Model predictive controller for eliminating transmission backlash in multi-servo drive systems of heliostats

Abstract

This invention provides a model predictive controller for eliminating backlash in a heliostat multi-servo drive system, specifically for heliostat multi-servo drive systems. For speed control, an improved dead-zone model is proposed to model the backlash, and a dynamic model of the dual-motor system is established based on this model. A model predictive speed controller and control system based on the dead-zone model are designed according to the dynamic model, and a feedback correction loop is used to correct the prediction results. For position control, an improved backlash elimination strategy using a variable offset torque distribution method is proposed, and a dual-motor system model based on the backlash elimination strategy is established. A model predictive position controller and control system based on the backlash elimination strategy are designed based on this model. The controller of this invention can eliminate the influence of backlash in the heliostat multi-servo system, achieving fast and stable speed regulation without overshoot and fast response and high positioning accuracy in position control.

Description

Technical Field

[0001] This invention relates to the field of heliostat multi-servo drive system technology, and in particular to a model prediction controller for eliminating transmission backlash in a heliostat multi-servo drive system. 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] To address this deficiency, this invention proposes a model predictive controller to eliminate transmission backlash in a multi-servo drive system for heliostats, aiming to eliminate the influence of transmission backlash in the multi-servo drive system for heliostats in order to achieve precise control of the heliostat angle. Summary of the Invention

[0008] The purpose of this invention is to provide a model predictive controller that eliminates transmission backlash in a multi-servo drive system for a heliostat, thereby eliminating the influence of transmission backlash in the multi-servo drive system for a heliostat and achieving precise control of the heliostat angle.

[0009] To achieve the above objectives, the present invention provides the following technical solution:

[0010] A model predictive controller for eliminating backlash in a heliostat multi-servo drive system is based on a dual-motor system with backlash, comprising a hardware layer, an intermediate layer, and an algorithm layer. The hardware layer includes: three gears—a drive gear one, a load gear, and a drive gear two meshing sequentially; three motors—drive motor one, a load motor, and drive motor two—for driving the gears; three drivers—driver one, a load driver, and driver two—for torque loop control; a controller for model predictive control and solution calculation; a host computer for reading and storing data generated during system operation; a switching power supply; and cables for power supply or communication. The algorithm layer includes a model predictive control system; the model predictive control system includes a model predictive speed control system and a model predictive position control system. The model predictive speed control system is a dual-motor system model predictive speed control based on a backlash dead zone model; the model predictive position control system is a dual-motor system model predictive position control based on a backlash elimination strategy.

[0011] The present invention provides a preferred embodiment in which the model predictive speed control system is implemented through a dual-motor system dynamic model based on a backlash dead zone model and a model predictive speed controller.

[0012] This invention provides a preferred embodiment in which the dual-motor system dynamic model based on the backlash dead zone model is established by modeling the backlash based on the first drive gear, the load gear, the second drive gear, the first drive motor, the load motor, and the second drive motor, and then using the backlash dead zone model to establish the dual-motor system dynamic model based on the 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 meshing, a spring damping model is used to describe the torque transmission; when they are not meshing, a first-order spring model is used to describe the torque transmission.

[0013] This invention provides a preferred embodiment in which 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 controller, the torque of the two drive motors is obtained through rolling optimization, the position of the load is estimated, the estimated load speed is obtained through differentiation, and feedback correction is performed by comparing it with the output of the prediction model, and finally the output of the load speed is obtained.

[0014] The present invention provides a preferred embodiment in which the model predictive position control system is implemented through a backlash elimination strategy, a dual-motor system dynamics model based on the backlash elimination strategy, and a model predictive position controller.

[0015] This invention provides a preferred embodiment in which the backlash elimination strategy utilizes the dual-motor backlash elimination principle. Based on the drive gear one, load gear, drive gear two, drive motor one, load motor two, and drive motor two, during the starting and commutation processes, the two drive gears increase the offset torque T in opposite directions on the load gear. m1 and T m2 One drive gear provides the driving torque, and the other drive gear provides the resistance torque. After starting and reversing, the bias torque is stopped, and the two drive gears jointly provide the driving torque to drive the load gear. This prevents free tooth backlash between the drive gear and the load gear, eliminates the influence of tooth backlash, and establishes a backlash elimination strategy.

[0016] This invention provides a preferred embodiment, wherein the backlash elimination strategy is as follows: when the load torque is 0 and the reference torque is 0, the two drive motors respectively provide the load with offset torques of equal magnitude and opposite direction to hold the load in place, preventing the load from rotating freely in the backlash; when the load needs to rotate in the forward direction, the reference torque increases in the forward direction, T m1 Gradually increase, T m2 As the torque gradually decreases, the net torque gradually increases, and the load begins to rotate in the forward direction. At this time, the gears of the two drive motors remain in close contact with the motors, achieving backlash-free transmission. When the reference torque continues to increase and exceeds T1, the torque required by the load is entirely provided by motor one. At this time, motor two will rotate with the load gear and will not provide power. Subsequently, the drive gear and the load gear remain in contact through the action of the motor torque and the load torque. When the reference torque continues to increase and exceeds T2, motor one maintains a constant torque T2, and the torque of motor two begins to increase. When the reference torque exceeds T3, the required torque is evenly distributed between the two motors.

[0017] The present invention provides a preferred embodiment in which the dynamic model of the dual-motor system based on the backlash elimination strategy is established under the backlash elimination strategy, where the backlash is eliminated at any time, adjacent gears are always in a close engagement state, the dual-motor system is regarded as a whole, the speed of the three gears is the same at any time, and the positions differ only by the backlash width of the initial condition. In this way, the dynamic model of the dual-motor system as a whole is dynamically modeled, and the dynamic model of the dual-motor system based on the backlash elimination strategy is established.

