Method and system for decoupled distribution of planar motor heat losses
By iterating the peak shrinkage process and decoupling compensation updates, the problem of concentrated heat loss caused by uneven coil current distribution in planar motors is solved, and dynamic uniform distribution of coil current is achieved, which improves the operating accuracy and reliability of the motor and meets the requirements of real-time control.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- HARBIN INST OF TECH
- Filing Date
- 2026-06-24
- Publication Date
- 2026-07-21
Smart Images
Figure CN122437457A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of magnetic levitation motor motion control technology, specifically relating to a method and system for uniformly decoupling and distributing heat loss of a planar motor. Background Technology
[0002] With the continuous development of high-end manufacturing equipment, the demand for long-stroke, high-precision, six-degree-of-freedom tracking and positioning platforms is increasing. Planar motors, with their direct-drive characteristics and simplified mechanical structure, avoid the backlash and friction introduced by traditional transmission chains, and have become a key actuator for improving system control accuracy and bandwidth. However, a planar motor is essentially a nonlinear multi-input multi-output system: the current in the coil array serves as the system input, interacting with the magnetic field generated by the permanent magnet array, thereby outputting six degrees of freedom electromagnetic force and torque to drive the motion of the mover. In practical applications, the number of controllable coils often exceeds the six degrees of freedom of a rigid body, making the planar motor a typical overdrive system.
[0003] To achieve high-precision motion control, the control system needs to precisely decouple the generalized force and torque commands of the six degrees of freedom and rationally distribute them to each underlying coil. The pseudo-inverse matrix allocation method is currently the most commonly used decoupling allocation scheme due to its simple analytical form and high computational efficiency. However, this method relies entirely on linear mapping relationships of kinematics or electromagnetic forces for mathematical solutions, failing to fully consider the physical and thermodynamic constraints of the coil array in actual operation. Specifically, due to the uneven distribution of electromagnetic thrust coefficients in different positions, traditional pseudo-inverse allocation methods, which only optimize by minimizing the L2 norm of the current vector, often result in severely uneven current distribution in each coil. This imbalance further leads to concentrated local heat loss on the motor surface, causing thermal expansion stress deformation, and even thermal failure in extreme cases, severely restricting the long-term operational accuracy and reliability of the motor.
[0004] To address the aforementioned issue of uneven heat loss, some existing technologies attempt to employ precise numerical optimization methods based on quadratic programming. While these methods can solve for optimal allocation solutions with amplitude constraints, they tend to cause the current in some high-load coils to remain at boundary peak levels for extended periods, while adjacent coils remain idle, thus exacerbating the uneven heat loss of the coil array. Furthermore, when the theoretically calculated current exceeds the hardware amplitude limit, a simple unidirectional numerical truncation strategy can disrupt the physical mapping between force and torque, resulting in uncontrollable decoupling errors. Simultaneously, quadratic programming methods typically involve complex matrix operations and online inversion of high-dimensional matrices, leading to high computational complexity and long processing times per step, making it difficult to meet the demands of high-frequency real-time control in industrial settings.
[0005] Therefore, how to achieve dynamic and uniform distribution of coil current, reduce local heat loss, and meet real-time requirements while ensuring the decoupling accuracy of force and torque is a technical problem that urgently needs to be solved in this field. Summary of the Invention
[0006] To address the problem of concentrated local heat loss, thermal expansion deformation, and even thermal damage caused by uneven coil current distribution in overdrive planar motors, this invention provides a method and system for uncoupling and distributing heat loss uniformly in planar motors.
[0007] In a first aspect, the planar motor heat loss uniform decoupling distribution method of the present invention includes the following steps:
[0008] Step 1: Obtain the reference torque command for the current control cycle, as well as the electromagnetic force and torque coefficient matrix corresponding to the current pose of the motor mover;
[0009] Step 2: Based on the reference torque command and the electromagnetic force and torque coefficient matrix, execute the iterative peak contraction process; in each iteration, first perform nonlinear peak contraction on the coil current vector according to the current contraction threshold, and then update the coil current vector through decoupling compensation to obtain a new round of coil current vector;
[0010] Step 3: Determine if the iteration termination condition has been met; if yes, output the current coil current vector as a current decoupling command to the planar motor; if no, return to step 2 to continue iteration.
[0011] Preferably, step one specifically involves: receiving a six-degree-of-freedom reference torque command from the motion control system, and reading the electromagnetic force and torque coefficient matrix of the motor mover under the current pose from the electromagnetic model or lookup table.
[0012] Preferably, the iterative peak shrinkage process further includes an initialization step before starting: setting the iteration number to zero; calculating the initial unconstrained pseudo-reverse current allocation solution based on the electromagnetic force and torque coefficient matrix and the reference torque command, as the initial coil current vector; and setting the initial peak shrinkage threshold based on the ratio of the L2 norm of the initial coil current vector to the square root of the total number of coils.
[0013] Preferably, the method for determining the iteration termination condition in step three is as follows: determine whether the current shrinkage threshold is less than the maximum absolute value of each element of the coil current vector, and whether the current iteration number has not exceeded the maximum allowed iteration number; if both conditions are met, the iteration continues; if either condition is not met, the iteration terminates and the current coil current vector is output.
