A model predictive control method and system for industrial 3D printers

Abstract

The present invention proposes a model predictive control method and system for an industrial 3D printer, the method comprising: obtaining basic information of a motor in the 3D printer; calculating the state information of the motor at this moment according to the basic information of the motor; constructing a model predictive controller; using the model predictive controller to calculate the torque and flux of the motor according to the state information, and performing beat compensation to obtain an optimal voltage vector, thereby controlling the motor in the 3D printer; the system is used to implement the above method. The present invention adopts an open-winding brushless DC motor, increases torque output on the original motor, and adopts model predictive control to cope with high requirements for printing quality, as well as tracking of complex paths and smooth output of torque.

Description

Technical Field

[0001] The present invention relates to a three-dimensional printer control method and system, and in particular to a model prediction control method and system for an industrial-grade three-dimensional printer. Background Art

[0002] This section merely provides background information related to the present disclosure and is not necessarily prior art.

[0003] In recent years, as the industrial demand for 3D printers has increased, the requirements for 3D printers have also increased. As the speed continues to increase, the disadvantage of stepper motors that they are prone to losing steps at high speeds has become apparent, and in order to reduce torque pulsation, open-winding brushless DC motors have begun to be used.

[0004] However, in the prior art, the above method has some defects, including:

[0005] First, stepper motors are prone to step loss when running at high speeds. Especially at higher speeds, the control accuracy and stability of stepper motors are difficult to guarantee, resulting in reduced printing accuracy and even printing failure. Although some problems can be alleviated by increasing the drive current or using high-precision drive algorithms, it is still difficult to completely avoid the instability of steps when running at high speeds, which limits its use in high-demand industrial applications. Secondly, traditional brushless DC motors are prone to torque pulsation at low speeds, affecting the stability of the printing process. Although some methods have proposed technologies to reduce torque pulsation, in practical applications, it is still difficult to effectively reduce the impact of torque pulsation under a wide range of working conditions. Finally, the control strategies currently adopted by many 3D printers have a slow response speed when facing rapidly changing working conditions, especially under high loads or complex motion trajectories, and may experience lag, affecting the printing effect. This is because the existing control algorithms cannot accurately predict changes in the printing process in real time, resulting in a large deviation between motion control and actual conditions.

[0006] It should be noted that the information disclosed in the above background technology section is only used to enhance the understanding of the background of the present disclosure, and therefore may include information that does not constitute the prior art known to ordinary technicians in the field. Summary of the invention

[0007] Purpose of the invention: The technical problem to be solved by the present invention is to provide a model predictive control method and system for an industrial-grade 3D printer in view of the deficiencies in the prior art.

[0008] In order to solve the above technical problems, the present invention discloses a model predictive control method and system for an industrial 3D printer, wherein the method comprises:

[0009] Step 1, obtaining basic information of the motor in the 3D printer, the basic information including: a given speed value, a rotor angle and a three-phase current value;

[0010] Step 2, calculating the state information of the motor at this moment according to the basic information of the motor, the state information including: speed, back electromotive force value and torque change;

[0011] Step 3, construct a model predictive controller;

[0012] Step 4, according to the state information, use a model predictive controller to calculate the torque and flux of the motor, and perform beat compensation to obtain an optimal voltage vector, and control the motor in the 3D printer accordingly to complete the model predictive control of the industrial-grade 3D printer.

[0013] Furthermore, the motor in step 1 is an open-winding brushless DC motor.

[0014] Furthermore, the motor model of the open-winding brushless DC motor is as follows:

[0015] The torque equation of the open-winding brushless DC motor is established as follows:

[0016]

[0017] Among them, e a 、e b 、e c is the back electromotive force of the three phases of the open-winding brushless DC motor; i a 、i b 、i c is the three-phase current of the open-winding brushless DC motor, T e is the output electromagnetic torque, and ω is the mechanical angular velocity of the rotor of the open-winding brushless DC motor.

