Spraying system flow control method and spraying system

Abstract

The present invention provides a flow control method for a spraying system and a spraying system. The flow control method for a spraying system includes: determining a controlled object model; calculating a hysteresis term k based on a control delay period and a solution period of a liquid medium pumped by a water pump; determining a predicted range p of a control effective zone state at a current time t; and determining a controlled flow u generated by the water pump based on an incremental model prediction value and a future control amount. t This application enables the flow rate of the liquid medium output by the spraying system performing the spraying operation to be accurately controlled, thereby achieving the purpose of eliminating steady-state errors; at the same time, this application can also flexibly adjust the detection accuracy of the state estimation value by adjusting the order of the state matrix A according to the characteristics of different water pumps and processors, thereby achieving a reasonable and accurate estimation of the controlled flow rate u formed by the water pump. t and can reduce computational overhead.

Description

Technical Field

[0001] The present invention relates to the technical field of precise flow control, and in particular to a flow control method for a spraying system and a spraying system. Background Art

[0002] Drone spraying systems use circulating pumps to pump liquids. These pumps include conventional water pumps and diaphragm pumps. Conventional water pumps achieve dynamic sealing through packing and mechanical seals, but this can lead to leakage after a period of use. Diaphragm pumps, however, lack dynamic sealing, separating the liquid medium from the atmosphere via a diaphragm. This allows for leak-free pumping, making them the mainstream circulating pumps used on drones and other operating devices.

[0003] In order to ensure precise quantitative spraying in a spraying system, it is necessary to precisely control the flow rate of the liquid medium output by the diaphragm pump. The existing technology includes PID control based on a proportional unit P, an integral unit I, and a differential unit D, as well as Model Reference Adaptive Control (MRAC) based on model reference to achieve precise control of the flow rate of the liquid medium. For the precise control of the flow rate of liquid media such as pesticides, PID control has many reasons such as long response time, severe hysteresis, and difficulty in debugging, which makes it unsuitable for the precise control of the flow rate of the spraying system to achieve precise spraying operations. At the same time, for MRAC control, the model of the controlled object needs to be an adaptive control system whose dynamic characteristics are as close as possible to the known reference model. Therefore, MRAC control cannot completely eliminate steady-state errors, and there is a technical problem that the establishment of the controlled object model in the early stage is complex and inaccurate, making it impossible to precisely control the flow rate.

[0004] In view of this, it is necessary to improve the flow control method of the spraying system in the prior art to solve the above problems. Summary of the Invention

[0005] The purpose of the present invention is to disclose a spraying system flow control method and a spraying system, so as to solve the problem in the prior art of accurately controlling the flow of a liquid medium output by a spraying system that is configured on an operating equipment such as an unmanned aerial vehicle and performs a spraying operation, so as to achieve the purpose of eliminating steady-state errors.

[0006] To achieve one of the above objectives, the present invention provides a method for controlling flow of a spraying system, comprising:

[0007] Determine the controlled object model;

[0008] Calculate the hysteresis term k based on the control delay period and the solution period of the liquid medium pumped by the water pump;

[0009] Determine the control effective zone state prediction range p at the current time t;

[0010] Determine the controlled flow u formed by the water pump based on the incremental model prediction value and future control quantity t .

[0011] As a further improvement of the present invention, the controlled object model uses the PWM value as the flow input value and outputs the flow output value mea_flow based on the open-loop model of the controlled object.

[0012] As a further improvement of the present invention, the control delay period is determined by the initial delay time of the water pump and the actual delay time of the water pump based on an open-loop object model.

[0013] As a further improvement of the present invention, the control effective zone state prediction range p is jointly determined by the control effective zone state response time, tracking expected value overshoot and tracking expected value steady-state error of the controlled object model, wherein the control effective zone state response time is less than or equal to 0.2 seconds, the tracking expected value overshoot is less than or equal to 5%, and the tracking expected value steady-state error is 0.

[0014] As a further improvement of the present invention, the method for determining the controlled flow u formed by the water pump based on the incremental model prediction value and the future control amount is as follows: t The process includes looping through the following steps:

[0015] Estimation of state value based on Kalman filter method And the estimated value of the predicted output y_est;

[0016] Calculate the prediction vector output by the output state in the control effective area state prediction range p

[0017] Introduce the index function J to calculate the differential flow rate Δu corresponding to the incremental model prediction value at the current time t t , and the differential flow Δu t Substitute into the controlled object model to determine the controlled flow u generated by the water pump corresponding to the current time t t .