[0018] This invention provides a preferred embodiment in which the model predictive position controller includes load position estimation, a state prediction model, rolling optimization, and an extended state observer. A reference position is used as the input to the model predictive position controller. After rolling optimization, the total torque required by the load is obtained. Then, a backlash elimination strategy is used to distribute the torque to obtain the torque T required by drive motor one and drive motor two. m1 and T m2 The actual position of the load is estimated and fed back to the model predictive position controller for closed-loop control.

[0019] This invention provides a preferred embodiment in which the state prediction model employs a control flow with one-time lag compensation: at time k, the controller writes the optimal input calculated in the previous time step. And read the current system state x. k Then, using the dual-motor system model and the current state x, k Predict the system state at the next moment. Then use the predicted results Calculate the optimal input at time k+1 And it acts on the dual-motor system at time k+1.

[0020] Compared with existing technologies, the above technical solution has the following beneficial technical effects:

[0021] (1) For speed control, this invention proposes an improved dead-zone model (backlash dead-zone model) to model backlash, and establishes a dynamic model of a dual-motor system based on this model. A model-predictive speed controller and control system based on the dead-zone model are designed according to the dynamic model, and a feedback correction loop is used to correct the prediction results. For position control, an improved backlash elimination strategy based on variable offset torque distribution is proposed, and a dual-motor system model based on the backlash elimination strategy is established. A model-predictive position controller and control system based on the backlash elimination strategy are designed based on this model, and an extended state observer is used to estimate external disturbances to compensate for prediction errors. The controller designed in this invention can eliminate the influence of transmission backlash in a heliostat multi-servo system, achieving fast and stable speed regulation without overshoot and fast response and high positioning accuracy position control.

[0022] (2) This invention uses a backlash dead zone model for model predictive speed control. The input of this model is the relative displacement between the driving and driven parts, and the output is the transmitted torque generated by the driving part. Since the dead zone model considers the influence of system stiffness and internal damping on the backlash, this model can realistically describe the physical process when traversing the backlash, thus being more in line with reality.

[0023] (3) The present invention adopts a backlash elimination strategy with variable offset torque distribution, which not only eliminates the influence of tooth backlash, but also solves the problems of motor efficiency and uneven force distribution, reduces the impact of backlash elimination on other system performance, and can simultaneously meet the composite requirements of system backlash elimination and synchronization to a certain extent.

[0024] (4) This invention employs 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 possesses good dynamic response characteristics, balancing steady-state and dynamic response performance. Since the application scenario of this controller is gear transmission, to reduce gear wear, it is desirable that the tracking response does not undergo abrupt changes, while simultaneously requiring a rapid response. Therefore, it is expected that the tracking curve exhibits a trend of slow start-up and termination, and fast response in the middle (e.g., Figure 17 (As shown). PID is an error-based control scheme that cannot simultaneously meet the dynamic response requirements while pursuing steady-state response; while model predictive control can achieve this goal through the constraint element in the solution of constrained optimization problems. Therefore, model predictive control is more suitable for the application scenario of gear transmission.

[0025] (5) This invention designs a controller with a backlash elimination strategy, which is insensitive to the size of the gear backlash 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 with a controller with a backlash elimination strategy. Attached Figure Description

[0026] 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.

[0027] Figure 1 This is a diagram of a dual-motor control system architecture with backlash in a model predictive controller for eliminating transmission backlash in a multi-servo drive system of a heliostat, provided as a specific embodiment of the present invention.

[0028] Figure 2 A schematic diagram of a dual-motor control system with backlash in a model predictive controller for eliminating transmission backlash in a multi-servo drive system of a heliostat, provided as a specific embodiment of the present invention.

[0029] Figure 3 This is a schematic diagram of the structure of a dual-motor system in a model predictive controller for eliminating transmission backlash in a multi-servo drive system of a heliostat, provided as a specific embodiment of the present invention.

[0030] Figure 4 A block diagram of a dual-motor system in a model predictive controller for eliminating transmission backlash in a multi-servo drive system of a heliostat, provided as a specific embodiment of the present invention;

[0031] Figure 5 A schematic diagram of backlash in a model predictive controller for eliminating transmission backlash in a multi-servo drive system for a heliostat, provided as a specific embodiment of the present invention.

[0032] Figure 6 The following is a system block diagram of a dual-motor system model prediction speed controller based on a backlash dead zone model in a model prediction controller for eliminating transmission backlash in a multi-servo drive system of a heliostat, provided as a specific embodiment of the present invention.

[0033] Figure 7 The diagram illustrates the speed control prediction time domain and control time domain of a dual-motor system based on a backlash dead zone model in a model predictive controller for eliminating transmission backlash in a multi-servo drive system of a heliostat, as provided in a specific embodiment of the present invention.

[0034] Figure 8 A schematic diagram of the backlash elimination principle of a dual-motor model prediction controller in a multi-servo drive system for eliminating transmission backlash in a heliostat, provided as a specific embodiment of the present invention;

[0035] Figure 9 An improved variable bias torque distribution curve based on a backlash elimination strategy in a model predictive controller for eliminating transmission backlash in a multi-servo drive system of a heliostat, provided as a specific embodiment of the present invention;

[0036] Figure 10 A gear contact state diagram under an improved variable bias torque strategy in a model predictive controller for eliminating transmission backlash in a heliostat multi-servo drive system, provided as a specific embodiment of the present invention.

