Pump and water turbine low-vibration high-stability starting process method based on quartic polynomial rotating speed control

Abstract

This application relates to the field of pump and turbine start-up control technology, and particularly to a method for low-vibration and high-stability start-up process of pumps and turbines based on fourth-order polynomial speed control. The method includes: acquiring the motion trajectory requirements of the pump and turbine; selecting a target speed curve model based on the motion trajectory requirements; solving the target speed curve model according to the boundary conditions of the target speed curve model to obtain the target speed curve; converting the target speed curve into an analog voltage command signal; and inputting the analog voltage command signal into a servo driver to control the start-up of the pump and turbine according to the analog voltage command signal. This solves the problems of high impact, insufficient smoothness, and poor flexibility in the start-up control of pump and turbine motors in related technologies.

Description

Technical Field

[0001] This application relates to the field of pump and turbine start-up control technology, and in particular to a method for low-vibration and high-stability start-up process of pumps and turbines based on fourth-order polynomial speed control. Background Technology

[0002] In industrial and civil applications, water pumps and turbines are among the most widely used general-purpose mechanical equipment. Their startup process is a critical stage in the operation of water pump and turbine systems, and the control of the speed curve directly affects the system's safety, reliability, and service life.

[0003] In related technologies, if the traditional water pump and turbine motor start-up method is used, a huge inrush current of up to 5-8 times the rated current will be generated, causing serious disturbance to the power grid. If the star-delta start-up method is used, it is only suitable for no-load or light-load start-up, and there is a secondary inrush current at the moment of switching from star to delta. The autotransformer step-down start-up method is expensive, complex in structure, and has high maintenance costs. Summary of the Invention

[0004] This application provides a method for low-vibration and high-stability startup of water pumps and turbines based on fourth-order polynomial speed control, in order to solve the problems of high impact, insufficient smoothness and poor flexibility in the startup control of water pumps and turbine motors.

[0005] The first aspect of this application provides a method for low-vibration and high-stability startup of a water pump and turbine based on fourth-order polynomial speed control, comprising the following steps: obtaining the motion trajectory requirements of the water pump and turbine; selecting a target speed curve model according to the motion trajectory requirements; solving the target speed curve model according to the boundary conditions of the target speed curve model to obtain the target speed curve; converting the target speed curve into an analog voltage setpoint signal; and inputting the analog voltage setpoint signal into a servo driver to control the startup of the water pump and turbine according to the analog voltage setpoint signal.

[0006] Optionally, selecting a target speed curve model of a quartic polynomial based on motion trajectory requirements includes: determining at least one of the control complexity and the required smoothness of the process based on motion trajectory requirements; selecting a quartic polynomial based on at least one of the control complexity and the required smoothness of the process, and using the quartic polynomial as the target speed curve model.

[0007] Optionally, the expression for the target speed curve model is:

[0008] in, n ( t ( ) represents the target speed curve model. t For startup time,A , B , C , D , E Let be the coefficients of the fourth-degree polynomial to be determined.

[0009] Optionally, the boundary conditions of the target speed curve model include: the initial speed of the pump and the turbine are the first target speeds, the final speeds of the pump and the turbine are the second target speeds, the initial speed change rate of the pump and the turbine is the first target change rate, the final speed change rate is the second target change rate, and the midpoint speed of the pump and the turbine is the characteristic speed.

[0010] Optionally, the target speed curve is obtained by solving the target speed curve model based on the boundary conditions of the target speed curve model, including: substituting the boundary conditions into the target speed curve model to establish a linear equation system; expressing the linear equation system as a speed curve matrix; determining the coefficients of the target speed curve model based on the solution results of the speed curve matrix; and generating the target speed curve based on the coefficients of the target speed curve model.

[0011] Optionally, the expression for the rotational speed curve matrix is:

[0012] in, α For time in each boundary condition t The coefficient matrix consisting of the powers of and their derivatives. x For the coefficients to be determined A , B , C , D , E The unknown vector formed β This is the result vector consisting of the starting boundary conditions; The expression for the coefficients of the target speed curve model is: A= B= C= D=0 E=0 in, A , B , C , D , E Let be the coefficients of the fourth-degree polynomial to be determined. T To accelerate startup time, k For a certain percentage of the rated speed, a The second target speed.