[0018] As a further improvement of the present invention, the state estimation value The calculation formula is:

[0019]

[0020] in, is the incremental model prediction value The known predicted value of It is the predicted value of the state quantity formed at the current time t for any subsequent sampling time t+i, A is the state matrix, and B is the control matrix;

[0021] The state matrix A is:

[0022]

[0023] The control matrix B is:

[0024]

[0025] As a further improvement of the present invention, the prediction vector The calculation formula is:

[0026] Among them, G is the prediction matrix, ΔU is the prediction vector The differential flow rate formed by the current control quantity and the future control quantity input is independent of the current control quantity and the future control quantity input;

[0027] The prediction matrix G is:

[0028]

[0029] The prediction vector

[0030] The C is the measurement matrix, and the measurement matrix C is:

[0031] C=[-0.002553190225170530.00255319022517009 0.01276595112585420.00765957067551101].

[0032] As a further improvement of the present invention, the predicted output quantity estimated value y_est is determined by the following prediction equation:

[0033] r t+k+i|t =SP t +α(r t+k+i-1|t -SP t );

[0034] Among them, the variable SP t is the cutoff frequency diagonal matrix of the predicted output reference value corresponding to the current time t, and the variable r t+k+i|t is the i-th reference vector of the predicted output reference value, and the variable r t+k+i|t The initial value r t+k|t To predict the output estimate y_est, 1≤i≤p, the variable α is the cutoff frequency diagonal matrix.

[0035] As a further improvement of the present invention, the controlled flow u corresponding to the current moment t t The calculation formula is: t =u t-1 +Δu t ;

[0036] The parameter Δu t is the differential flow of the current control quantity corresponding to the current time t, the parameter u t-1 is the controlled flow at time t-1.

[0037] As a further improvement of the present invention, the index function J is introduced to calculate the differential flow rate Δu corresponding to the incremental model prediction value at the current time t t The calculation formula is:

[0038]

[0039] Wherein, variable W is the diagonal positive definite matrix of tracking error weight, parameter λ is the differential flow Δu t The diagonal weighted positive definite matrix of the variable R t Tracking value for the state;

[0040] Minimize the index function J and determine the differential flow Δu ​​corresponding to the current time t t ,and The variable K f is the feedback gain matrix.

[0041] As a further improvement of the present invention, the feedback gain matrix K f for:

[0042]

[0043] Among them, the variable G2 is the predictive control matrix, and the predictive control matrix G2 is:

[0044]

[0045] The variable β is a diagonal matrix of the single-step planning length, the variable m∈[0,p-1], the variable j∈[0,m], and the variable i∈[0,j].

[0046] Based on the same inventive concept, the present invention also discloses a spraying system deployed on a mobile working device, comprising:

[0047] A liquid storage tank, a water pump connected to the liquid storage tank, and a control unit for controlling the water pump;

[0048] The control unit executes the steps of the spraying system flow control method as described in any of the above inventions to determine the controlled flow u t .

[0049] Compared with the prior art, the present invention has the following beneficial effects:

[0050] The present application can accurately control the flow rate of the liquid medium output by the spraying system for performing the spraying operation, thereby achieving the purpose of eliminating steady-state errors. At the same time, the present application can also flexibly adjust the state estimation value by adjusting the order of the state matrix A according to the characteristics of different water pumps and processors. The detection accuracy is high, so as to obtain a reasonable and accurate estimation of the controlled flow u generated by the water pump. t and can reduce computational overhead. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Figure 1 This is an overall flow chart of a method for controlling flow of a spraying system according to the present invention;

[0052] Figure 2 This is an algorithm logic diagram of a flow control method for a spraying system according to the present invention;

[0053] Figure 3 This is a topology diagram of the spraying system deployed in mobile working equipment;

[0054] Figure 4 This is a flow rate comparison curve of the same model of water pump using the spray system flow control method of the present invention and the prior art using MRAC from an initial state of 0 L / min to a steady-state value. The horizontal axis is time in seconds; the vertical axis is amplitude in L / min.