[0037] Figure 11 The block diagram of a model predictive position control system for a dual-motor system based on a backlash elimination strategy in a model predictive controller for eliminating transmission backlash in a multi-servo drive system of a heliostat is provided for a specific embodiment of the present invention.

[0038] Figure 12 The diagram illustrates the position control prediction time domain and control time domain of a dual-motor system based on a backlash elimination strategy in a model predictive controller for eliminating transmission backlash in a multi-servo drive system of a heliostat, as provided in a specific embodiment of the present invention.

[0039] Figure 13 The control flowchart of a model predictive controller for eliminating transmission backlash in a multi-servo drive system of a heliostat, without considering one-step lag compensation, is provided as a specific embodiment of the present invention.

[0040] Figure 14 The control flowchart of a model predictive controller with one-step lag compensation in a multi-servo drive system for eliminating transmission backlash in a heliostat is provided as a specific embodiment of the present invention.

[0041] Figure 15 A flowchart of the model prediction speed control of a dual-motor system in a model prediction controller for eliminating transmission backlash in a multi-servo drive system of a heliostat is provided as a specific embodiment of the present invention.

[0042] Figure 16 A flowchart of model prediction position control for a dual-motor system in a model prediction controller for eliminating transmission backlash in a multi-servo drive system of a heliostat is provided as a specific embodiment of the present invention.

[0043] Figure 17 The figure shows a comparison of the expected tracking curves of a model predictive controller for eliminating transmission backlash in a multi-servo drive system for heliostats, provided as a specific embodiment of the present invention, using model predictive control in controller design and a traditional PID control scheme.

[0044] Figure 18 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.

[0045] The attached figures are labeled as follows:

[0046] Drive gear 11, drive gear 212, load gear 13;

[0047] Drive motor 1 21, drive motor 2 22, load motor 23;

[0048] Driver 1 31, Driver 2 32, Load Driver 33;

[0049] Controller 4, host computer 5. Detailed Implementation

[0050] 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.

[0051] Please refer to Figure 1 , Figure 1 This is a diagram illustrating the architecture of a dual-motor control system with backlash in this embodiment. This embodiment presents a model predictive controller for eliminating transmission backlash in a heliostat multi-servo drive system. Based on a dual-motor system with backlash, the layers from bottom to top are a hardware layer, an intermediate layer, and an algorithm layer.

[0052] Please refer to Figure 2 , Figure 2 This is a schematic diagram of the dual-motor control system with backlash in this embodiment. The hardware layer is the foundation of the entire system, including three gears: a drive gear one, a load gear, and a drive gear two that mesh sequentially; drive motor one, load motor, and drive motor two, which respectively rotate drive gear one, load gear, and drive gear two; driver one, load driver, and driver two, which respectively implement torque loop control of drive motor one, load motor, and drive motor two; a controller, which is used to perform calculations such as model predictive control and optimization problem solving; a host computer, which is used to read and store data generated during system operation; a switching power supply; and cables for power supply or communication.

[0053] Solving constrained optimization problems in model predictive control, specifically for finding the optimal control torque u*. Since the objective function is quadratic and the dynamic equations and time-domain constraints are linear, this problem is a quadratic programming problem; solving this optimization problem is essentially solving a quadratic programming problem.

[0054] The middle layer consists of TwinCAT 3.1 components running in the controller, including I / O for communication, abstract CNC motor axes, PLC and C++ programs for programming algorithms and communication, and oscilloscope Scope components for storing data.

[0055] The algorithm layer consists of methods used in actual control, implemented in C++, including Model Predictive Control (MPC), Quadratic Programming (QP), Extended State Observer (ESO), and other algorithms.

[0056] Model predictive control includes a model predictive speed control system and a model predictive position control system. The model predictive speed control system is a dual-motor system model predictive speed control system based on a backlash dead zone model; the model predictive position control system is a dual-motor system model predictive position control system based on a backlash elimination strategy. Next, this embodiment will provide a more detailed description of the dual-motor system model predictive speed control system based on a backlash dead zone model and the dual-motor system model predictive position control system based on a backlash elimination strategy:

[0057] (I) Predictive speed control system for dual-motor system based on backlash dead zone model

[0058] In this embodiment, the model predictive speed control system for a dual-motor system based on the backlash dead zone model is implemented through a dynamic model of the dual-motor system based on the backlash dead zone model and a model predictive speed controller.

[0059] 1. Dynamic model of a dual-motor system based on the backlash dead zone model (improved dead zone model)

[0060] Please refer to Figure 3 , Figure 3 This is a schematic diagram of the dual-motor system in this embodiment. The dual-motor system model established in this embodiment uses two drive motors (drive motor one and drive motor two) to drive the load. The torque is transmitted between the drive motors 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.

[0061] Please refer to Figure 4 , Figure 4 This is a block diagram of the dual-motor system in this embodiment. In the diagram, T... m1 T m2 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.

[0062] Please refer to Figure 5 , Figure 5 This is a schematic diagram of tooth backlash. Tooth 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 be in contact, allowing the load gear to rotate freely in the gap, resulting in the load speed and position being temporarily uncontrollable.

[0063] based on Figure 5 In this system, the driving gear and load gear are assumed to maintain the same meshing state during the prediction of future system dynamics; that is, the gears are expected to 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 load gear when the system passes through the backlash. A spring-damped model is used to describe torque transmission when the gears are meshing, ensuring that the torque does not jump before and after meshing.

