gears is taken into account.

[0049] Please refer to Figure 2 T in the figure m1 Tm2 and T L J represents the electromagnetic torque (output torque) and load torque of the two motors, respectively. m1 J m2 and J L b represents the moment of inertia of drive motor one, drive motor two, and the load. m1 b m2 and b L θ represents the damping coefficient of drive motor one, drive motor two, and the load. m1 θ m2 and θ L The positions of the rotors of drive motor one, drive motor two, and the load are indicated; τ1 and τ2 represent the transmitted torque between drive gear one, drive gear two, and the load gear; α1 and α2 represent the backlash widths (backlash one and backlash two) between drive gear one, drive gear two, and the load gear; k1 and k2 represent the stiffness coefficients of drive gear one and drive gear two, respectively; and c1 and c2 represent the damping coefficients of drive gear one and drive gear two, respectively.

[0050] Please refer to Figure 3 Backlash refers to the gap between two meshing gears. This phenomenon mainly occurs during the commutation of the drive motor. During the commutation process, the tooth surfaces may not contact each other. At this time, the load gear can rotate freely in the gap, causing the load speed and position to be temporarily uncontrollable.

[0051] based on Figure 3 In this embodiment, the driving gear and the load gear are assumed to maintain the meshing state of the gears without changing during the prediction of the system's future dynamics. This means the gears will remain in their current meshed or disengaged state for a short period. Under this assumption, this embodiment proposes an improved dead zone model (i.e., a backlash dead zone model) to model the backlash and describe the torque transmission between the driving gear and the load gear when the system passes through the backlash. When the gears are meshing, a spring-damped model is used to describe the torque transmission, ensuring that the torque does not jump before and after meshing; when disengaged, the gear dynamics are considered as a first-order spring model, as shown in equations (1) and (2).

[0052] (1)

[0053] (2)

[0054] In equations (1) and (2) for Figure 3 Angular displacement difference between the drive gear and the load gear express The first derivative, For torque transmission between the drive gear and the load gear, α is half the clearance between the drive gear and the load gear (i.e., backlash), θm θ is the angular displacement of the drive motor. l The angular displacement of the load. denoted as ρ, where c is the gear stiffness coefficient, m is the gear transmission ratio, and n is an adjustable parameter.

[0055] The improved dead-zone model ensures that, under the above assumptions, the optimization problem solved when predicting the future output of the system is a strictly convex optimization problem, making the rolling optimization problem have a unique optimal solution. If the traditional dead-zone model is used to predict the future output of the system, in some cases the optimization problem solved will not be a strictly convex optimization problem, and may not have a unique optimal solution, leading to problems in solving the optimal torque and affecting the control effect. To ensure that the rolling optimization problem has a unique optimal solution, this invention proposes a backlash model suitable for solving optimization problems, namely the improved dead-zone model. Unlike the original dead-zone backlash model, in the improved model, when the gears are not meshed, the gear dynamics are treated as a first-order spring model; when the gears are meshed, a spring-damped model is used to describe the torque transmission, ensuring that the torque before and after meshing does not jump.

[0056] The dynamic equation of the dual-motor system based on the backlash dead zone model is shown in equation (3). Figure 1 and Figure 2 (For reference only)

[0057] (3)

[0058] Figure 2 In equation (3), T m1 T m2 and T L J represents the electromagnetic torque (output torque) and load torque (including friction torque, damping torque, externally applied torque, and all unmodeled disturbances) of drive motor one and drive motor two, respectively. m1 J m2 and J L b represents the moment of inertia of drive motor one, drive motor two, and the load. m1 b m2 and b L θ represents the damping coefficient of drive motor one, drive motor two, and the load. m1 θ m2 and θ L This indicates the positions of the rotors of drive motor one, drive motor two, and the load. τ1 and τ2 represent the transmitted torque between drive gear one, drive gear two, and the load gear. α1 and α2 represent the backlash widths (backlash one and backlash two) between drive gear one, drive gear two, and the load gear. m1 and τ m2 These are the transmission torques between drive gear one, drive gear two, and load gear, respectively, obtained through an improved dead zone model, and represented by equation (1). , , , , , These represent the acceleration of drive motor one, the speed of drive motor one, the acceleration of drive motor two, the speed of drive motor two, the acceleration of the load, and the speed of the load, respectively. k1 and k2 represent the stiffness coefficients of drive gear one and drive gear two, respectively, and c1 and c2 represent the damping coefficients of gear drive gear one and drive gear two, respectively.