[0055] Figure 5 A topological diagram of a terminal device for running a method for controlling flow of a spraying system according to the present invention. DETAILED DESCRIPTION

[0056] The present invention is described in detail below with reference to the various embodiments shown in the accompanying drawings, but it should be noted that these embodiments are not limitations of the present invention, and any equivalent transformations or substitutions in functions, methods, or structures made by ordinary technicians in this field based on these embodiments are all within the scope of protection of the present invention.

[0057] Ginseng Figures 1 to 4 As shown, the technical solutions disclosed in the various embodiments disclosed in this application are intended to accurately predict the flow rate output by a water pump. For example, the flow control method for a spraying system disclosed in this application solves the flow hysteresis phenomenon of a peristaltic pump (i.e., a subordinate concept of a water pump) to minimize the steady-state error of the peristaltic pump, thereby achieving accurate prediction and control of the flow rate output by the water pump.

[0058] Ginseng Figure 1As shown, the spraying system flow control method includes the following steps S1 to S3.

[0059] Step S1: Determine a controlled plant model. The controlled plant model uses PWM values ​​as flow input values ​​and outputs a flow output value mea_flow based on an open-loop model of the controlled plant. The controlled plant model is constructed using simulation software running on a computer system.

[0060] Step S2: Calculate the hysteresis term k based on the control delay period and the calculation period of the liquid medium pumped by the water pump. The quotient of the control delay period (Delaytime) and the calculation period (CalPeriod) is the hysteresis term k. The control delay period is determined by the initial pump delay time and the measured pump delay time based on the open-loop plant model. Both the initial pump delay time and the measured pump delay time are pre-determined and input into the controlled plant model.

[0061] Step S3: Determine the predicted range p of the control effective area state at the current time t.

[0062] The effective control zone state prediction range p is determined by the effective control zone state response time, the tracking expected value overshoot, and the tracking expected value steady-state error of the controlled object model. It should be noted that a larger effective control zone state prediction range p improves the accuracy of the controlled object model description, but this also requires higher processing power from the control unit 30 executing the sprinkler system flow control method and results in inefficient computing power consumption. A smaller effective control zone state prediction range p, on the other hand, results in poorer accuracy of the controlled object model. Therefore, it is necessary to rationally determine the effective control zone state prediction range p. Therefore, in this embodiment, the effective control zone state response time is less than or equal to 0.2 seconds, the tracking expected value overshoot is less than or equal to 5%, and the tracking expected value steady-state error is 0. More specifically, the tracking expected value overshoot is 4%, and the effective control zone state response time is 0.2 seconds.

[0063] Step S4: Determine the controlled flow u generated by the water pump based on the incremental model prediction value and the future control quantity t Specifically, combined with Figure 2 As shown, the controlled flow u formed by the water pump is determined based on the incremental model prediction value and the future control quantity t The process includes looping through steps 401 to 403. Thus, the hysteresis of the sprinkler system including the water pump and the uncertainty of the controlled object model are solved by using the incremental model-based predicted value and the future control variable.

[0064] Step 401: Estimate the state value based on the Kalman filter method And the estimated value of the predicted output y_est. State estimate The calculation formula is:

[0065] in, is the incremental model prediction value The known predicted value of It is the predicted value of the state quantity formed at the current time t for any subsequent sampling time t+i, A is the state matrix, and B is the control matrix. To ensure the state estimation value In this embodiment, the state matrix A can be a 3×3 homogeneous matrix, a 4×4 homogeneous matrix, or a 5×5 homogeneous matrix. The higher the order of the state matrix A, the better the state estimation value. The higher the prediction accuracy of the output estimation value y_est, the higher the computing power consumption will be. Therefore, the state matrix A in this embodiment can be preferably a 4×4 homogeneous matrix, and the state estimation value can be flexibly adjusted by adjusting the order of the state matrix A. It improves the detection accuracy and helps reduce the computational overhead.

[0066] The state matrix A is:

[0067]

[0068] The elements 2.04262922983781, -1.30969947804135, and 0.246644726402176 in the state matrix A are determined by Mathlab when the controlled object model is modeled, and can be determined according to the characteristics of the water pump 20 .

[0069] The control matrix B is:

[0070]

[0071] The number of rows in the control matrix B is equal to that of the state matrix A, but the number of columns is 1.

[0072] Then, substitute the state matrix A and control matrix B into the aforementioned state estimation value In the calculation formula,

[0073] At the same time, the prediction vector The calculation formula is:

[0074] Among them, G is the prediction matrix, ΔU is the prediction vector The differential flow is independent of the current control quantity and the future control quantity input. The differential flow can be a positive value, that is, the current control quantity and the future control quantity input are positive numbers; the differential flow can be a negative value, that is, the current control quantity and the future control quantity input are negative numbers.