[0014] Preferably, the specific process of nonlinear peak contraction in step two is as follows: for each current value in the coil current vector, if its absolute value is greater than the current contraction threshold, the current direction is retained and the amplitude is limited to the current contraction threshold; if its absolute value is not greater than the current contraction threshold, the current value remains unchanged.
[0015] Preferably, the specific process of decoupling compensation update in step two is as follows: using the initial unconstrained pseudo-inverse current allocation solution, the current vector after nonlinear peak contraction, and the electromagnetic force and torque coefficient matrix, a new round of coil current vector is obtained through zero-space projection compensation calculation to ensure that the physical mapping relationship between force and torque remains unchanged.
[0016] Preferably, after each iteration, a threshold step operation is performed: the current shrinkage threshold is increased by a preset incremental step size, the iteration number is incremented by 1, and then the iteration termination condition is determined.
[0017] Secondly, the planar motor heat loss uniform decoupling distribution system of the present invention includes:
[0018] The data acquisition module is used to acquire the reference torque command for the current control cycle, as well as the electromagnetic force and torque coefficient matrix corresponding to the current position of the motor mover;
[0019] The iterative peak shrinkage module is used to combine the reference torque command and the electromagnetic force and torque coefficient matrix to execute the iterative peak shrinkage process; in each iteration, the coil current vector is nonlinearly shrunk according to the current shrinkage threshold, and a new round of coil current vector is obtained by decoupling compensation.
[0020] The termination judgment and output module is used to determine whether the iteration termination condition is met. If the condition is met, the current coil current vector is output as a current decoupling instruction. If the condition is not met, the iteration peak shrinkage module is driven to continue iterating.
[0021] Preferably, the iterative peak shrinkage module includes:
[0022] The initialization unit is used to set the iteration count to zero, calculate the initial unconstrained pseudo-inverse current distribution solution as the initial coil current vector, and set the initial peak shrinkage threshold.
[0023] A nonlinear shrinking unit is used to truncate the amplitude of each current value in the coil current vector according to the current shrinking threshold, while preserving the current direction;
[0024] The decoupling compensation unit is used to calculate the new coil current vector by using the initial unconstrained pseudo-inverse current distribution solution, the current vector after nonlinear contraction, and the electromagnetic force and torque coefficient matrix through zero-space projection compensation.
[0025] The threshold update unit is used to increase and shrink the threshold and update the iteration number according to the preset incremental step size after each iteration.
[0026] Preferably, the termination judgment and output module judges as follows: it judges whether the current shrinkage threshold is less than the maximum absolute value of each element of the coil current vector and whether the current iteration number does not exceed the maximum allowed iteration number; if both conditions are met, the iteration peak shrinkage module is triggered to continue iterating; if either condition is not met, the iteration is terminated and the current coil current vector is output to the power amplifier module.
[0027] The beneficial effects of this invention are as follows: Addressing the technical problem of uneven coil current distribution in overdriven planar motors leading to concentrated local heat loss, thermal expansion deformation, and even thermal damage, traditional pseudo-inverse distribution methods, which optimize by minimizing the current L2 norm, can minimize the sum of squares of the total current but cannot suppress current peaks in individual coils. This results in an imbalance in current distribution, with a few coils experiencing high loads and most coils experiencing low loads, thus causing localized heat concentration. This invention introduces a dynamic contraction threshold and a nonlinear peak contraction operation. In each iteration, it actively identifies and reduces excessively large amplitude components in the coil current vector while preserving their original sign and direction. Therefore, without altering the equivalence of electromagnetic force and torque output, it smoothly distributes the current peaks originally concentrated in a few coils across the entire coil array.
[0028] To ensure that the physical mapping relationship between force and torque is not disrupted, this invention further utilizes the null-space projection characteristics of the electromagnetic force and torque coefficient matrix for decoupling compensation updates, ensuring that the current vector after each contraction still accurately satisfies the desired six-degree-of-freedom force and torque commands. Through a threshold stepping strategy, the contraction threshold is gradually increased from its initial value, allowing the iterative process to approximate the optimal uniform distribution solution from coarse to fine, avoiding the decoupling errors caused by single-step forced reduction in traditional truncation methods.
[0029] Compared with existing technologies, this invention can significantly improve the spatial distribution uniformity of coil current without increasing theoretical decoupling error, fundamentally eliminate the phenomenon of local heat loss concentration, thereby effectively suppressing thermal expansion stress deformation and thermal damage risk, and ensuring the accuracy and reliability of long-term operation of planar motor.
[0030] Meanwhile, the iterative peak shrinkage algorithm used in this invention only involves basic operations such as vector element comparison, sign preservation, and null space projection. It does not require online inversion of high-dimensional matrices or complex quadratic programming solutions. The single-step computational complexity is low, which can meet the needs of high-frequency real-time control in industrial sites. Attached Figure Description
[0031] Figure 1 This is a block diagram of the overall architecture of the planar motor closed-loop control system in an embodiment of the present invention.
[0032] Figure 2 This is a flowchart illustrating the algorithm for the planar motor current decoupling and allocation method in an embodiment of the present invention.