[0013] Optionally, converting the target speed curve into an analog voltage setpoint signal includes: determining a speed setpoint based on the target speed curve; loading the speed setpoint into an arbitrary waveform generator; and generating an analog voltage setpoint signal through the arbitrary waveform generator.

[0014] A second aspect of this application provides a low-vibration, high-stability starting system for a water pump and turbine based on fourth-order polynomial speed control, comprising: an acquisition module for acquiring the motion trajectory requirements of the water pump and turbine; a solution module for selecting a fourth-order polynomial target speed curve model according to the motion trajectory requirements, setting boundary conditions according to the target speed curve model, and solving the coefficients of the target speed curve model according to the boundary conditions to obtain the target speed curve; and a starting module for converting the target speed curve into an analog voltage setpoint signal, wherein a servo driver controls the starting of the water pump and turbine according to the analog voltage setpoint signal.

[0015] Optionally, the solver module is further used to: determine at least one of the control complexity and the required smoothness of the process based on the motion trajectory requirements; select a quartic polynomial based on at least one of the control complexity and the required smoothness of the process, and use the quartic polynomial as the target speed curve model.

[0016] Optionally, the expression for the target speed curve model is:

[0017] in, n ( t ( ) represents the target speed curve model. t For startup time, A , B , C , D , E Let be the coefficients of the fourth-degree polynomial to be determined.

[0018] Optionally, the boundary conditions of the target speed curve model include: the initial speed of the pump and the turbine are the first target speeds, the final speeds of the pump and the turbine are the second target speeds, the initial speed change rate of the pump and the turbine is the first target change rate, the final speed change rate is the second target change rate, and the midpoint speed of the pump and the turbine is the characteristic speed.

[0019] Optionally, the solver module is further used to: substitute boundary conditions into the target speed curve model to establish a linear equation system; express the linear equation system as a speed curve matrix; determine the coefficients of the target speed curve model based on the solution results of the speed curve matrix; and generate the target speed curve based on the coefficients of the target speed curve model.

[0020] Optionally, the expression for the rotational speed curve matrix is:

[0021] in, α For time in each boundary condition t The coefficient matrix consisting of the powers of and their derivatives. x For the coefficients to be determined A , B , C , D , E The unknown vector formed β This is the result vector consisting of the starting boundary conditions; The expression for the coefficients of the target speed curve model is: A= B= C= D=0 E=0 in, A , B , C , D , E Let be the coefficients of the fourth-degree polynomial to be determined. T To accelerate startup time, k For a certain percentage of the rated speed, a The second target speed.

[0022] Optionally, the startup module is further configured to: convert the target speed curve into an analog voltage setpoint signal, including: determining a speed setpoint based on the target speed curve; loading the speed setpoint into an arbitrary waveform generator; and generating an analog voltage setpoint signal through the arbitrary waveform generator.

[0023] A third aspect of this application provides an electronic device, including: a memory, a processor, and a computer program stored in the memory and executable on the processor. The processor executes the program to perform a low-vibration, high-stability start-up process method for a water pump and turbine based on fourth-order polynomial speed control as described in the above embodiments.

[0024] The fourth aspect of this application provides a computer program product, including a computer program or instructions, which, when executed, implement the low-vibration, high-stability start-up method for a water pump and turbine based on fourth-order polynomial speed control as described in the above embodiments.

[0025] Therefore, this application has at least the following beneficial effects: The proposed method for low-vibration and high-stability startup of water pumps and turbines based on fourth-order polynomial speed control in this application obtains the motion trajectory requirements of the water pump and turbine, selects a target speed curve model based on these requirements, and solves for the specific target speed curve by combining the model's boundary conditions. Subsequently, the target speed curve is converted into an analog voltage command signal that is recognized by a servo driver. This analog voltage command signal is input to the servo driver, which then analyzes the signal and drives the water pump and turbine to start. By actively controlling the rate of change of speed, a smooth transition during the startup of the water pump and turbine is achieved, reducing startup shock and enabling precise control of the startup speed of the water pump and turbine. This improves the stability, flexibility, and operational safety of the water pump and turbine startup. Therefore, it solves the problems of high shock, insufficient smoothness, and poor flexibility in the startup control of water pump and turbine motors.