[0018] Furthermore, the model predictive controller described in step 3 includes:

[0019] Switch tube function conversion module, motor prediction model module, delay compensation module, prediction value calculation module and value function evaluation module; among them,

[0020] The switch tube function conversion module converts the voltage vector to be traversed according to the switch tube function and outputs the calculated winding voltage value (u a ,u b ,u c );

[0021] The motor prediction model module calculates the winding voltage value (u a ,u b ,u c) and the current value sampled at time k (i a ,i b ,i c ), predict the current value of k+1 control period [i d (k+1),i q (k+1)];

[0022] The delay compensation module is used to calculate the predicted current value [i d (k+2),i q (k+2)];

[0023] The predicted value calculation module calculates the torque T by combining the calculated predicted current value with the motor model. e (k+2) and stator flux value ψ s (k+2);

[0024] The value function evaluation module is used to set standards and select the optimal voltage vector from all voltage vectors.

[0025] Furthermore, in the switch tube function conversion module, the switch tube function vector is expressed as follows:

[0026]

[0027] in, The signal of the n2th switch tube in the n1th inverter is 0 or 1, indicating whether the switch tube is on or off; the switch tube function of the open-winding brushless DC motor is expressed as:

[0028]

[0029] or

[0030]

[0031] Among them, (u a ,u b ,u c ) represents the calculated winding voltage value, u a Indicates the calculated voltage of phase A, u b Indicates the calculated voltage of phase B, u c Indicates the calculated voltage of phase C, U dc represents the bus voltage, and fix is ​​the round-off function.

[0032] Furthermore, the motor prediction model module includes:

[0033] The three-phase currents of phase A, phase B, and phase C can be obtained by reading the sensor as (i a ,i b ,ic ), through C 3 / 2 Transformation and C 2r / 2s Transformation to obtain the current value (i d ,i q ), as follows:

[0034]

[0035] According to the mathematical relationship between current and voltage, we get:

[0036]

[0037] Among them, R s represents phase resistance, L represents inductance, ψ f is the stator flux value, ω is the mechanical angular velocity of the open-winding brushless DC motor rotor; Euler forward discretization and simplification are performed to obtain:

[0038]

[0039] Among them, [i d (k+1),i q (k+1)] is the current value of the k+1 control period, T s To control the cycle.

[0040] Furthermore, the delay compensation module includes:

[0041]

[0042] Among them, [i d (k+2),i q (k+2)] is the current value predicted during the actual control period k+2.

[0043] Furthermore, the predicted value calculation module includes:

[0044]

[0045] Among them, T e (k+2) and ψ s (k+2) is the electromagnetic torque and stator flux value used for motor performance output.

[0046] Furthermore, the value function evaluation module includes:

[0047] J=λ·|ψ s (k+2)-ψ s_ref |+|T e (k+2)-T e_ref |

[0048] Among them, λ is the weight factor, ψs_ref and T e_ref Indicates the given values ​​of stator flux and electromagnetic torque;

[0049] All predetermined voltage vectors are traversed, and a voltage vector corresponding to the minimum value of the cost function J is selected, and sent to the open-winding brushless DC motor controller for controlling the open-winding brushless DC motor.

[0050] The present invention also proposes a model prediction control system for an industrial 3D printer, which is used to implement the above method, including:

[0051] Switch tube function conversion module, motor prediction model module, delay compensation module, prediction value calculation module and value function evaluation module; among them,

[0052] The switch tube function conversion module converts the voltage vector to be traversed according to the switch tube function and outputs the calculated winding voltage value (u a ,u b ,u c );

[0053] The motor prediction model module calculates the winding voltage value (u a ,u b ,u c ) and the current value sampled at time k (i a ,i b ,i c ), predict the current value of k+1 control period [i d (k+1),i q (k+1)];

[0054] The delay compensation module is used to calculate the predicted current value [i d (k+2),i q (k+2)];

[0055] The predicted value calculation module calculates the torque T by combining the calculated predicted current value with the motor model. e (k+2) and stator flux value ψ s (k+2);

[0056] The value function evaluation module is used to set standards and select the optimal voltage vector from all voltage vectors.