[0033] Figure 3 This is a diagram showing the coil heat loss distribution of the existing pseudo-inverse distribution method.
[0034] Figure 4 This is a diagram showing the heat loss distribution of the coil in an embodiment of the present invention. Detailed Implementation
[0035] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. Although some embodiments of the present invention are shown in the drawings, it should be understood that the present invention can be implemented in various forms and should not be construed as limited to the embodiments set forth herein. Rather, these embodiments are provided to provide a more thorough and complete understanding of the present invention. It should be understood that the accompanying drawings and embodiments of the present invention are for illustrative purposes only and are not intended to limit the scope of protection of the present invention.
[0036] It should be understood that the various steps described in the method embodiments of the present invention may be performed in different orders and / or in parallel. Furthermore, the method embodiments may include additional steps and / or omit the steps shown. The scope of the present invention is not limited in this respect.
[0037] The term "comprising" and its variations as used herein are open-ended, meaning "including but not limited to"; the term "based on" means "at least partially based on"; and the term "one embodiment" means "at least one embodiment". Definitions of other terms will be given in the following description. It should be noted that the concepts of "first," "second," etc., mentioned in this invention are used only to distinguish different devices, modules, or units, and are not intended to limit the order of functions performed by these devices, modules, or units or their interdependencies.
[0038] It should be noted that the terms "a" and "a plurality of" used in this invention are illustrative rather than restrictive. Those skilled in the art should understand that, unless otherwise expressly indicated in the context, they should be understood as "one or more".
[0039] The names of the messages or information exchanged between the multiple devices in the embodiments of the present invention are for illustrative purposes only and are not intended to limit the scope of these messages or information.
[0040] In related technologies, traditional current decoupling and distribution methods for planar motors have significant shortcomings in terms of heat loss uniformity. To gain a deeper understanding of the causes and consequences of these shortcomings, a detailed analysis is first conducted from two dimensions: the electromagnetic principles and thermodynamic characteristics of planar motors.
[0041] A planar motor is essentially a multiple-input multiple-output (MIMO) system. The number of controllable coils in its bottom array typically far exceeds the six degrees of freedom of the actuator, making it a typical overdriven system. To achieve six-degree-of-freedom motion control, the control system needs to precisely decouple the desired generalized force and torque commands and distribute them appropriately to each bottom coil. In this process, the electromagnetic force and torque coefficient matrix... This describes the force and torque contributions generated by a unit current in each coil under the current mover pose. The matrix has a dimension of 6×m, where 6 corresponds to six degrees of freedom, and m is the total number of controllable coils in the coil array (usually m is much greater than 6). Due to the spatial distribution characteristics of the coil array and the non-uniformity of the permanent magnet's magnetic field, the electromagnetic thrust coefficient varies significantly at different locations: some coils are in strong magnetic field regions, generating a larger thrust per unit current; while other coils are in weak magnetic field regions, generating a smaller thrust per unit current. This physical characteristic is one of the fundamental reasons for the subsequent uneven current distribution.
[0042] Let's examine the mathematical essence of the pseudo-inverse allocation method. This method has become the most commonly used decoupling allocation scheme due to its simple calculation and clear analytical form. The algorithm seeks the solution with the minimum L2 norm (i.e., sum of squares) among the current vectors that satisfy the force-torque mapping relationship. Minimizing the L2 norm is equivalent to minimizing the total current energy. While this optimization objective is mathematically optimal, it has serious flaws from a physical implementation perspective: to minimize the total current energy, the algorithm concentrates the current on coils with higher thrust coefficients because these coils can generate the same force and torque with a smaller current. This is the fundamental reason why the pseudo-inverse allocation method leads to uneven current distribution. Specifically, when a coil is in a strong magnetic field region, its corresponding electromagnetic thrust coefficient is larger, and the pseudo-inverse solution will cause this coil to bear the main load; while coils in weak magnetic field regions are allocated smaller currents or even zero current. This "stronger gets stronger, weaker gets weaker" allocation pattern is mathematically optimal, but its drawbacks become apparent when a thermodynamic perspective is introduced.
[0043] The Joule heat loss of a coil is proportional to the square of the current, i.e., heat loss P equals the square of current I multiplied by resistance R. When the current is concentrated in a few coils, the heat loss of these coils increases exponentially. If a pseudo-reverse distribution method results in k high-load coils carrying more than 80% of the total current, then the heat generated by these k coils will be tens of times that of the remaining coils. This localized heat loss concentration can lead to a series of serious consequences: First, changes in the coefficient of thermal expansion in high-temperature regions cause uneven thermal deformation of the motor structure, disrupting the uniformity of the air gap between the mover and stator, thus affecting the linearity and positioning accuracy of the electromagnetic force output; second, long-term thermal cycling stress may accelerate the aging of the coil insulation layer, even causing coil burnout; third, localized temperature rise can alter the magnetic properties of the permanent magnet, potentially leading to irreversible demagnetization in extreme cases. These problems severely restrict the long-term operational accuracy and reliability of planar motors, becoming a key bottleneck limiting their widespread application in high-precision manufacturing equipment.