[0075] The prediction matrix G is:

[0076]

[0077] The prediction vector

[0078] The C is the measurement matrix, and the measurement matrix C is:

[0079] C=[-0.002553190225170530.00255319022517009 0.01276595112585420.00765957067551101].

[0080] Similarly, the number of rows of the observation matrix C is 1 and the number of columns is 4. Substitute the state matrix A, control matrix B and observation matrix C into the prediction matrix G.

[0081] The predicted output estimate y_est is determined by the following prediction equation:

[0082] r t+k+i|t =SP t +α(r t+k+i-1|t -SP t );

[0083] Among them, the variable SP t is the cutoff frequency diagonal matrix of the predicted output reference value corresponding to the current time t, and the variable r t+k+i|t is the i-th reference vector of the predicted output reference value, and the variable r t+k+i|t The initial value r t+k|t To predict the output estimate y_est, 1≤i≤p, the variable α is the cutoff frequency diagonal matrix.

[0084] Step 402: Calculate the prediction vector output by the output state in the control effective area state prediction range p

[0085] Step 403: Introduce the index function J to calculate the differential flow rate Δu corresponding to the incremental model prediction value at the current time t t , and the differential flow Δu t Substitute into the controlled object model to determine the controlled flow u generated by the water pump 20 corresponding to the current time t t The purpose of introducing the index function J is to realize the rolling optimization of the controlled object model to solve the controlled flow u corresponding to the current time t t Differential flow rate Δu t The controlled flow u corresponding to the current time t t The calculation formula is: t =u t-1 +Δu t ; Parameter Δut is the differential flow of the current control quantity corresponding to the current time t, and the parameter u t-1 is the controlled flow at time t-1. Specifically, the index function J is introduced to calculate the differential flow Δu ​​corresponding to the incremental model prediction value at the current time t t The calculation formula is:

[0086]

[0087] Wherein, variable W is the diagonal positive definite matrix of tracking error weight, parameter λ is the differential flow Δu t The diagonal weighted positive definite matrix of the variable R t is the state tracking value. Since the initial value r t+k|t Equal to the estimated value of the predicted output y_est, let

[0088] Minimize the index function J, that is Determine the differential flow rate Δu corresponding to the current time t t , and Δu t =K f (R t -Y t 1 ), the variable K f is the feedback gain matrix.

[0089] Feedback gain matrix K f for:

[0090]

[0091] Among them, the variable G2 is the predictive control matrix, and the predictive control matrix G2 is:

[0092]

[0093] Wherein, variable β is the diagonal matrix of the single-step planning length and variable β is specifically 0.95, variable m∈[0,p-1], variable j∈[0,m], variable i∈[0,j], and variables m, j, and i are all integers. The value of variable β can be manually adjusted to control the size of the diagonal elements contained in the predictive control matrix G2. At this point, the controlled flow u at the current time t is calculated t Therefore, when the controlled flow u at the current time t is calculated t Then, return to step 401.

[0094] Combine Figure 4 As shown, Figure 4The flow rate comparison experimental data of the same model of water pump using the spray system flow control method of the present invention and the prior art using MRAC from the initial state of 0L / min to the steady state value are shown. Figure 4 The continuous line shown represents the flow variation curve generated by the incremental model predictive control included in the spray system flow control method of the present invention, and the dotted line represents the flow variation curve generated by the MRAC in the prior art.

[0095] Further integration Figure 4 It can be seen that when the flow rate rises from an initial state of 0 L / min and before reaching the steady-state value of 10 L / min, when reaching a certain flow rate represented by the horizontal dotted dashed line, the rise time determined by the spray system flow control method disclosed in this application is 0.183 seconds, while the prior art requires 0.23 seconds to reach the same flow rate, thereby reducing the hysteresis of water pump 20. Furthermore, the steady-state flow rate of 10 L / min ultimately output by this application completely coincides with the actual flow rate of water pump 20, while the steady-state flow rate generated by the prior art MRAC is only 9.6 L / min, which deviates somewhat from the actual flow rate of water pump 20. Furthermore, the continuous line and the dashed line reach their respective steady-state values ​​at times t1 and t2, respectively. The definite integral area formed by the continuous line, 10.0 L / min, and time t1 is smaller than the definite integral area formed by the dashed line, 9.6 L / min, and time t2, and time t1 is earlier than time t2. As can be seen, the spray system flow control method disclosed herein can more quickly reach a steady-state flow rate from an initial state of 0 L / min, resolving the technical issue with prior art MRAC control, which cannot completely eliminate steady-state errors. Furthermore, compared to PID control, the spray system flow control method disclosed herein is more effective in reducing fluctuations in the actual flow rate output by the water pump 20 and the adjustment period required to reach a steady-state value.