[0057] Beneficial effects:

[0058] The present invention adopts an open-winding brushless DC motor as the main control object and uses a model predictive control algorithm as the main control method. On this basis, in order to reduce the beat property of the control, a deadbeat controller is designed. The value function is designed according to the 1-norm. This can not only improve the stability of the system control, but also improve the reliability of the system. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] The present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments, and the above and / or other advantages of the present invention will become more clear.

[0060] Figure 1 It is a schematic diagram of the process of the present invention.

[0061] Figure 2 It is a structural schematic diagram of the deadbeat controller provided by the present invention.

[0062] Figure 3 The invention provides a voltage vector diagram of an open-winding brushless DC motor.

[0063] Figure 4 It is a logic block diagram of the system of the present invention. DETAILED DESCRIPTION

[0064] The present invention provides a model prediction control method and system for an industrial 3D printer, which are used to achieve high-precision and stable control of the industrial 3D printer under high-speed conditions.

[0065] In the first aspect, the present invention provides a model predictive control method for an industrial 3D printer, wherein the given speed is obtained through a controller, the real-time motor rotor angle and three-phase current value are obtained from a sensor, and the speed, back electromotive force value and torque change at this moment are calculated based on the given speed, and the values ​​are input into the model predictive controller. In the model predictive controller, the torque and flux are calculated based on the above values, and the beat compensation is performed. Thus, the entire voltage vector set is traversed, and the optimal voltage vector is found according to the value function to realize the control of the open-winding brushless DC motor.

[0066] According to a model predictive control method for an industrial 3D printer provided by the present invention, a mathematical model of an open-winding brushless DC motor is established, including establishing a torque equation of the open-winding brushless DC motor:

[0067]

[0068] where e a 、e b 、e c It is expressed as the back electromotive force of the three phases of the motor; i a 、i b 、i cExpressed as the three-phase current of the motor, T e It is represented as the output electromagnetic torque, and ω is represented as the motor speed.

[0069] Design the model equation in model predictive control through the voltage equation:

[0070] Establish the switch function as vector = [P 1a P 1b … P 2e P 2f ],

[0071] When the switch tube needs to be turned on, it is assigned a value of 1, and when the switch tube needs to be turned off, it is assigned a value of 0. a Indicates the calculated voltage of phase A, u b Indicates the calculated voltage of phase B, u c Indicates the calculated voltage of phase C, U dc represents the bus voltage, fix is ​​the round-off function;

[0072] So the voltage can be expressed as:

[0073] or By C 3 / 2 Transformation and C 2r / 2s The voltage value in the dq coordinate system is obtained by transformation.

[0074]

[0075] For the current, the sensor can read the current of the three phases A, B, and C, and pass it through C 3 / 2 Transformation and C 2r / 2s The current value in the dq coordinate system is obtained by transformation. The specific change formula is as follows:

[0076]

[0077] Substituting the values ​​into this, we can simplify:

[0078]

[0079] Thus, the current value at the kth moment can be obtained, that is, the current at the kth moment is obtained through the sensor.

[0080] The model predictive controller obtains the current at the k+1 and k+2 moments to calculate the electromagnetic torque and stator flux that need to be predicted. The specific method is as follows:

[0081] Establish the mathematical relationship between current and voltage, where R s represents phase resistance, L represents inductance, ψ f is the stator flux value.

[0082]

[0083] By performing Euler forward discretization on the formula, we can obtain:

[0084]

[0085] Due to the hysteresis of current prediction, the current is calculated backward for the next control cycle, and the current value of the dq axis at the k+2th moment is calculated as:

[0086]

[0087] Therefore, the electromagnetic torque value and stator flux prediction value obtained by the prediction model under deadbeat control can be obtained as follows:

[0088]

[0089] The optimal voltage vector is selected according to the 1-norm design value function, including:

[0090] J=λ·|ψ s (k+2)-ψ s_ref |+|T e (k+2)-T e_ref |

[0091] Among them, λ is the weight factor, and ref represents the given value.

[0092] Traverse all the given voltage vectors ( Figure 3 All the voltage vectors in the voltage vector diagram shown can be understood as existing originally), and the voltage vector corresponding to the minimum value of the value function J is selected and sent to the open-winding brushless DC motor controller to control the open-winding brushless DC motor.