[0044] To address the shortcomings of pseudo-inverse allocation methods, some existing technologies attempt to employ precise numerical optimization methods based on quadratic programming. Quadratic programming methods use current amplitude boundaries as hard constraints to seek the optimal solution that satisfies these constraints. However, the optimization objective of these methods is usually still primarily minimizing current energy, and their allocation results exhibit a similar tendency to pseudo-inverse methods: concentrating the load on "high-efficiency" coils. This means that although quadratic programming can ensure that the current in each coil does not exceed the limit, the current in high-load coils remains at the boundary peak state for a long time, while adjacent coils are idle, and the unevenness of heat loss is not fundamentally improved. More importantly, when the theoretically calculated current exceeds the hardware amplitude limit (i.e., above the upper limit of the current amplitude), the problem persists. or below - Traditional methods often employ a unidirectional numerical cutoff strategy, directly limiting the over-limit current to a boundary value. This simplistic and crude approach disrupts the physical mapping relationship between force and torque, generating uncontrollable decoupling errors and severely reducing the motion control accuracy of the planar motor.
[0045] Besides decoupling accuracy and thermal homogenization issues, real-time computation is also a significant engineering constraint. Planar motor control systems require high real-time response capabilities, typically with control cycles on the order of microseconds to milliseconds. However, quadratic programming methods usually involve complex matrix operations and online inversion of high-dimensional matrices, resulting in a computational complexity of O(n log n). ), where m is the number of coils. When the coil array is large (e.g., m > 100), the calculation time for a single step can reach tens of milliseconds or even higher, making it difficult to meet the requirements of high-frequency real-time control in industrial settings. This means that while existing optimization methods are theoretically feasible, they are difficult to implement in practical engineering applications.
[0046] In summary, the current decoupling and distribution problem of planar motors is essentially an intersection of electromagnetics, thermodynamics, and control theory. Existing technologies address this problem with a clear "divide and conquer" approach: electromagnetics focuses on the accuracy of force-torque mapping, thermodynamics on heat loss distribution, and control theory on real-time performance and stability. However, these three aspects are inherently coupled: improving the accuracy of force-torque mapping may worsen heat distribution; improving heat distribution may sacrifice decoupling accuracy; and balancing both may reduce computational real-time performance. Therefore, how to achieve dynamic and uniform distribution of coil current, reduce local heat loss, and meet real-time requirements while ensuring accurate force-torque decoupling remains a long-standing but unresolved technical challenge in this field.
[0047] To address the series of problems existing in the aforementioned related technologies, this embodiment provides a method and system for uncoupling and distributing heat loss uniformly in a planar motor.
[0048] This invention provides a method for uniformly decoupling and distributing heat loss in a planar motor, comprising the following steps:
[0049] Step 1: Obtain the reference torque command for the current control cycle, as well as the electromagnetic force and torque coefficient matrix corresponding to the current pose of the motor mover;
[0050] Specifically, this step receives the six-degree-of-freedom reference torque command from the motion control system. And read the electromagnetic force and torque coefficient matrix of the motor mover in the current pose from the electromagnetic model or lookup table. Electromagnetic force and torque coefficient matrix This describes the electromagnetic force and torque contributions generated by each coil unit current under the current mover pose, serving as the foundational data for subsequent current decoupling and allocation. The matrix has a dimension of 6×m, where 6 corresponds to six degrees of freedom (three translational and three rotational), and m is the total number of controllable coils in the coil array. By accurately obtaining the coefficient matrix under the current pose, the mapping relationship between coil current and desired force / torque can be accurately established, providing precise physical model support for subsequent iterative peak contraction processes and ensuring the accuracy of decoupling allocation.
[0051] Traditional methods directly perform pseudo-inverse solving after obtaining the coefficient matrix, without any intervention to homogenize the subsequent current distribution. In contrast, this invention introduces an iterative peak shrinkage process after step one. The key is that the coefficient matrix obtained in step one is not only used for initial solution calculation but also repeatedly used in subsequent decoupling compensation updates. The null space projection characteristic ensures that the current vector after each iteration still accurately satisfies the force-torque mapping relationship. This lays the data foundation for the core objective of achieving thermal homogenization without sacrificing decoupling accuracy. Through precise data acquisition in step one, this invention guarantees the feasibility and accuracy of subsequent iterative optimization from the outset.
[0052] Step 2: Based on the reference torque command and the electromagnetic force and torque coefficient matrix, execute the iterative peak contraction process; in each iteration, first perform nonlinear peak contraction on the coil current vector according to the current contraction threshold, and then update the coil current vector through decoupling compensation to obtain a new round of coil current vector;
[0053] Specifically, this step is the core of this invention in solving the problem of uneven heat loss. From the coupling relationship between electromagnetic force and heat loss, coil heat loss is proportional to the square of the current; therefore, reducing the current peak value can reduce local heat loss with quadratic efficiency. However, directly reducing the current peak value disrupts the mapping relationship between force and torque, leading to decoupling errors. The innovation of this invention lies in: by introducing a dynamic shrinkage threshold and a nonlinear peak shrinkage operation, it actively identifies and reduces excessively large amplitude components in the coil current vector in each iteration, while preserving their original sign and direction. Thus, without changing the equivalence of electromagnetic force and torque output, the current peak value originally concentrated in a few coils is smoothly distributed across the entire coil array.