[0059] (II) Model Predictive Speed ​​Controller for Dual-Motor System Based on Backlash Dead Zone Model

[0060] Please refer to Figure 4 Based on the established dynamic model of the dual-motor system using the backlash dead zone model, this embodiment designs a model predictive speed controller for the dual-motor system using the backlash dead zone model. This model predictive speed controller includes load position estimation, state prediction model, rolling optimization, and feedback correction, with a reference speed... The optimal input torque T is input to the model predicts the velocity controller. m1 * , T m2 * Simultaneously estimate the location of the load. Load estimation location The estimated load speed is obtained through differentiation. , and the output speed of the prediction model The comparison is used for feedback correction, and the final output of the load speed is obtained.

[0061] The difference between the load estimation speed and the output speed of the prediction model is defined as the prediction error. This error is fed back to compensate for the reference input of the next control cycle, that is, the reference input of the next cycle = expected input - prediction error.

[0062] Prediction error , It is the load speed output at time k+1 predicted at time k. If the estimated speed output of the load is at time k+1, then the reference speed for the next cycle is... Rolling optimization essentially yields the optimal torque for both motors. In the system model, the optimal input torque u* is a vector, u* = [T]. m1 * , T m2 * ].

[0063] Regarding load position estimation, since most multi-motor systems do not have position sensors installed at the load end, and the control objective is the load's position and velocity, the load position needs to be estimated based on the system state and the values ​​of the position sensors at the drive motor end. This embodiment uses a hysteresis model to estimate the load position. Because the system has two drive motors, two estimated load positions can be obtained. This embodiment averages these two estimates as the final estimated load position. Based on the differential relationship between position and velocity, the estimated system state, including position and velocity, is then obtained.

[0064] Hysteresis model:

[0065]

[0066] Where α is half the backlash width, m is the gear ratio, and θ m θ represents the position of the drive gear. L This indicates the position of the load gear.

[0067] The advantage of using the hysteresis model is that when the load has a small moment of inertia and large damping and friction, it can better describe the kinematic relationship between gears. The moment the driving wheel disengages, the load speed can be considered to drop rapidly to zero, and the position remains at the position at the time of disengagement.

[0068] Regarding the state prediction model, after writing the model shown in equation (3) as a state-space expression and discretizing the time, a discrete-time prediction model can be obtained. In the prediction model, Np and Nc represent the number of calculation steps in the prediction time domain and the control time domain, respectively. The prediction time domain and control time domain of the speed control of the dual-motor system are as follows: Figure 5 As shown.

[0069] During the operation of the heliostat system, the required angle and angular velocity of each heliostat servo system are calculated in advance based on the geographical locations of the heliostat and the solar collector. During speed control, the reference speed curve of the servo system is given and used as the reference speed of the dual-motor system in the control time domain during the kth control cycle.

[0070] At time k, the initial velocity estimate of the dual-motor system can be obtained by differentiation based on the aforementioned load position estimate. Then, based on the future N c The reference input sequence of the step The future N is obtained by solving the optimization problem. c Optimal torque sequence of the step and at time k+1 The first component It acts on the system, and at the same time, it can predict the future N at time k through the prediction model. c Step system output Meanwhile, in the prediction time domain N p Medium system input torque retention Unchanged, we obtain the future N p The predicted output of the step.

[0071] Rolling optimization refers to solving the optimization problem in each cycle, and the solution in each cycle requires obtaining the system state from the previous cycle. The solution to the optimization problem is actually a sequence. Because of the use of finite-time domain prediction and the existence of external disturbances and model uncertainties, we cannot apply the entire optimal control sequence obtained from solving the optimization problem to the system. Instead, we apply the first component of the optimal solution at each sampling time step to the system. That is, at time k, the optimal solution is applied... The first component Acting on the system; at time k+1, using the newly obtained system state Re-predict the future output of the system based on the initial conditions and solve the optimization problem, then apply the optimized solution... The first component This process is applied to the system in a cyclical manner, and within each control cycle, the optimal set of inputs is found by solving an optimization problem. This minimizes the error between the predicted output and the reference output. As the "current time" moves forward, the prediction time domain also rolls forward, hence the name "rolling optimization."