[0096] In summary, in this embodiment, the prediction vector output by the control effective area state prediction range p The PWM value corresponding to the final PWM signal is outputted by the incremental prediction model to the water pump 20. The actual flow rate feedback signal formed by the actual flow rate formed by the water pump 20 is continuously inputted into the incremental prediction model to form the final steady-state value. At the same time, the incremental prediction model cyclically calculates the state estimation value determined by the Kalman filter method. Correction is made, and the calculated lag term k is corrected, thereby improving the prediction vector output by the control effective area state prediction range p accuracy.

[0097] Combine Figure 3Based on the specific implementation of the method for controlling the flow rate of a spraying system disclosed in the above embodiment, this embodiment also discloses a specific implementation of a spraying system 1000. The spraying system 100 is deployed on a mobile working device 1000. The spraying system 100 includes: a liquid storage tank 10, a water pump 20 connected to the liquid storage tank 10, and a control unit 30 for controlling the water pump 20. The control unit 30 executes the steps of the method for controlling the flow rate of a spraying system disclosed in the above embodiment to determine and output the controlled flow rate u t The mobile working equipment 1000 includes but is not limited to a drone or an unmanned vehicle. The control unit 30 may be an electronic device such as a single chip microcomputer or an FPGA that can store a computer program and execute the steps of the spraying system flow control method through computer code.

[0098] Combine Figure 5 Based on the spraying system flow control method and spraying system disclosed in the aforementioned specific embodiments, the present application also discloses a control unit 30. The control unit 30 includes a processor 51, a memory 52, and a computer program stored in the memory 52 and executable on the processor 51. When the computer program is executed by the processor 51, the steps of the spraying system flow control method disclosed in the aforementioned embodiments are implemented. At the same time, a communication bus 53 for communication connection is established between the processor 51 and the storage device 52. The processor 51 is used to execute one or more programs stored in the storage device 52, which is the spraying system flow control method as described in the aforementioned embodiment. The storage device 52 is composed of storage units 521 to 52z, and the parameter z is a positive integer greater than or equal to 1. The control unit 30 can be understood as an electronic device and is deployed in mobile operating equipment such as drones and unmanned scales. For the specific technical solution of the spraying system flow control method that the control unit 30 relies on / includes, please refer to the above description and will not be repeated here.

[0099] In addition, the functional units in the various embodiments of the present invention may be integrated into a single processing unit, or each unit may exist physically separately, or two or more units may be integrated into a single unit. The aforementioned integrated units may be implemented in the form of hardware or software functional units. If the integrated units are implemented in the form of software functional units and sold or used as independent products, they may be stored in a computer-readable medium. Based on this understanding, the technical solution of the present invention, or the portion that contributes to the prior art, or all or part of the technical solution, may be embodied in the form of a software product. The computer software product is stored in a storage medium and includes several instructions for causing a computer device (which may be a personal computer, server, or network device, etc.) or a processor to execute all or part of the steps of the methods of the various embodiments of the present invention. The aforementioned storage medium includes various media that can store program code, such as a USB flash drive, a mobile hard drive, a read-only memory (ROM), a random access memory (RAM), a magnetic disk, or an optical disk.

[0100] The series of detailed descriptions listed above are only specific descriptions of feasible implementation methods of the present invention. They are not intended to limit the scope of protection of the present invention. Any equivalent implementation methods or changes that do not deviate from the technical spirit of the present invention should be included in the scope of protection of the present invention.

[0101] In addition, it should be understood that although this specification is described in terms of implementation methods, not every implementation method contains only one independent technical solution. This narrative method of the specification is only for the sake of clarity. Those skilled in the art should regard the specification as a whole. The technical solutions in each embodiment can also be appropriately combined to form other implementation methods that can be understood by those skilled in the art.