[0054] The iterative peak shrinkage process of this invention is essentially a feasible region shrinkage strategy. All coil current vectors that satisfy the force-torque mapping relationship constitute a linear affine space, in which each current vector can accurately generate the desired six-degree-of-freedom force and torque output. The pseudo-inverse solution is the point with the smallest L2 norm in this space, but this point is often located in a corner of the space, resulting in extremely uneven current distribution. This invention uses a nonlinear peak shrinkage operation to push the current vector away from the corners along the coordinate axis, moving it towards the central region of the space; then, through decoupling compensation update, the moved vector is projected back into the affine space. Under this operation, the current vector gradually converges towards a region with uniform current distribution while maintaining decoupling accuracy. Compared with the unidirectional truncation strategy of the prior art, the iterative shrinkage method of this invention can achieve smooth distribution of current peaks, avoiding decoupling errors caused by forced truncation. At the same time, through gradually increasing threshold control, the current distribution asymptotically transitions from an initially extremely uneven state to a uniform state, avoiding current distortion caused by excessive shrinkage.
[0055] Step 3: Determine if the iteration termination condition has been met; if yes, output the current coil current vector as a current decoupling command to the planar motor; if no, return to step 2 to continue iteration.
[0056] The termination judgment and output module makes the following judgments: it determines whether the current shrinkage threshold is less than the maximum absolute value of each element of the coil current vector and whether the current iteration number has not exceeded the maximum allowed iteration number; if both conditions are met, the iteration peak shrinkage module is triggered to continue iterating; if either condition is not met, the iteration is terminated and the current coil current vector is output to the power amplifier module.
[0057] Specifically, this step controls the timing of the iteration process termination. The termination condition needs to balance the heat loss homogenization effect with computational real-time performance: if termination is too early, the current distribution has not been sufficiently homogenized, and the problem of concentrated heat loss remains unresolved; if termination is too late, unnecessary computational overhead is added. This invention achieves adaptive termination by judging the relationship between the current shrinkage threshold and the maximum absolute value of the coil current vector, combined with the upper limit of the iteration count. When the shrinkage threshold reaches or exceeds the maximum absolute value of the coil current, it means that the nonlinear peak shrinkage operation can no longer further reduce the current peak value, and the current distribution has reached a homogenized state. At this point, the iteration terminates and the optimal current allocation solution is output. If the termination condition is not met, the process returns to step two to continue iterating, gradually bringing the current distribution closer to the optimal homogenized allocation state.
[0058] Furthermore, the iterative peak shrinkage process includes an initialization step before starting: setting the iteration number to zero; calculating the initial unconstrained pseudo-reverse current allocation solution based on the electromagnetic force and torque coefficient matrix and the reference torque command, as the initial coil current vector; and setting the initial peak shrinkage threshold based on the ratio of the L2 norm of the initial coil current vector to the square root of the total number of coils.
[0059] Specifically, the initialization step provides a reasonable starting point for the iterative peak shrinkage process.
[0060] Initialize the number of iterations .
[0061] The initial coil current vector is calculated using the pseudo-inverse method, i.e.:
[0062] ;
[0063] In the formula, Let the initial coil current vector be... This is the matrix of electromagnetic force and torque coefficients. For the pose, the electromagnetic force and torque coefficient matrix Describes the current mover pose The electromagnetic force and torque contribution generated by the unit current in each coil are shown below. Let be the transpose of the electromagnetic force and torque coefficient matrices. This solution is the least-norm 2 solution that satisfies the force-torque mapping relationship and can be used as a benchmark for subsequent iterative optimization.
[0064] Initial peak shrinkage threshold Set as the ratio of the L2 norm of the initial coil current vector to the square root of the total number of coils, i.e. In the formula, The total number of coils, This represents the vector L2 norm. This threshold reflects the average level of the initial current distribution. Setting the shrinkage threshold to this value means that in the first iteration, current components with amplitudes exceeding the average level will be shrunk, while current components with amplitudes below the average level will remain unchanged, thus achieving an initial homogenization effect of peak shaving and valley filling.
[0065] Furthermore, the specific process of nonlinear peak contraction in step two is as follows: for each current value in the coil current vector, if its absolute value is greater than the current contraction threshold, the current direction is retained and the amplitude is limited to the current contraction threshold; if its absolute value is not greater than the current contraction threshold, the current value remains unchanged.
[0066] Specifically, the nonlinear peak shrinkage operation is the core operator for current homogenization in this invention. From a signal processing perspective, this operation is essentially a nonlinear limiting function: for current components with amplitudes exceeding a threshold, they are compressed to the threshold value; for components with amplitudes below the threshold, they remain unchanged. Unlike traditional linear scaling or hard truncation, this invention employs a nonlinear shrinkage method that preserves the sign direction, effectively reducing current peaks while retaining the sign information of each coil current (corresponding to the direction of electromagnetic force), avoiding errors in force and torque direction caused by sign reversal. From the perspective of heat loss distribution, the peak shrinkage operation removes excess current from high-load coils. This removed current will be redistributed to low-load coils in subsequent decoupling compensation steps, thereby achieving spatial redistribution of heat load.