[0093] In a second aspect, the present invention further provides a model predictive control system for an industrial 3D printer, comprising:

[0094] The open-winding brushless DC motor mathematical model building module is used to build the prediction model during model prediction;

[0095] A deadbeat controller module, used for performing deadbeat compensation on a model predictive control method based on a deadbeat control method;

[0096] The control output module uses the constructed value function to select the optimal voltage vector to minimize the value function value and sends it to realize the control of the open-winding brushless DC motor.

[0097] In a third aspect, the present invention provides an electronic control device, comprising a controller, a storage, a central processing unit, a host computer, and a high-level computer control program running on the storage used, characterized in that the high-level control language program can implement any of the steps of the above-mentioned model predictive control method for an industrial-grade 3D printer.

[0098] In a fourth aspect, the present invention provides a permanent readable and writable storage medium on which a written computer program can be stored, and when the computer program is processed by a central processing unit, the steps of the model predictive control method for an industrial-grade 3D printer described in any one of the above can be implemented.

[0099] In a fifth aspect, the present invention provides a computer program platform, covering a computer program, characterized in that the computer program, when executed by a central processing unit, can implement the steps of any of the above-mentioned model predictive control methods for industrial-grade 3D printers.

[0100] Example:

[0101] Embodiments of the present invention provide a model predictive control method and system for an industrial-grade three-dimensional printer.

[0102] Figure 1 The flow chart of the industrial 3D printer model prediction control method provided by the present invention includes but is not limited to the following steps:

[0103] Step 1: Establish the mathematical model of the open-winding brushless DC motor.

[0104] Step 101: First, establish the torque equation of the open-winding brushless DC motor:

[0105]

[0106] Step 102: Establish a model predictive control calculation model based on the torque equation:

[0107] Establish the switch function as vector = [P 1a P 1b … P 2e P 2f ],

[0108] So the voltage can be expressed as:

[0109]

[0110] For example, the voltage vector to be calculated is (100001 010010), then through the first calculation formula, the relationship is as follows:

[0111]

[0112] By C 3 / 2 Transformation and C 2r / 2s Transform to get the voltage value in the dq coordinate system. For example, the rotor angular velocity is but:

[0113]

[0114] For current, the current i of the three phases A, B, and C can be obtained by reading the sensor. a 、i b 、i c , passing it through C 3 / 2 Transformation and C 2r / 2s Transform to obtain the current value i in the dq coordinate system d 、i q The specific change formula is as follows:

[0115]

[0116] Substituting the values ​​into this, we can simplify:

[0117]

[0118] Establish the mathematical relationship between current and voltage,

[0119]

[0120] By performing Euler forward discretization on the formula, we can obtain:

[0121]

[0122] Simplifying, we get:

[0123]

[0124] The calculated torque is:

[0125]

[0126] And the electromagnetic flux value,

[0127]

[0128] Step 2: Design a deadbeat controller to compensate for the deadbeat of the model predictive control algorithm.

[0129] Figure 2 This is the deadbeat controller principle of the present invention, such as Figure 2 As shown, it performs sampling in the sampling period, calculates the electromagnetic torque and stator flux value in the sending period, and performs compensation through calculation.

[0130] Step 201: Due to the hysteresis of current prediction, the current is calculated backward to the next control cycle.

[0131]

[0132] Step 202: Thus, the predicted electromagnetic torque value under deadbeat control can be obtained.

[0133]

[0134] And the predicted value of stator flux,

[0135]

[0136] Step 203: Substitute the results of all voltage vector calculations into the value function to find the voltage vector with the smallest value of the value function through rolling optimization, and send it to the motor controller to generate a PWM wave to act on the switch tube of the inverter.