[0072] To achieve better load speed control and minimize motor torque fluctuations in the dual-motor system, the output error is selected. The cost function, composed of the L2 norm of the input and the L2 norm of the input increment, is shown in equation (4).

[0073] (4)

[0074] Here, J represents the dependent variable of the cost function, which is used to measure the optimization effect and has no actual physical meaning. This represents the prediction of the future N at time k of the operation of the dual-motor system. c The predicted output of the step. During the operation of the heliostat system, the required angular velocity for each heliostat servo system is calculated in advance based on the geographical locations of the heliostats and the solar collector. This provides the system's reference output curve, which in a discrete system would be a series of reference points. In the k-th control cycle, define It is the reference output for the dual-motor system in the control time domain. . Indicates the future N at time k. c The sequence of optimal input torque increments for a dual-motor system. ,in It is the system's input vector in the k-th control cycle. It represents the input increment of the dual-motor system at time k in the future.

[0075] W y W is the weight matrix for the tracking error. u This is the weight matrix for the input increment. When tracking performance is of greater importance, increase W. y This can accelerate the system's tracking response speed, while avoiding excessive jitter in the motor torque, thus increasing W. u This can reduce the jitter of the input torque. Meanwhile, W y W u Appropriate values ​​need to be selected based on the parameters of the dual-motor system to ensure good speed tracking of the load while minimizing torque jitter.

[0076] In a dual-motor system, the output torque of each motor cannot be infinite, nor can the torque variation be infinite. Therefore, it is necessary to add a parameter to the system input in the prediction time domain. and its increment The constraint keeps it between the set maximum and minimum values.

[0077] Solving this optimization problem yields the optimal reference torque (optimal input torque) required by the drive motor at the next moment (next control cycle).

[0078] At time k+1, with the newly obtained system state Re-predict the future output of the system based on the initial conditions and solve the optimization problem, then apply the optimized solution... The first component It is applied to the system at time k+2, and this process is repeated to achieve rolling optimization control.

[0079] Regarding feedback correction

[0080] Because the prediction model may contain errors, and the measurement or identification results of model parameters may not be very accurate; the surrounding environment changes continuously during actual system operation, which will cause changes in system parameters; in addition, the load torque and moment of inertia will also change over time. Therefore, this embodiment adds a feedback correction circuit to the model prediction speed controller of the dual-motor system, compares the output of the prediction model with the estimated value of the actual system output, and feeds back the error to the reference input of the next control cycle.

[0081] The entire predictive control process in this embodiment is as follows:

[0082] In practical implementation, the time consumed by reading system status and calculating control algorithms needs to be considered. In actual control, communication and calculation cannot be completed instantaneously and require a significant amount of time. Predictive models based on backlash dead zone models and backlash elimination strategies do not consider this factor, assuming these steps can be completed immediately in each control cycle and the results applied to the dual-motor system. Figure 6 It can be seen that the optimal input calculated at time k can only be applied to the dual-motor system at time k+1, causing the input to lag by one beat, thus affecting the dynamic characteristics of the system, and in severe cases, it may cause the system to fail to converge.

[0083] To address this issue, this embodiment designs a predictive control process with one-beat lag compensation, such as... Figure 7 As shown, at time k, the controller writes the system input calculated in the previous time step. and read system status x k Then, using a dual-motor system model and the current state x k Predict the state at the next moment Then use the predicted Calculate the optimal input at time k+1 At time k+1, the controller writes the system input calculated at time k. and read system status x k+1 Then, using a dual-motor system model and the current state x k+1 Predict the state at the next moment Then use the predicted Calculate the optimal input at time k+2 The optimal input calculated at time k is applied to the dual-motor system at time k+2. Without one-time lag compensation, the optimal input calculated at time k can only be applied to the dual-motor system at time k+1, causing a one-time input lag, which affects the dynamic characteristics of the system and may even lead to non-convergence in severe cases. With one-time compensation, the optimal input calculated at time k can be applied to the dual-motor system at time k, enhancing the real-time performance of the system response and giving the system better dynamic performance.

[0084] This embodiment presents a model-predictive speed control method (flow) for a dual-motor system based on a backlash dead zone model:

[0085] Please refer to Figure 8 In each control cycle, a prediction error correction (i.e., feedback correction) prediction model is used, assuming that the model error does not change in the control time domain and the prediction time domain.