[0067] In a preferred embodiment, the nonlinear peak shrinkage operation is performed as follows: based on the current shrinkage threshold (the first... (shrinkage threshold in the next iteration) For the current coil current vector (the first...) (coil current assignment vector in the next iteration) Perform an element-wise nonlinear peak shrinkage operation. This operation preserves the sign and direction of the peak by dividing by the absolute value of the element and truncates its amplitude to a shrinkage threshold. The specific calculation formula for the nonlinear peak shrinkage operation is as follows:
[0068] ;
[0069] In the formula, For the first The coil current vector output after the nonlinear peak contraction process is the current result after amplitude limiting and truncation.
[0070] This step is for Each coil current element within the circuit is judged individually:
[0071] When the amplitude of the single-channel current is greater than the first Shrinkage threshold in the next iteration At this time: the original positive and negative directions of the current are preserved, and the current amplitude is forcibly limited to [value missing]. ;
[0072] When the amplitude of the single-channel current is less than or equal to At this time: the current value of the coil remains completely unchanged and no interruption is performed.
[0073] Furthermore, the specific process of decoupling compensation update in step two is as follows: using the initial unconstrained pseudo-inverse current allocation solution, the current vector after nonlinear peak contraction, and the electromagnetic force and torque coefficient matrix, a new round of coil current vector is obtained through zero-space projection compensation calculation to ensure that the physical mapping relationship between force and torque remains unchanged.
[0074] Specifically, decoupling compensation update is a crucial step in ensuring the accuracy of force and torque decoupling during the iteration process. It is implemented based on the null space projection theory in linear algebra: when a modification is applied to the current vector (such as nonlinear peak shrinkage), the modified current vector may no longer precisely satisfy the force and torque mapping relationship. To restore this mapping relationship, a compensation term located in the null space of the coefficient matrix needs to be added to the current vector while keeping the modification direction unchanged. Since vectors in the null space do not generate any electromagnetic force or torque, the compensation operation will not change the desired force and torque output, but it enables the current vector to gradually approach the optimal uniform distribution solution while satisfying physical constraints. In specific implementation, this invention uses the initial unconstrained pseudo-inverse solution as a benchmark, projecting the difference between the shrunken current vector and the initial solution onto the value space of the coefficient matrix, thereby calculating the current component that needs compensation. This design ensures lossless decoupling accuracy during the iteration process, meaning that the heat loss homogenization operation does not introduce additional force and torque errors.
[0075] In a preferred embodiment, the specific calculation process for decoupling compensation update is as follows:
[0076] Using the initial unconstrained solution And after the first The coil current vector output after sub-nonlinear peak contraction processing Combining the null-space projection characteristics of the electromagnetic force and torque coefficient matrices, the coil current distribution vector for the next iteration is calculated and updated:
[0077] ;
[0078] In the formula, For the first The coil current assignment vector in the next iteration.
[0079] Furthermore, after each iteration, a threshold step operation is performed: the current shrinkage threshold is incremented by a preset incremental step size, the iteration count is incremented by 1, and then the iteration termination condition is determined.
[0080] Specifically, the threshold step operation controls the convergence speed and homogenization accuracy of the iterative process. From the perspective of optimization theory, in the early stages of iteration, the threshold is low, and only large-amplitude current peaks are contracted; as the iteration progresses, the threshold gradually increases, and more and more current components are included in the contraction range, and the current distribution gradually becomes more uniform. If the threshold increases too quickly, it may lead to unstable convergence; if it increases too slowly, the number of iterations increases, and the computational cost rises. This invention uses a fixed incremental step size. The linear increasing strategy, through the reasonable selection of step size (such as...) Using an initial threshold of 5% to 10% can achieve a good balance between convergence speed and homogenization effect. After each iteration, the number of iterations is... Add 1, which is used for subsequent termination condition judgment.
[0081] Furthermore, the method for determining the iteration termination condition in step three is as follows: determine whether the current shrinkage threshold is less than the maximum absolute value of each element of the coil current vector, and whether the current iteration number has not exceeded the maximum allowed iteration number; if both conditions are met, the iteration continues; if either condition is not met, the iteration terminates and the current coil current vector is output.
[0082] Specifically, the design of the iteration termination condition needs to consider both the homogenization of the solution and the real-time computation. The first condition determines the current shrinkage threshold. Is it still less than the infinity norm of the coil current vector (i.e., the maximum absolute value of each element)? If so, it means that there are still components in the current current vector whose amplitude exceeds the shrinkage threshold, and the nonlinear peak shrinkage operation still has room for further homogenization; if not, that is, the shrinkage threshold has reached or exceeded the maximum absolute value of the current, then all current components have been shrunk or have never exceeded the threshold, the current distribution has reached or is close to a uniform state, and continuing iteration will not produce significant improvement. The second condition determines the current iteration number. Is it less than or equal to the maximum allowed number of iterations? This prevents computational resources from being exhausted when iteration fails to converge in extreme cases. Iteration continues only when both conditions are met; if either condition is not met, iteration terminates and the current coil current vector is output as the final current decoupling instruction.