[0064] Please refer to Figure 18 Spring-damped model: The interaction force F between the systems consists of two parts: elastic force and damping force. The elastic force is proportional to the system's deformation Δx, with the proportionality constant being the elastic coefficient k; the damping force is proportional to the reciprocal of the deformation. It is directly proportional, and the proportionality coefficient is the damping coefficient c; the specific formula is as follows:

[0065] When using a spring-damped model to describe the torque transmission between two gears, due to the presence of backlash, the deformation of the gear is the angle difference Δθ between the two gears leading (-) or lagging (+) by half the backlash width α, the elastic coefficient is the gear stiffness coefficient k, and the damping coefficient is the gear damping coefficient c.

[0066] When not engaged, the gear dynamics are considered as a first-order spring model, as shown in equations (1) and (2). Equation (1) is the transmitted torque described by the improved dead zone model, and equation (2) is a specific description of the variable Δθ in equation (1). The improved dead zone model includes equations (1) and (2).

[0067]

[0068] Δθ=θ m -mθ l (2)

[0069] In equations (1) and (2), Δθ is Figure 5 Angular displacement difference between the drive gear and the load gear Let θ represent the first derivative of Δθ, τ be the torque transmission between the driving gear and the load gear, α be half the clearance (backlash) between the driving gear and the load gear, and θ be the torque of Δθ. mθ is the angular displacement of the drive motor. l denoted as angular displacement of the load, k as the gear stiffness coefficient, c as the gear damping coefficient, m as the gear transmission ratio, and n as an adjustable parameter.

[0070] 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.

[0071] The dynamic equations of the dual-motor system based on the backlash dead zone model are shown in equation (3). Figure 3 and Figure 4 (For reference only)

[0072]

[0073] Figure 4 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 The values ​​represent 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. 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 the gears driving drive gear one and drive gear two, respectively. τ m1 and τ m2These 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.

[0074] 2. Model Predictive Speed ​​Controller for Dual-Motor System Based on Backlash Dead Zone Model

[0075] Please refer to Figure 6 , Figure 6 This is a system block diagram of a model predictive speed controller for a dual-motor system based on a backlash dead zone model. Based on the established dynamic model of the dual-motor system based on the backlash dead zone model, this embodiment designs a model predictive speed controller for the dual-motor system based on 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 input is fed into the model predictive speed controller, and after rolling optimization, the optimal input torque T for the two drive motors (drive motor one and drive motor two) is obtained. m1 * ,T m2 * Simultaneously estimate the location of the load. Load estimation location The estimated load speed is obtained through differentiation. With the output speed of the prediction model The comparison is used for feedback correction, and the final output of the load speed is obtained.

[0076] 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 the reference input of the next control cycle, i.e., the reference input of the next cycle = expected input - prediction error.

[0077] 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, where u* = [T]. m1 * ,T m2 * ].

[0078] Regarding load location estimation

[0079] Since most multi-motor systems do not have position sensors installed at the load end, and the control objective is the position and velocity of the load, it is necessary to estimate the load position 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. In this embodiment, the average of the two estimates 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 then obtained.

[0080] Hysteresis model:

[0081]

[0082] 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.

[0083] 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.

[0084] Regarding state prediction models

[0085] 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, N p and N c These 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 for speed control of a dual-motor system are as follows: Figure 7 As shown, Figure 7 This diagram illustrates the speed control prediction time domain and control time domain of the dual-motor system based on the backlash dead zone model in this embodiment.

[0086] 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.

[0087] At time k, based on the aforementioned load position estimation, the initial velocity estimate ω(k) of the dual-motor system can be obtained through differentiation. Then, based on the future N... c The reference input sequence ω for the step r (k+1)=[ω r (k+1),ω r (k+2),…,ω r (k+Nc )] T The future N is obtained by solving the optimization problem. c The optimal torque sequence U of the step * (k+1)=[u * (k+1|k) T ,u * (k+2|k) T ,…,u * (k+N c |k) T ] T And at time k+1, U * The first component u of (k+1) * (k+1|k) acts on the system, and the future N at time k can be predicted using a prediction model. c The system output ω of the step p (k+1)=[ω p (k+1|k),ω p (k+2|k),…,ω p (k+N c |k)] T Meanwhile, in the prediction time domain N p The input torque of the medium system is maintained by u * (k+N c |k+N c -1) remains unchanged, yielding the future N. p The predicted output of the step.

[0088] Regarding scrolling optimization

[0089] 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 U. * (k+1)=[u * (k+1|k) T ,u * (k+2|k) T ,…,u * (k+N c |k) T ] T 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 U... * The first component u of (k) *(k|k-1) acts on the system; at time k+1, using the newly obtained system state y(k+1) as the initial condition, the future output of the system is predicted again and the optimization problem is solved. Then the optimization solution U * The first component u of (k+1) * (k+1|k) is applied to the system, and this process is repeated cyclically. Within each control cycle, the optimal set of inputs u is found by solving an optimization problem. * (k+1|k),u * (k+2|k+1)... 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".

[0090] To achieve better load speed control and minimize motor torque fluctuations in the dual-motor system, the output error ω is selected. p (k+1)-ω r The cost function, consisting of the L2 norm of (k+1) and the L2 norm of the input increment, is shown in equation (4).

[0091] J = ||W y (ω p (k+1)-ω r (k+1))|| 2 +||W u ΔU(k)|| 2 (4)

[0092] Here, J represents the dependent variable of the cost function, a metric used to measure the optimization effect, and has no actual physical meaning. ω p (k+1) represents the prediction of the future N at time k of the operation of the dual-motor system. c The predicted output for the step. ω p (k+1)=[ω p (k+1|k),ω p (k+2|k),…,ω p (k+N c |k)] T 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 a reference output curve for the system, which in a discrete system is a series of reference points ω. r In the k-th control cycle, ω is defined. r (k+1) is the reference output of the dual-motor system in the control time domain. ω r (k+1)=[ω r (k+1),ω r (k+2),…,ω r (k+N c )] TΔU(k) ​​represents the future N at time k. c The sequence of optimal input torque increments for a dual-motor system. in It is the system input vector in the k-th control cycle, and Δu(k) is the input increment of the dual-motor system at the k-th time in the future.