[0026] Additional aspects and advantages of this application will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of this application. Attached Figure Description

[0027] The above and / or additional aspects and advantages of this application will become apparent and readily understood from the following description of the embodiments taken in conjunction with the accompanying drawings, wherein: Figure 1 This is a flowchart of a low-vibration, high-stability start-up method for a water pump and turbine based on fourth-order polynomial speed control, according to an embodiment of this application. Figure 2 This is a schematic diagram of an apparatus for a low-vibration and high-stability start-up method for a water pump and turbine based on fourth-order polynomial speed control, according to an embodiment of this application. Figure 3 This is a comparison chart of the design speed and the experimentally measured speed of a water pump and a water turbine provided according to an embodiment of this application under a 0.5s start-up time; Figure 4 This is a graph showing the head variation characteristics of a centrifugal pump during a 0.5s start-up time, according to an embodiment of this application. Figure 5 This is a structural diagram of a low-vibration, high-stability start-up system for a water pump and turbine based on fourth-order polynomial speed control, according to an embodiment of this application. Figure 6 This is a structural diagram of an electronic device provided according to an embodiment of this application. Detailed Implementation

[0028] The embodiments of this application are described in detail below. Examples of these embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain this application, and should not be construed as limiting this application.

[0029] The following description, with reference to the accompanying drawings, describes a method for low-vibration, high-stability startup of a water pump and turbine based on fourth-order polynomial speed control, according to an embodiment of this application. Addressing the problems of high impact, insufficient smoothness, and poor flexibility in the startup control of water pumps and turbine motors mentioned in the background art, this application provides a method for low-vibration, high-stability startup of a water pump and turbine based on fourth-order polynomial speed control. In this method, the motion trajectory requirements of the water pump and turbine are obtained, a target speed curve model is selected based on these requirements, and the specific target speed curve is obtained by solving the model's boundary conditions. Subsequently, the target speed curve is converted into an analog voltage command signal that is recognized by a servo driver. This analog voltage command signal is input to the servo driver, which analyzes the signal and drives the water pump and turbine to start. By actively controlling the rate of change of speed, a smooth transition during the startup of the water pump and turbine is achieved, thereby realizing control over the startup process of the water pump and turbine, reducing startup impact, and precisely regulating the actual speed of the water pump and turbine to change according to the preset speed curve, thus improving the stability, flexibility, and operational safety of the water pump and turbine startup. This solves the problems of high impact, insufficient smoothness, and poor flexibility in the start-up control of water pumps and turbine motors.

[0030] Specifically, Figure 1 This is a schematic flowchart illustrating a low-vibration, high-stability startup method for a water pump and turbine based on fourth-order polynomial speed control, provided in an embodiment of this application.

[0031] like Figure 1 As shown, the method for low-vibration and high-stability startup of water pumps and turbines based on fourth-order polynomial speed control includes the following steps: In step S101, the motion trajectory requirements of the water pump and water turbine are obtained.

[0032] Among them, a water pump is a fluid transport machine that converts mechanical energy into the kinetic and pressure energy of liquid, and is a device that realizes the directional transport, pressurization or lifting of liquid; a water turbine is a fluid power machine that converts the potential energy and kinetic energy of water flow into mechanical energy; the motion trajectory requirement is the change law of the spatial position, motion path, attitude change, speed / acceleration and other fluctuations of the moving parts of the equipment over time.

[0033] It is understandable that the embodiments of this application obtain the motion trajectory requirements of water pumps and water turbines, clarifying the characteristics of water pumps as fluid transport machinery that converts mechanical energy into liquid kinetic energy and pressure energy, and water turbines as fluid power machinery that converts water flow potential energy and kinetic energy into mechanical energy. The application identifies the moving parts and motion forms of the equipment, and, combined with the working principles and operating characteristics of water pumps and water turbines, forms a clear definition of the motion trajectory requirements of water pumps and water turbines. This accurately anchors the target points for obtaining the trajectory of water pumps and water turbines, unifies the basic direction of trajectory acquisition, and aligns with the actual operating characteristics of water pumps and water turbines. This eliminates the general ambiguity in trajectory acquisition and forms a trajectory acquisition requirement system that fits the actual needs of the fluid machinery industry.