[0083] In a preferred embodiment, the specific process for determining the iteration termination condition is as follows:
[0084] Determine the current number Shrinkage threshold in the next iteration Is it strictly less than the first? Coil current allocation vector in the next iteration infinite norm And the current iteration number Is it less than or equal to the maximum allowed number of iterations? ;
[0085] If both conditions are met, the next iteration continues; if either condition is not met, the iteration terminates and the current coil current vector is output.
[0086] Example:
[0087] See Figure 2 The specific process of the planar motor current decoupling allocation algorithm provided in this embodiment of the invention is as follows:
[0088] Step S1: System state input and iterative initialization. Obtain the six-degree-of-freedom reference torque command for the current control cycle. , and the electromagnetic force and torque coefficient matrix K(q) of the motor mover at the current position and attitude.
[0089] Step S2: State vector and threshold initialization. Initialize the number of iterations. The initial unconstrained pseudo-reverse current distribution solution is calculated as follows:
[0090] ;
[0091] At the same time, initialize the peak shrinkage threshold:
[0092] ;
[0093] Step S3: Determine the termination condition of the iteration loop. Determine the current iteration... Shrinkage threshold in the next iteration Is it strictly less than the first? Coil current allocation vector in the next iteration infinite norm And the current iteration number Is it less than or equal to the maximum allowed number of iterations? If both conditions are met, proceed to step S4; if either condition is not met, terminate the iteration loop and proceed directly to step S7.
[0094] Step S4: Nonlinear peak contraction of coil current. Based on the current contraction threshold. For the current coil current vector Perform element-wise nonlinear peak shrinkage operation: if the absolute value of the current is greater than the threshold, shrink the amplitude to the threshold and retain the original sign and direction; otherwise, leave it unchanged.
[0095] Step S5: Force and torque decoupling compensation update. Utilizing the initial unconstrained solution... And after the first The coil current vector output after sub-nonlinear peak contraction processing Combining the null-space projection characteristics of the electromagnetic force and torque coefficient matrix, the first... Coil current allocation vector in the next iteration .
[0096] Step S6: Threshold stepping and iteration count update. Update the current shrinkage threshold by a preset increment step. Increment the threshold to obtain the shrinkage threshold for the next iteration. Simultaneously, update the iteration count. Increment by 1, and return to step S3 to execute the next iteration.
[0097] Step S7: Output current decoupling command. A coil current decoupling command that meets the iteration termination condition is sent to the power amplifier module to drive the planar motor.
[0098] This invention also provides a planar motor heat loss uniformity decoupling distribution system, comprising:
[0099] The data acquisition module is used to acquire the reference torque command for the current control cycle, as well as the electromagnetic force and torque coefficient matrix corresponding to the current position of the motor mover;
[0100] The iterative peak shrinkage module is used to combine the reference torque command and the electromagnetic force and torque coefficient matrix to execute the iterative peak shrinkage process; in each iteration, the coil current vector is nonlinearly shrunk according to the current shrinkage threshold, and a new round of coil current vector is obtained by decoupling compensation.
[0101] The termination judgment and output module is used to determine whether the iteration termination condition is met. If the condition is met, the current coil current vector is output as a current decoupling instruction. If the condition is not met, the iteration peak shrinkage module is driven to continue iterating.
[0102] Specifically, see Figure 1 The diagram shows the overall closed-loop control architecture of the system. The external position reference command and the actual pose signal output by the pose calculation module are interpolated at the pose deviation calculation node, and the deviation signal is input to the position closed-loop controller. The position closed-loop controller outputs a six-degree-of-freedom reference torque command to the iterative peak contraction module. The iterative peak contraction module performs iterative peak contraction and decoupling compensation calculations, and outputs a coil current command to the power amplifier. The power amplifier drives the coil array inside the planar motor to generate electromagnetic force, driving the planar motor mover to complete multi-degree-of-freedom motion. The laser displacement sensor collects the motion signal of the planar motor mover in real time, transmits it to the pose calculation module to convert it into the actual pose, and sends it back to the deviation calculation node to form closed-loop control.
[0103] Furthermore, the iterative peak shrinkage module includes:
[0104] The initialization unit is used to set the iteration count to zero, calculate the initial unconstrained pseudo-inverse current distribution solution as the initial coil current vector, and set the initial peak shrinkage threshold.
[0105] A nonlinear shrinking unit is used to truncate the amplitude of each current value in the coil current vector according to the current shrinking threshold, while preserving the current direction;
[0106] The decoupling compensation unit is used to calculate the new coil current vector by using the initial unconstrained pseudo-inverse current distribution solution, the current vector after nonlinear contraction, and the electromagnetic force and torque coefficient matrix through zero-space projection compensation.
[0107] The threshold update unit is used to increase and shrink the threshold and update the iteration number according to the preset incremental step size after each iteration.
[0108] While the invention has been described herein with reference to specific embodiments, it should be understood that these embodiments are merely examples of the principles and applications of the invention. Therefore, it should be understood that many modifications can be made to the exemplary embodiments, and other arrangements can be designed without departing from the spirit and scope of the invention as defined by the appended claims. It should be understood that different dependent claims and features described herein can be combined in ways different from those described in the original claims. It is also understood that features described in conjunction with individual embodiments can be used in other described embodiments.