[0093] 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.

[0094] 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 constraints on the system input u and its increment Δu in the prediction time domain to keep them between the set maximum and minimum values.

[0095] Solving this optimization problem yields the optimal reference torque (optimal input torque) required by the drive motor at the next moment (next control cycle).

[0096] At time k+1, using the newly obtained system state ω(k+1) as the initial condition, re-predict the future output of the system and solve the optimization problem, then apply the optimization solution U... * The first component u of (k+2) * (k+2|k+1) is applied to the system at time k+2, and this cycle repeats to achieve rolling optimization control.

[0097] Regarding feedback correction

[0098] 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.

[0099] (II) Predictive Position Control System Based on Backlash Elimination Strategy for Dual-Motor System

[0100] In this embodiment, the model predictive position control system for a dual-motor system based on a backlash elimination strategy is implemented through a dynamic model of the dual-motor system based on a backlash elimination strategy and a model predictive position controller.

[0101] 1. Dynamic model of a dual-motor system based on backlash elimination strategy

[0102] Please refer to Figure 8 , Figure 8 This is a schematic diagram of the backlash elimination principle of the dual motors in this embodiment. Two independent drive gears mesh with the load gear. During startup and commutation, the two drive gears apply opposite bias torques to the load gear. At this time, one drive gear provides the driving torque, and the other drive gear provides the resistance torque. After startup and commutation are completed, the bias torque is stopped, and the two drive gears jointly provide the driving torque to drive the load gear.

[0103] In this way, the bias torque always acts on the load gear during starting and reversing, so that the two drive gears are always against the different tooth surfaces of the load gear. As a result, the output torque of the two drive gears will not be zero at the same time. Under these circumstances, there will be no free tooth backlash between the drive gear and the load gear, that is, the load gear cannot move back and forth between the gaps, thereby eliminating the influence of tooth backlash and achieving the goal of high tracking accuracy.

[0104] When the load needs to rotate clockwise, T m1 Greater than T m2 This causes the load to rotate. At this time, T m2 This is the bias torque that ensures the gears always maintain contact. When the load needs to change the direction of rotation, T is increased. m2 , making T m2 Greater than T m1 When a reverse load is applied without creating a gap, T m1 This is the bias torque.

[0105] Based on the above principles, this embodiment designs an improved backlash elimination strategy for variable offset torque distribution. Please refer to [reference needed]. Figure 9 , Figure 9 This is a graph showing the improved variable offset torque distribution based on the backlash elimination strategy in this embodiment.

[0106] When the load torque and the reference torque are both zero, the two motors provide equal but opposite bias torques to the load, clamping it and preventing it from rotating freely in the backlash. When the load needs to rotate in the forward direction, the reference torque increases in the forward direction, and T... m1 Gradually increase, T m2As the reference torque gradually decreases, the net torque gradually increases, and the load begins to rotate in the forward direction. At this time, the gears of both motors remain in close contact with the load gear, achieving backlash-free transmission. When the reference torque continues to increase and exceeds T1, the torque required by the load is entirely provided by drive motor one. At this time, drive motor two will rotate with the load gear and does not provide power. Thereafter, the motor torque and load torque work together to keep the motor gears and load gear in contact. When the reference torque continues to increase and exceeds T2, drive motor one maintains a constant torque T2, while drive motor two begins to increase. When the reference torque exceeds T3, the required torque is evenly distributed between the two motors. When the load needs to rotate in the reverse direction, the situation is the same as above. T1, T2, and T3 are manually set critical values. T1 and T2 are selected appropriately based on the dual-motor system, T3 = 2 × T2, and the offset torque T... bias =T1 / 2.

[0107] Please refer to Figure 10 , Figure 10 This diagram illustrates the gear contact states under the improved variable bias torque strategy (backlash elimination strategy) in this embodiment. Assuming counter-clockwise rotation of each gear is the positive direction, under the improved variable bias torque strategy, due to the different torque directions of the two drive motors, the contact states of the three gears are as follows: Figure 10 The three scenarios are shown.

[0108] Under the backlash elimination strategy, backlash is eliminated at any time, and adjacent gears are always in close contact. Therefore, the dual-motor system can be regarded as a whole, and the speed of the three gears is the same at any time, with their positions differing only by the backlash width of the initial condition. At this time, the dynamic model of the dual-motor system as a whole is performed, as shown in Equation (5).

[0109]

[0110] J m1 and J m2 It is the moment of inertia of the two motors, T m1 and T m2 It is the output torque of the two motors, J L It is the moment of inertia of the load, θ L It is the load location. The load position θ L The second derivative of the load, T, is the acceleration of the load. L It is the load torque, which includes friction torque, damping torque, externally applied torque, and all unmodeled disturbances.

[0111] This embodiment first employs a backlash elimination strategy using variable offset torque distribution, which eliminates the influence of backlash and solves the problems of motor efficiency and uneven force distribution. It also reduces the impact of backlash elimination on other system performance, and can, to some extent, simultaneously meet the combined requirements of system backlash elimination and synchronization. Secondly, it improves upon the traditional variable offset torque distribution method by designing an improved backlash elimination strategy. This addresses the problem that the traditional variable offset torque method does not consider the issue that when the reference torque is near the offset torque, the output torque of one motor will be near zero. If the reference torque oscillates near the offset torque, the output torque of one motor will oscillate near zero. The gear of this motor will repeatedly strike the load gear in the backlash, causing mechanical structure vibration and reduced lifespan.