Claims

1. A method for controlling the flow rate of a spraying system, characterized in that: include: Determine the controlled object model; Calculate the hysteresis term k based on the control delay period and the solution period of the liquid medium pumped by the water pump; Determine the control effective zone state prediction range p at the current time t; The following steps are executed in a loop: Estimation of state value based on Kalman filter method And the estimated value of the predicted output y_est; Calculate the first prediction vector output by the output state in the control effective area state prediction range p Introduce the index function J to calculate the differential flow rate Δu corresponding to the incremental model prediction value at the current time t t , and the differential flow Δu t Substitute into the controlled object model to determine the controlled flow u generated by the water pump corresponding to the current time t t .

2. The method for controlling the flow rate of a spraying system according to claim 1, wherein: The controlled object model uses the PWM value as the flow input value and outputs the flow output value mea_flow based on the open-loop model of the controlled object.

3. The method for controlling the flow rate of a spraying system according to claim 1, wherein: The control delay period is determined by the initial delay time of the water pump and the measured delay time of the water pump based on an open-loop object model.

4. The method for controlling the flow rate of a spraying system according to claim 1, wherein: The control effective zone state prediction range p is jointly determined by the control effective zone state response time, tracking expected value overshoot and tracking expected value steady-state error of the controlled object model, wherein the control effective zone state response time is less than or equal to 0.2 seconds, the tracking expected value overshoot is less than or equal to 5%, and the tracking expected value steady-state error is 0.

5. The method for controlling the flow rate of a spraying system according to claim 1, wherein: The state estimate The calculation formula is: in, is the incremental model prediction value The known predicted value of It is the predicted value of the state quantity formed at the current time t for any subsequent sampling time t+i, A is the state matrix, and B is the control matrix; The state matrix A is: The control matrix B is:

6. The method for controlling the flow rate of a spraying system according to claim 5, wherein: The first prediction vector The calculation formula is: Among them, G is the prediction matrix, ΔU is the first prediction vector The differential flow rate formed by the current control quantity and the future control quantity input is independent of Y t 1 is the second prediction vector; The prediction matrix G is: The second prediction vector The C is the measurement matrix, and the measurement matrix C is: C＝[-0.00255319022517053 0.00255319022517009 0.01276595112585420.00765957067551101]。 7. The method for controlling the flow rate of a spraying system according to claim 6, wherein: The predicted output value y_est is determined by the following prediction equation: r t+k+i|t =SP t +α(r t+k+i-1|t -SP t ); Among them, the variable SP t is the cutoff frequency diagonal matrix of the predicted output reference value corresponding to the current time t, and the variable r t+k+i|t is the i-th reference vector of the predicted output reference value, and the variable r t+k+i|t The initial value r t+k|t To predict the output estimate y_est, 1≤i≤p, the variable α is the cutoff frequency diagonal matrix.

8. The method for controlling the flow rate of a spraying system according to claim 6, wherein: The controlled flow u corresponding to the current time t t The calculation formula is: t =u t-1 +Δu t ; The parameter Δu t is the differential flow of the current control quantity corresponding to the current time t, the parameter u t-1 is the controlled flow at time t-1.

9. The method for controlling the flow rate of a spraying system according to claim 8, wherein: Introduce the index function J to calculate the differential flow rate Δu corresponding to the incremental model prediction value at the current time t t The calculation formula is: Wherein, variable W is the diagonal positive definite matrix of tracking error weight, parameter λ is the differential flow Δu t The diagonal weighted positive definite matrix of the variable R t Tracking value for the state; Minimize the index function J and determine the differential flow Δu ​​corresponding to the current time t t , and Δu t =K f (R t -Y t 1 ), the variable K f is the feedback gain matrix.

10. The method for controlling the flow rate of a spraying system according to claim 9, wherein: The feedback gain matrix K f for: Among them, the variable G2 is the predictive control matrix, and the predictive control matrix G2 is: The variable β is a diagonal matrix of the single-step planning length, the variable m∈[0,p-1], the variable j∈[0,m], and the variable i∈[0,j].

11. A spraying system deployed on a mobile working device, characterized in that: include: A liquid storage tank, a water pump connected to the liquid storage tank, and a control unit for controlling the water pump; The control unit executes the steps of the spraying system flow control method according to any one of claims 1 to 10 to determine the controlled flow u t .

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