Claims
1. A method for uniformly decoupling and distributing heat loss in a planar motor, characterized in that, Includes the following steps: Step 1: Obtain the reference torque command for the current control cycle, as well as the electromagnetic force and torque coefficient matrix corresponding to the current pose of the motor mover; Step 2: Based on the reference torque command and the electromagnetic force and torque coefficient matrix, execute the iterative peak contraction process; In each iteration, the coil current vector is first subjected to nonlinear peak shrinkage according to the current shrinkage threshold, and then a new coil current vector is obtained through decoupling compensation. Step 3: Determine if the iteration termination condition has been met; if yes, output the current coil current vector as a current decoupling command to the planar motor; if no, return to step 2 to continue iteration.
2. The planar motor heat loss uniform decoupling distribution method according to claim 1, characterized in that, Step one specifically involves receiving a six-degree-of-freedom reference torque command from the motion control system and reading the electromagnetic force and torque coefficient matrix of the motor mover under its current pose from the electromagnetic model or lookup table.
3. The planar motor heat loss uniform decoupling distribution method according to claim 2, characterized in that, Before the iterative peak shrinkage process is started, an initialization step is also included: setting the iteration number to zero; calculating the initial unconstrained pseudo-reverse current allocation solution based on the electromagnetic force and torque coefficient matrix and the reference torque command, as the initial coil current vector; and setting the initial peak shrinkage threshold based on the ratio of the L2 norm of the initial coil current vector to the square root of the total number of coils.
4. The planar motor heat loss uniform decoupling distribution method according to claim 1, characterized in that, The method for determining the termination condition in step three is as follows: determine whether the current shrinkage threshold is less than the maximum absolute value of each element of the coil current vector, and whether the current iteration number has not exceeded the maximum allowed iteration number; if both conditions are met, the iteration continues; if either condition is not met, the iteration terminates and the current coil current vector is output.
5. The planar motor heat loss uniform decoupling distribution method according to claim 1, characterized in that, The specific process of nonlinear peak contraction in step two is as follows: for each current value in the coil current vector, if its absolute value is greater than the current contraction threshold, the current direction is retained and the amplitude is limited to the current contraction threshold; if its absolute value is not greater than the current contraction threshold, the current value remains unchanged.
6. The planar motor heat loss uniform decoupling distribution method according to claim 3, characterized in that, The specific process of decoupling compensation update in step two is as follows: using the initial unconstrained pseudo-inverse current allocation solution, the current vector after nonlinear peak contraction, and the electromagnetic force and torque coefficient matrix, a new round of coil current vector is obtained through zero-space projection compensation calculation to ensure that the physical mapping relationship between force and torque remains unchanged.
7. The planar motor heat loss uniform decoupling distribution method according to claim 1, characterized in that, After each iteration, a threshold step operation is performed: the current shrinkage threshold is incremented by a preset incremental step size, the iteration count is incremented by 1, and then the iteration termination condition is checked.
8. A planar motor heat loss uniform decoupling distribution system, the system being used to implement the method described in any one of claims 1 to 7, characterized in that, include: The data acquisition module is used to acquire the reference torque command for the current control cycle, as well as the electromagnetic force and torque coefficient matrix corresponding to the current position of the motor mover; The iterative peak shrinkage module is used to execute the iterative peak shrinkage process by combining the reference torque command and the electromagnetic force and torque coefficient matrix. In each iteration, the coil current vector is nonlinearly peak-shrinked according to the current shrinkage threshold, and a new coil current vector is obtained by decoupling compensation. The termination judgment and output module is used to determine whether the iteration termination condition is met. If the condition is met, the current coil current vector is output as a current decoupling instruction. If the condition is not met, the iteration peak shrinkage module is driven to continue iterating.
9. The planar motor heat loss uniform decoupling distribution system according to claim 8, characterized in that, The iterative peak shrinkage module includes: The initialization unit is used to set the iteration count to zero, calculate the initial unconstrained pseudo-inverse current distribution solution as the initial coil current vector, and set the initial peak shrinkage threshold. A nonlinear shrinking unit is used to truncate the amplitude of each current value in the coil current vector according to the current shrinking threshold, while preserving the current direction; The decoupling compensation unit is used to calculate the new coil current vector by using the initial unconstrained pseudo-inverse current distribution solution, the current vector after nonlinear contraction, and the electromagnetic force and torque coefficient matrix through zero-space projection compensation. The threshold update unit is used to increase and shrink the threshold and update the iteration number according to the preset incremental step size after each iteration.
10. The planar motor heat loss uniform decoupling distribution system according to claim 8, characterized in that, The termination judgment and output module makes the following judgments: it determines whether the current shrinkage threshold is less than the maximum absolute value of each element of the coil current vector and whether the current iteration number has not exceeded the maximum allowed iteration number; if both conditions are met, the iteration peak shrinkage module is triggered to continue iterating; if either condition is not met, the iteration is terminated and the current coil current vector is output to the power amplifier module.