[0034] Specifically, to obtain the motion trajectory requirements of water pumps and turbines, the following steps are required: First, a characteristic survey of the water pumps and turbines needs to be completed. This involves clarifying the fluid transport properties of water pumps (converting mechanical energy into liquid kinetic and pressure energy) and the fluid dynamic properties of water turbines (converting water flow potential and kinetic energy into mechanical energy). Simultaneously, the mainstream application forms and working principles of different structural types of water pumps and turbines should be identified. Second, for water pumps and turbines of different structural types, the moving parts should be disassembled one by one to clarify the specific motion form and inherent motion characteristics of each moving part. This includes defining the controlled and regulated motion attributes of rotating parts such as the pump shaft and impeller, and the linear or compound motion attributes of reciprocating parts such as the piston, crank, and connecting rod. The motion attributes are clarified to understand the variable operating condition fixed motion attributes of rotating components such as the turbine main shaft and runner, as well as the small-amplitude oscillation or rotational motion attributes of adjusting components such as guide vanes and nozzles. This process extracts the requirements for acquiring the motion trajectories of water pumps and turbines. Then, combining the core working characteristics of water pumps and turbines, the attributes of moving components, and the factors influencing their trajectories, the process identifies the needs for accurate acquisition of fixed trajectories for water pumps and monitoring of the stroke trajectories of reciprocating components. Finally, the extracted requirements are integrated and optimized by combining them with actual application scenarios such as water conservancy projects and industrial production, as well as the actual technical requirements for equipment operation and maintenance, to form a system that fits the industry's actual situation and is adapted to the operating characteristics and requirements of water pumps and turbines.

[0035] This application's embodiments acquire the motion trajectory requirements of water pumps and water turbines, clarifying the characteristics of water pumps as fluid transport machinery that converts mechanical energy into liquid kinetic and pressure energy, and water turbines as fluid power machinery that converts water flow potential and kinetic energy into mechanical energy. It identifies the moving parts and motion patterns of the equipment, and, combined with the working principles and operating characteristics of water pumps and water turbines, clearly defines the motion trajectory requirements of water pumps and water turbines. This precisely anchors the target points for acquiring the trajectory of water pumps and water turbines, unifies the basic direction of trajectory acquisition, and aligns with the actual operating characteristics of water pumps and water turbines. This eliminates the general ambiguity in trajectory acquisition work and forms a trajectory acquisition requirement system that fits the actual needs of the fluid machinery industry.

[0036] In step S102, the target rotational speed curve model is selected according to the motion trajectory requirements, and the target rotational speed curve is obtained by solving the target rotational speed curve model according to the boundary conditions of the target rotational speed curve model.

[0037] The target speed curve model is a mathematical model that quantitatively describes the change of the speed of moving parts with time and operating conditions, based on the motion trajectory requirements of the pump and turbine, combined with the structural characteristics, motion laws, and actual operating conditions of the pump and turbine. The boundary conditions are constraints and limiting criteria set for solving the target speed curve model, based on multiple factors such as the motion trajectory requirements of the pump and turbine, the mechanical performance of the equipment itself, the actual operating conditions, industry safety standards, and the characteristics of the fluid medium. The target speed curve is a quantitative curve of the speed change with time / operating conditions obtained by mathematically deriving the target speed curve model adapted to the motion trajectory requirements of the pump and turbine, combined with the comprehensively determined boundary conditions.

[0038] It is understood that the embodiments of this application select a target speed curve model based on the motion trajectory requirements of the water pump and turbine. Then, considering the equipment's mechanical performance, actual operating conditions, industry safety standards, and trajectory control requirements, the boundary conditions corresponding to the target speed curve model are defined. Finally, the boundary conditions of the target speed curve model are solved through mathematical solutions and algorithmic deduction to obtain a target speed curve that fits the trajectory requirements and practical application requirements. The scientific setting of the boundary conditions defines a reasonable range for model solving that conforms to the actual equipment and adapts to the operating conditions. This ensures that the selection of the target speed curve model is always anchored to the motion trajectory requirements, transforming the abstract mathematical model and constraints into a concrete target speed curve. This ensures that the obtained target speed curve meets the requirements of motion trajectory for equipment speed control and conforms to various actual constraints of equipment operation. From model selection to setting dynamic boundary conditions and then to the solution process, everything revolves around the trajectory requirements and equipment operation, minimizing the impact and vibration on mechanical components and effectively suppressing the impact effect during the start-up process of the water pump and turbine, achieving smoothness and flexibility in the start-up of the water pump and turbine.