[0086] Step S100: When the dual-motor system is operating in the speed loop, the relevant matrix W needs to be initialized before the start of the first control cycle. y Wu These matrices remain unchanged in each control cycle, and pre-calculation can save the time consumed by the algorithm in each control cycle.

[0087] Step S200: Within each control cycle, a reference speed is given. Read the status of the dual-motor system, i.e., the motor rotor position θ m1 and θ m2 .

[0088] Step S300 obtains the load position θ by estimating the motor rotor position. L .

[0089] Step S400 obtains the load speed through differentiation. .

[0090] Step S500 calculates the prediction error and corrects the prediction model.

[0091] Step S600 involves solving the optimization problem with inequality constraints online to obtain the optimal input torque u* of the system.

[0092] Step S700: Since u* is a vector composed of the torques of drive motor one and drive motor two. The optimal input torque for both motors can then be obtained. and .

[0093] Step S800 applies the optimal input torque as a control quantity to the dual-motor system.

[0094] The foregoing has provided a detailed description of a model predictive controller for eliminating transmission backlash in a heliostat multi-servo drive system. Specific examples have been used to illustrate the principles and implementation methods of this application. The descriptions of the embodiments above are merely for the purpose of helping to understand the method and core ideas of this application. It should be noted that those skilled in the art can make various improvements and modifications to this application without departing from its principles, and these improvements and modifications also fall within the protection scope of the claims of this application.

Claims

1. A model predictive speed control device for a dual-motor system based on a backlash dead zone model, characterized in that, The device is based on a dual-motor system with backlash; it is a model-predicted speed control of a dual-motor system based on a backlash dead zone model, including a dynamic model of the dual-motor system based on a backlash dead zone model and a model-predicted speed controller. The dual-motor system dynamics model based on the backlash dead zone model is based on drive motor one and drive motor two driving the load. Drive motor one and drive motor two transmit torque to the load through drive gear one, drive gear two, and load gear, respectively. There is backlash between drive gear one and drive gear two and load gear, which is used to establish a backlash dead zone model. The backlash dead zone model is used to describe the torque transmission between the two gears when the system passes through the backlash. When the gears are meshed, a spring-damped model is used to describe the torque transmission; when they are not meshed, a first-order spring model is used to describe the torque transmission. The model predictive speed controller includes load position estimation, state prediction model, rolling optimization, and feedback correction. The reference speed is input to the model predictive speed control device, and the torque of the two drive motors is obtained through rolling optimization. The position of the load is estimated, and the estimated load speed is obtained through differentiation. The estimated load speed is compared with the output of the prediction model for feedback correction, and finally the output load speed is obtained. The spring-damped model is as follows: the force F consists of two parts: elastic force and damping force, where the elastic force is proportional to the deformation of the system, and the proportionality coefficient is the elastic coefficient. The damping force is directly proportional to the reciprocal of the deformation, with the proportionality constant being the damping coefficient c; the specific formula is: When using a spring-damped model to describe the transmitted torque between two gears, due to the presence of backlash, the deformation of the gears is the angle difference between the two gears leading (-) or lagging (+) half the backlash width, and the elastic coefficient is the gear stiffness coefficient. The damping coefficient is the damping coefficient c of the gear. The first-order spring model adopts the following equations (1) and (2): (1) (2) In equations (1) and (2) The difference in angular displacement between the drive gear and the load gear. For torque transmission between the drive gear and the load gear, α is half the clearance between the drive gear and the load gear, and θ m θ is the angular displacement of the drive motor. l The angular displacement of the load. is the stiffness coefficient of the gear, c is the damping coefficient of the gear, m is the gear ratio, and n is an adjustable parameter. The dynamic equation of the dual-motor system based on the backlash dead zone model is shown in equation (3). (3) T m1 T m2 and T L J represents the electromagnetic torque and load torque of drive motor one and drive motor two, respectively. m1 J m2 and J L b represents the moment of inertia of drive motor one, drive motor two, and the load. m1 b m2 and b L τ represents the damping coefficient of drive motor one, drive motor two, and the load. m1 and τ m2 These are the transmitted torques between drive gear one, drive gear two, and load gear, respectively, obtained through the improved dead zone model, and represented by equation (1); , , , , , The acceleration of drive motor one, the speed of drive motor one, the acceleration of drive motor two, the speed of drive motor two, the acceleration of the load, and the speed of the load are respectively. In the load position estimation, a hysteresis model is used to estimate the load position. Two estimated load positions are obtained based on the outputs of the two drive motors. The average of the two estimated values ​​is taken as the estimated load position. Based on the differential relationship between position and velocity, the estimated system state including position and velocity is obtained.