[0112] 2. Model Predictive Position Controller for Dual-Motor System Based on Backlash Elimination Strategy

[0113] Please refer to Figure 11 , Figure 11 This is a block diagram of the model predictive position control system for a dual-motor system based on a backlash elimination strategy in this embodiment. The control system consists of a model predictive position controller, a backlash elimination strategy, and a dual-motor system dynamic model based on the backlash elimination strategy. The model predictive position controller comprises load position estimation, a state prediction model, rolling optimization, and an extended state observer. The backlash elimination strategy adopts the aforementioned improved variable bias torque distribution method, and a dual-motor system dynamic model based on this strategy is established. The reference position is used as the input to the model predictive position controller to obtain the total torque u required by the load. After torque distribution, the torque T required to drive drive motor one and drive motor two is obtained. m1 T m2 The actual position of the load is estimated and fed back to the controller for closed-loop control.

[0114] Regarding load location estimation under the improved bias torque strategy

[0115] The system under improved bias torque only has the following characteristics: Figure 10 Of the three states (a), (b), and (c) in the equation, only states (a) and (b) are used in load position estimation; state (c) is not used. When the dual-motor system starts operating in the position loop, the initial position of the load should be determined first. Initially, a small positive torque is applied to both drive motors to drive the load to rotate slowly, ensuring the gear contact state is as described above. Figure 10 In (a) of this process, at any given moment, the values ​​of the position sensors at the two drive motor ends are given to be 0 rad, and the current position of the load is defined as the initial position of 0 rad; then the torque of the two drive motors is set to a small negative torque, so that the gear contact state is as follows. Figure 10 In (b), at this point, the backlash angle α = θ between the load and the second drive gear is calculated and recorded. m1 -θ m2In subsequent operation, the load position can be calculated according to equation (6).

[0116]

[0117] θ m1 θ m2 and θ L This indicates the positions of the rotors of drive motor one, drive motor two, and the load, and the torque T required to drive drive motor one and drive motor two. m1 T m2 .

[0118] Since the load initializes its position to 0 when it engages with drive gear 1, it is assumed that in subsequent stages, the load gear's position is the same as that of drive gear 1 but in the opposite direction when it engages with drive gear 1. However, when the load position is initialized to 0, it does not contact drive gear 2, but is different from it by the backlash width at an initial moment. Therefore, it is assumed that in subsequent moments, when the load contacts drive gear 2, its position is also different from that width from drive gear 2.

[0119] Regarding the improved state prediction model under the bias torque strategy

[0120] By writing the model shown in equation (5) into a state-space expression and discretizing it, the state prediction model of the dual-motor system can be obtained. Please refer to... Figure 12 , Figure 12 This diagram illustrates the position control prediction time domain and control time domain of the dual-motor system based on the backlash elimination strategy in this embodiment.

[0121] At time k, the initial position estimate θ(k) of the dual-motor system can be obtained based on the load location estimate. Then, based on the geographical locations of the heliostat and the solar collector, the angle that each heliostat servo system needs to reach is calculated as the future N of the dual-motor system. c The reference input sequence θ for the step r (k+1)=[θ r (k+1),θ r (k+2),…,θ r (k+N c )] T The future N is obtained by solving the optimization problem. c The optimal torque sequence U of the step * (k+1)=[u * (k+1|k) T ,u * (k+2|k) T ,…,u * (k+N c |k) T ] T And at time k+1, U *The first component u of (k+1) * (k+1|k) acts on the system, and the future N at time k can be predicted using a prediction model. c The system output θ of the step p (k+1)=[θ p (k+1|k),θ p (k+2|k),…,θ p (k+N c |k)] T Meanwhile, in the prediction time domain N p The input torque of the medium system is maintained by u * (k+N c |k+N c -1) remains unchanged, yielding the future N. p The predicted output of the step.

[0122] Rolling optimization of system input under improved variable bias torque strategy

[0123] At time k+1, using the newly obtained system state θ(k+1) as the initial condition, re-predict the future output of the system and solve the optimization problem. Then, the optimization solution U... * The first component u of (k+2) * (k+2|k+1) is applied to the system at time k+2, and this process is repeated cyclically. Within each control cycle, the optimal set of inputs u is found by solving an optimization problem. * (k+1|k),u * (k+2|k+1)..., thereby achieving rolling optimization control.

[0124] When the heliostat is operating in position mode, it is expected that the load position will move quickly to the specified position without oscillation or overshoot when the reference position changes. In order to achieve better position tracking and minimize the jitter of the motor reference torque, a cost function is designed for the dual-motor system as shown in Equation (7).

[0125] J = ||W y (θ p (k+1)-θ r (k+1))|| 2 +||W u ΔU(k)|| 2 (7)

[0126] J represents the dependent variable of the cost function, used to measure the optimization effect, and has no actual physical meaning. θ p (k+1) represents the prediction of the future N at time k of the operation of the dual-motor system. c The predicted output for the step. θ p (k+1)=[θ p (k+1|k),θp (k+2|k),…,θ p (k+N c |k)] T During the operation of the heliostat system, the required angle 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 is a series of reference points θ. r In the k-th control cycle, θ is defined. r (k+1) is the reference output of the dual-motor system in the control time domain. θ r (k+1)=[θ r (k+1),θ r (k+2),…,θ r (k+N c )] T

[0127] ΔU(k) ​​represents the future N at time k. c The sequence of optimal input torque increments for a dual-motor system. in Δu(k) is the input torque of the system in the k-th control cycle, and Δu(k) is the input increment of the dual-motor system at the k-th future time. Matrix U is composed of N... c The matrix formed by stacking the system input vectors of each control cycle (as shown in the formula above) is used in position control. This is the total input torque of the dual-motor system. The torque of each motor is obtained after torque distribution. This is achieved by adjusting N... c Each control input u in each control cycle is constrained to constrain the entire sequence U.