[0137] Figure 3 All the synthetic voltage vectors of the open-winding brushless DC motor are obtained by vector calculation through two inverters and are distributed on the vertices of two hexagons of different sizes. The voltage vectors traversed by the model prediction algorithm are among these voltage vectors. Because they are synthesized by two inverters, these voltage vectors can be obtained through calculation. Based on the above theory, 49 voltage vectors can be calculated, of which 6 voltage vectors have an amplitude of √3U dc The large vector of 12 voltage vectors has an amplitude of 3 / 2U dc The mid vector of the 12 voltage vectors is √3 / 2U dc The voltage vector on the largest hexagon is called the large vector, the middle hexagon is called the medium vector, the inner hexagon is called the small vector, and the middle dot is the zero vector. In the switch tube function, the large vector and the zero vector are calculated using the first formula, and the medium vector and the small vector are calculated using the second formula.

[0138] Figure 4 The logic block diagram of the industrial 3D printer model predictive control system is shown in Figure 2. Figure 4As shown, the given speed is obtained by the microprocessor and compared with the actual sampled speed, and then input into the PI controller to obtain the given torque. In addition, the sampled three-phase current and rotor angle are obtained through the sensor, and the current speed is calculated by this. In the model prediction module, the dq axis current obtained by the sampled current and the voltage corresponding to each voltage vector are calculated and converted into dq axis, and the obtained value is input into the deadbeat controller. The optimal voltage vector is obtained by rolling optimization and traversal calculation through the value function and sent to the controller. The controller generates the required PWM wave and inputs it into the inverter, which acts on the open-winding brushless DC motor to form a closed loop.

[0139] On the other hand, the present invention also provides a computer program product, wherein the computer program includes a computer program stored in a permanent readable and writable storage medium, wherein the computer program includes program instructions, and when the program instructions are responded to by a central processing unit, the central processing unit is able to execute the industrial-grade three-dimensional printing model prediction control method provided in the above-mentioned embodiments.

[0140] In a specific implementation, the present application provides a computer storage medium and a corresponding data processing unit, wherein the computer storage medium can store a computer program, and when the computer program is executed by the data processing unit, the invention content of the model predictive control method and system for an industrial 3D printer provided by the present invention and some or all steps in each embodiment can be executed. The storage medium can be a disk, an optical disk, a read-only memory (ROM) or a random access memory (RAM), etc.

[0141] Those skilled in the art can clearly understand that the technical solutions in the embodiments of the present invention can be implemented by means of computer programs and their corresponding general hardware platforms. Based on such an understanding, the technical solutions in the embodiments of the present invention can be essentially or partly contributed to the prior art in the form of computer programs, i.e., software products, which can be stored in a storage medium and include several instructions for enabling a device including a data processing unit (which can be a personal computer, a server, a single-chip microcomputer, an MCU or a network device, etc.) to execute the methods described in various embodiments of the present invention or certain parts of the embodiments.

[0142] The present invention provides a model predictive control method and system idea and method for an industrial 3D printer. There are many methods and ways to implement the technical solution. The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principle of the present invention. These improvements and modifications should also be regarded as the protection scope of the present invention. All components not specified in this embodiment can be implemented by existing technologies.

Claims

1. A model predictive control method for an industrial 3D printer, characterized in that: include: Step 1, obtaining basic information of the motor in the 3D printer, the basic information including: a given speed value, a rotor angle and a three-phase current value; Step 2, calculating the state information of the motor at this moment according to the basic information of the motor, the state information including: speed, back electromotive force value and torque change; Step 3, construct a model predictive controller; Step 4, according to the state information, use a model predictive controller to calculate the torque and flux of the motor, and perform beat compensation to obtain an optimal voltage vector, and control the motor in the 3D printer accordingly to complete the model predictive control of the industrial-grade 3D printer.

2. The model predictive control method for an industrial 3D printer according to claim 1, characterized in that: The motor described in step 1 is an open-winding brushless DC motor.

3. The model predictive control method for an industrial 3D printer according to claim 2, characterized in that: The motor model of the open-winding brushless DC motor is as follows: The torque equation of the open-winding brushless DC motor is established as follows: Among them, e a 、e b 、e c is the back electromotive force of the three phases of the open-winding brushless DC motor; i a 、i b 、i c is the three-phase current of the open-winding brushless DC motor, T e is the output electromagnetic torque, and ω is the mechanical angular velocity of the rotor of the open-winding brushless DC motor.