2. The dual-motor system model prediction speed control device based on a backlash dead zone model according to claim 1, characterized in that, The state prediction model is obtained by writing the model shown in equation (3) into a state-space expression and then discretizing the time to obtain a discrete-time prediction model. In the prediction model, N p and N c Let represent the number of calculation steps in the prediction time domain and the control time domain, respectively. During speed control, a reference speed curve for the dual-motor system is given as the reference speed of the dual-motor system in the control time domain during the k-th control cycle. At time k, the initial speed estimate of the dual-motor system can be obtained by differentiation based on the aforementioned load position estimation. Then, based on the future N c The reference input sequence of the step The future N is obtained by solving the optimization problem. c Optimal torque sequence of the step and at time k+1 The first component It acts on the system, and at the same time, it can predict the future N at time k through the prediction model. c Step system output Meanwhile, in the prediction time domain N p Medium system input torque retention Unchanged, we obtain the future N p The predicted output of the step.

3. The dual-motor system model prediction speed control device based on a backlash dead zone model according to claim 2, characterized in that, The state prediction model employs a control flow with one-time lag compensation: at time k, the optimal input calculated in the previous time step is input. And read the current system state x. k Then, the state prediction model and the current state x are used. k Predict the system state at the next moment. Then use the predicted Calculate the optimal input at time k+1 And it acts on the dual-motor system at time k+1.

4. The dual-motor system model predictive speed control device based on a backlash dead zone model according to claim 2, characterized in that, In the rolling optimization, after obtaining the predicted speed, the optimal set of inputs is found by solving an optimization problem within each control cycle. To minimize the error between the predicted output and the reference output, and to minimize the jitter of the motor torque in the dual-motor system, the method chosen is based on the prediction error. The cost function, composed of the L2 norm of the input and the L2 norm of the input increment, is shown in equation (4). (4) in This represents the prediction of the future N at time k of the operation of the dual-motor system. c The predicted output of the step, In the k-th control cycle, define It is the reference output for the dual-motor system in the control time domain; ; Indicates the future N at time k. c A sequence of optimal input torque increments for a dual-motor system; ,in It is the system's input vector in the k-th control cycle. It represents the input increment of the dual-motor system at time k in the future; W y W is the weight matrix for the tracking error. u The weight matrix for the input increment; Solving this optimization problem yields the optimal input torque required by the drive motor at the next moment. ; At time k+1, with the newly obtained system state Re-predict the future output of the system based on the initial conditions and solve the optimization problem, then apply the optimized solution... The first component It is applied to the system at time k+2, and this process is repeated to achieve rolling optimization control.

5. A method for predictive speed control of a dual-motor system based on a backlash dead zone model using the device described in any one of claims 1 to 4, characterized in that, Includes the following steps: (1) Under the current control cycle, given the reference speed input, obtain the rotor positions of the two drive motors; (2) Obtain the estimated load position based on the rotor positions of the two drive motors; (3) The estimated load position is obtained by differentiation to obtain the estimated load speed; (4) Based on the current input torque and load, estimate the speed and obtain the predicted output speed through the prediction model; (5) Compare the predicted output speed with the estimated load speed to calculate the prediction error; (6) Compensate the error feedback to the reference speed input for the next control cycle; (7) The predicted output is used as the current state of the system to solve the optimization problem, and the optimal input torque of the dual motor system in the next control cycle is obtained to achieve one-step lag compensation; (8) Obtain the optimal input torque of the two drive motors and apply it to the next control cycle.

6. The model predictive speed control method for a dual-motor system based on a backlash dead zone model according to claim 5, characterized in that, In step (7), the optimal input torque of the dual-motor system is obtained by solving the optimization problem with torque constraints to achieve optimal tracking performance and minimum torque jitter. The cost function composed of the L2 norm of the output error and the L2 norm of the input increment is selected. The tracking performance and torque jitter are optimized by adjusting the weight matrix of the tracking error and the weight matrix of the input increment. Before step (1), there is also a step: the weight matrix of the tracking error and the weight matrix of the input increment are initialized before the start of the first control cycle and remain unchanged in each control cycle.

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