[0128] W y Let W be the weight matrix for tracking error, representing the degree of importance placed on tracking performance. Increasing W... y W u To input the weight matrix of the increment, increase W. u It can reduce the oscillation of the input torque.

[0129] In a heliostat servo system, the output torque of the motor cannot be infinite, nor can the torque variation be infinite. Therefore, it is necessary to add constraints on the optimization targets Δu and u to limit them within the set range.

[0130] The following optimization problem is formed by the cost function (7) of the system under the improved variable bias torque strategy and the torque constraint conditions: The input of this optimization problem is the reference position of the load. In order to optimize the tracking performance of the load position and minimize the jitter of the input torque, the input torque is constrained within a given range. The output of the optimization problem is the optimal reference torque of the dual-motor system. The rolling optimization control of the system can be realized by solving the above optimization problem for each cycle.

[0131] Design of an expanded state observer for the load torque of a dual-motor system

[0132] Due to certain assumptions made when establishing the dual-motor model, such as neglecting complex nonlinear friction and changes in load torque, coupled with errors in the model parameters, accurately describing a real dual-motor system through the model is very difficult. For model predictive control, model accuracy directly affects whether the optimization results can be effective in the real system; inaccurate models may lead to poor system regulation. To address this issue, this embodiment uses an extended state observer to monitor external disturbances in the dual-motor system.

[0133] For the dynamic model (5) of the dual-motor system based on the backlash elimination strategy established above, after writing it into a state-space expression, a linear extended state observer as shown in equation (8) can be established based on this expression.

[0134]

[0135] Where A, B, and C are the coefficient matrices of model (5) written in the state-space model, L = [β1 β2 β3] T Let be the error feedback gain matrix of the observer, β1, β2, β3 be the parameters of the observer, and T denote the transpose. To ensure observer convergence, we take β1 = 3ω0. ω0 is the bandwidth of the observer. Observations representing system velocity Observations indicating the system's location, y represents the observed output of the system, and y represents the actual output of the system.

[0136] All disturbances observed by the observer, including internal model biases and external disturbances, participate in the aforementioned state prediction process to compensate for the impact of these disturbances. In the velocity control prediction model, disturbances are not considered but are compensated for through a feedback correction stage. In position control, disturbances observed by the observer replace the feedback correction stage. Specifically, the disturbance term observed by the observer is added to the prediction model to obtain a prediction output that considers the disturbance. Therefore, the prediction output used to solve the optimization problem and obtain the optimal torque takes the disturbance into account, thus compensating for it.

[0137] The entire predictive control process in this embodiment is as follows:

[0138] 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 13 It can be seen that, Figure 13 This is the control flowchart of the model predictive controller in this embodiment without considering one-step lag compensation; 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 step, thereby affecting the dynamic characteristics of the system, and in severe cases, it may cause the system to fail to converge.

[0139] To address this issue, this embodiment designs a predictive control process with one-beat lag compensation, such as... Figure 14 As shown, Figure 14 This is the control flow diagram with one-time lag compensation. At time k, the controller writes the system input calculated in the previous time step. And read system status x k Then, using the state prediction model and the current state x k Predict the state at the next moment Then use the predicted results 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 results Calculate the optimal input at time k+2 The optimal input calculated at time k+1 is applied to the dual-motor system. 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.

[0140] Dual-motor system model predictive speed control process:

[0141] In each control cycle, a prediction error correction (i.e., feedback correction) prediction model is used, assuming that the model error remains unchanged in both the control and prediction time domains. Please refer to [reference needed]. Figure 15 , Figure 15 This is a flowchart of the predicted speed control process for the dual-motor system model in this embodiment.

[0142] 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 W u These matrices remain unchanged in each control cycle, and pre-calculation can save the time consumed by the algorithm in each control cycle.

[0143] 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 .

[0144] Step S300 obtains the load position θ by estimating the motor rotor position. L .

[0145] Step S400 obtains the load speed through differentiation.

[0146] Step S500 calculates the prediction error and corrects the prediction model.

[0147] Step S600 involves solving the optimization problem with inequality constraints online to obtain the optimal input torque u* of the system.

[0148] Step S700: Since u* is a vector composed of the torques of drive motor one and drive motor two. The optimal input torque of the two motors can then be obtained. and

[0149] Step S800 applies the optimal input torque as a control quantity to the dual-motor system.

[0150] Dual-motor system model predictive position control process:

[0151] Please refer to Figure 16 , Figure 16 This is a flowchart of the predicted position control for the dual-motor system model in this embodiment.

[0152] Step S100: When the dual-motor system is operating in the position loop, the system parameter W needs to be initialized before the start of the first control cycle. u W y , L etc.

[0153] Step S200: Given a reference position θ ref Obtain the state θ of the dual-motor system m1 θ m2 .

[0154] Step S300 obtains the load position θ by estimating the motor rotor position. L .

[0155] After obtaining the load location in step S400, the external disturbance d of the system can be calculated using the extended state observer.

[0156] Step S500 involves solving the optimization problem with inequality constraints online to obtain the optimal input torque u*.