4. The model predictive control method for an industrial 3D printer according to claim 3, characterized in that: The model predictive controller described in step 3 includes: Switch tube function conversion module, motor prediction model module, delay compensation module, prediction value calculation module and value function evaluation module; among them, The switch tube function conversion module converts the voltage vector to be traversed according to the switch tube function and outputs the calculated winding voltage value (u) corresponding to each vector. a ,u b ,u c ); The motor prediction model module calculates the winding voltage value (u a ,u b ,u c ) and the current value sampled at time k (i a ,i b ,i c ), predict the current value of k+1 control period [i d (k+1),i q (k+1)]; The delay compensation module is used to calculate the predicted current value [i d (k+2),i q (k+2)]; The predicted value calculation module calculates the torque T by combining the calculated predicted current value with the motor model. e (k+2) and stator flux value ψ s (k+2); The value function evaluation module is used to set standards and select the optimal voltage vector from all voltage vectors.

5. The model predictive control method for an industrial 3D printer according to claim 4, characterized in that: In the switch tube function conversion module, the switch tube function vector is expressed as follows: in, The signal of the n2th switch tube in the n1th inverter is 0 or 1, indicating whether the switch tube is on or off; the switch tube function of the open-winding brushless DC motor is expressed as: or Among them, (u d ,u b ,u c ) represents the calculated winding voltage value, u a Indicates the calculated voltage of phase A, u b Indicates the calculated voltage of phase B, u c Indicates the calculated voltage of phase C, U dc represents the bus voltage, and fix is ​​the round-off function.

6. The model predictive control method for an industrial 3D printer according to claim 5, characterized in that: The motor prediction model module comprises: The three-phase currents of phase A, phase B, and phase C can be obtained by reading the sensor as (i a ,i b ,i c ), through C 3 / 2 Transformation and C 2r / 2s Transformation to obtain the current value (i d ,i q ), as follows: According to the mathematical relationship between current and voltage, we get: Among them, R s represents phase resistance, L represents inductance, ψ f is the stator flux value, ω is the mechanical angular velocity of the open-winding brushless DC motor rotor; Euler forward discretization and simplification are performed to obtain: Among them, [i d (k+1),i q (k+1)] is the current value of the k+1 control period, T s To control the cycle.

7. The model predictive control method for an industrial 3D printer according to claim 6, characterized in that: The delay compensation module comprises: Among them, [i d (k+2),i q (k+2)] is the current value predicted during the actual control period k+2.

8. The model predictive control method for an industrial 3D printer according to claim 7, characterized in that: The predicted value calculation module comprises: Among them, T e (k+2) and ψ s (k+2) is the electromagnetic torque and stator flux value used for motor performance output.

9. The model predictive control method for an industrial 3D printer according to claim 8, characterized in that: The value function evaluation module includes: J=λ·|ψ s (k+2)-ψ s_ref |+|T e (k+2)-T e_ref | Among them, λ is the weight factor, ψ s_ref and T e_ref Indicates the given values ​​of stator flux and electromagnetic torque; All predetermined voltage vectors are traversed, and a voltage vector corresponding to the minimum value of the cost function J is selected, and sent to the open-winding brushless DC motor controller for controlling the open-winding brushless DC motor.

10. A model predictive control system for an industrial 3D printer, characterized in that: Used to implement any of the methods described in claims 1 to 9, comprising: Switch tube function conversion module, motor prediction model module, delay compensation module, prediction value calculation module and value function evaluation module; among them, The switch tube function conversion module converts the voltage vector to be traversed according to the switch tube function and outputs the calculated winding voltage value (u) corresponding to each vector. a ,u b ,u c ); The motor prediction model module calculates the winding voltage value (u a ,u b ,u c ) and the current value sampled at time k (i a ,i b ,i c ), predict the current value of k+1 control period [i d (k+1),i q (k+1)]; The delay compensation module is used to calculate the predicted current value [i d (k+2),i q (k+2)]; The predicted value calculation module calculates the torque T by combining the calculated predicted current value with the motor model. e (k+2) and stator flux value ψ s (k+2); The value function evaluation module is used to set standards and select the optimal voltage vector from all voltage vectors.

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