[0157] Step S600 uses an improved variable bias torque distribution strategy to obtain the optimal input torque for the two motors. and

[0158] Step S700 applies the optimal input torque as a control quantity to the dual-motor system.

[0159] 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 controller for eliminating transmission backlash in a multi-servo drive system for a heliostat, characterized in that, The dual-motor system with backlash includes a hardware layer, an intermediate layer, and an algorithm layer; among them, The hardware layer includes: The three gears are, in sequence, the drive gear one, the load gear, and the drive gear two; Three motors are used to drive the gear movement, namely drive motor one, load motor and drive motor two; Three drives are used to implement torque loop control, namely drive one, load drive and drive two; A controller is used to implement model predictive control and solve the problem; A host computer is used to read and store data generated during system operation; Switching power supplies and cables used for power supply or communication; The algorithm layer includes: a model predictive control system; The model predictive control system includes a model predictive speed control system and a model predictive position control system. The model predictive speed control system is a model predictive speed control for a dual-motor system based on a backlash dead zone model. The model predictive position control system is a model predictive position control for a dual-motor system based on a backlash elimination strategy. The model predictive speed control system is implemented through a dual-motor system dynamics model based on a backlash dead zone model and a model predictive speed controller. The dual-motor system dynamic model based on the backlash dead zone model is based on the backlash modeling of drive gear one, load gear two, drive motor one, load motor two, and drive motor two, establishing the backlash dead zone model, and establishing the dual-motor system dynamic model based on the backlash dead zone model. 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 controller, the torque of the two drive motors is obtained through rolling optimization, the position of the load is estimated, the estimated load speed is obtained through differentiation, and feedback correction is performed by comparing it with the output of the prediction model, and finally the output of the load speed is obtained. The model predictive position control system is implemented through a backlash elimination strategy, a dual-motor system dynamics model based on the backlash elimination strategy, and a model predictive position controller. The backlash elimination strategy utilizes the dual-motor backlash elimination principle. Based on the drive gear one, load gear, drive gear two, drive motor one, load motor two, and drive motor two, during startup and commutation, the two drive gears apply opposite bias torques T to the load gear. m1 and T m2 One drive gear provides power torque, and the other drive gear provides resistance torque. After starting and reversing, the bias torque is stopped, and the two drive gears jointly provide power torque to drive the load gear to move, so that there is no free tooth backlash between the drive gear and the load gear, eliminating the influence of tooth backlash, and thus establishing a backlash elimination strategy. The dynamic model of the dual-motor system based on the backlash elimination strategy is established under the backlash elimination strategy, where backlash is eliminated at any time, adjacent gears are always in close contact, the dual-motor system is regarded as a whole, the speed of the three gears is the same at any time, and the position differs only by the backlash width of the initial condition. In this way, the dynamic model of the dual-motor system as a whole is modeled, and the dynamic model of the dual-motor system based on the backlash elimination strategy is established. The model predictive position controller includes load position estimation, a state prediction model, rolling optimization, and an extended state observer. The reference position is used as the input to the model predictive position controller. After rolling optimization, the total torque required by the load is obtained. Then, a backlash elimination strategy is used to distribute the torque to obtain the torque T required by drive motor one and drive motor two. m1 and T m2 The actual position of the load is estimated and fed back to the model predictive position controller for closed-loop control; The tooth gap dead zone model includes equations (1) and (2): （1） （2） In equations (1) and (2) The difference in angular displacement between the drive gear and the load gear. The first derivative is represented as... 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 denoted as angular displacement of the load, k as stiffness coefficient of the gear, c as damping coefficient of the gear, m as gear ratio, and n as an adjustable parameter. The dynamic model of the dual-motor system based on the backlash dead zone model is as shown in equation (3): （3） In equation (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 τ represents the moment of inertia 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); , , , , , 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.

2. The model predictive controller for eliminating transmission backlash in a multi-servo drive system for heliostats as described in claim 1, characterized in that, The backlash dead zone model is used to describe the torque transmission between two gears when the system passes through backlash. When the gears are meshing, a spring-damped model is used to describe the torque transmission; when they are not meshing, a first-order spring model is used to describe the torque transmission.

3. The model predictive controller for eliminating transmission backlash in a multi-servo drive system for heliostats as described in claim 1, characterized in that, The backlash elimination strategy is as follows: when the load torque is 0 and the reference torque is 0, the two drive motors respectively provide the load with offset torques of equal magnitude and opposite direction to hold the load in place, preventing the load from rotating freely in the backlash; when the load needs to rotate in the forward direction, the reference torque increases in the forward direction, T m1 Gradually increase, T m2 As the torque gradually decreases, the net torque gradually increases, and the load begins to rotate in the forward direction. At this time, the gears of the two drive motors remain in close contact with the motors, achieving backlash-free transmission. When the reference torque continues to increase and exceeds T1, the torque required by the load is entirely provided by motor one. At this time, motor two will rotate with the load gear and will not provide power. Subsequently, the drive gear and the load gear remain in contact through the action of the motor torque and the load torque. When the reference torque continues to increase and exceeds T2, motor one maintains a constant torque T2, and the torque of motor two begins to increase. When the reference torque exceeds T3, the required torque is evenly distributed between the two motors.

4. The model predictive controller for eliminating transmission backlash in a multi-servo drive system for heliostats as described in claim 1, characterized in that, The state prediction model employs a control flow with one-time lag compensation: at time k, the controller writes the optimal input calculated in the previous time step. And read the current system state x. k Then, using the dual-motor system model and the current state x, k Predict the system state at the next time step, and then use the predicted state to calculate the optimal input at time k+1. And it acts on the dual-motor system at time k+1.

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