[0039] Specifically, selecting a target speed curve model based on motion trajectory requirements requires clarifying the characteristics of the pump and turbine trajectory and speed control requirements, as well as the quantification logic, applicable scenarios, speed regulation characteristics, and compatible equipment operation requirements of the target speed curve model. Subsequently, combining the equipment's mechanical performance and operating condition changes, a matching analysis is conducted between the target speed curve model and the motion trajectory requirements. The ability and adaptability of each target speed curve model to meet the trajectory requirements are evaluated, and it is determined whether the target speed curve model can transform the trajectory requirements into a quantifiable speed change pattern. Finally, a comprehensive evaluation is performed based on the matching analysis results to select a target speed curve model that perfectly matches the motion trajectory requirements and the actual operating requirements of the equipment.

[0040] To obtain the target speed curve, the boundary conditions of the target speed curve model must be considered. This involves taking into account the mechanical properties of the pump and turbine, the constraints of their motion trajectory, actual operating conditions, and industry safety regulations. Boundary conditions are then set for the target speed curve model, transforming these constraints into mathematical limiting indicators. Next, the selected target speed curve model is mathematically analyzed to clarify its mathematical expression, algorithm framework, and parameters to be solved. The quantified boundary conditions are then integrated into the solution system of the target speed curve model, forming a complete constrained solution system. Following this, an appropriate solution method, such as analytical, numerical, or simulation methods, is selected based on the model's type and complexity. Finally, using the selected solution method, the target speed curve model is solved under the set boundary conditions. The initial quantified relationship of speed variation with time and operating conditions is derived, ultimately yielding a directly applicable target speed curve, which is presented as a quantified graph.

[0041] Furthermore, in the embodiments of this application, selecting a target speed curve model of a quartic polynomial according to the motion trajectory requirements includes: determining at least one of the control complexity and the required smoothness of the process according to the motion trajectory requirements; selecting a quartic polynomial according to at least one of the control complexity and the required smoothness of the process, and using the quartic polynomial as the target speed curve model.

[0042] Among them, control complexity is the ease with which the entire speed control system can achieve the preset adjustment target and ensure that the motion trajectory meets the requirements when the speed of the moving parts of the pump and turbine is adjusted based on the motion trajectory requirements of the pump and turbine; process smoothness is the quantitative process requirement proposed for the speed change process of the moving parts of the pump and turbine to meet the motion trajectory requirements of the pump and turbine and ensure the processability, stability and service life of the equipment; and the quartic polynomial is the quartic integral function selected as the target speed curve model based on the control complexity and process smoothness determined by the motion trajectory requirements of the pump and turbine.

[0043] It is understood that this application embodiment is guided by the motion trajectory requirements of the water pump and turbine, determining at least one key indicator among control complexity and process smoothness requirements. Based on these indicators, a fourth-order polynomial is selected as the target speed curve model. This target speed curve model possesses fully customizable curve shape characteristics, allowing users to construct various types of start-up curves by freely combining different boundary conditions. This achieves a precise fit between the start-up curve and the specific load and actual process requirements of the equipment, fully leveraging the structural advantages of the fourth-order polynomial model. This ensures that the selection of the target speed curve model and the design of its curve shape accurately meet the requirements of equipment operation. A high degree of matching between the start-up curve and the equipment motion trajectory requirements, specific load, and process requirements is achieved, significantly improving the accuracy and flexibility of start-up curve design.

[0044] Specifically, determining the control complexity and process smoothness based on motion trajectory requirements requires clarifying the accuracy threshold of motion component speed control, trajectory stability requirements, operating condition adaptability range, and multi-component motion coordination requirements. In conjunction with the equipment's own structural characteristics, actual operating load characteristics, and industrial production process specifications, a quantitative judgment system for control complexity and process smoothness needs to be established, and the judgment dimensions for control complexity and process smoothness need to be clarified.

[0045] Control complexity consists of four parts: the number of dimensions of speed control, the required control accuracy, the response requirements to changes in operating conditions, and the hierarchy of the control system architecture. It is related to the accuracy of the motion trajectory requirements, the requirements for trajectory coordination among multiple components of the equipment, and the frequency of changes in operating conditions. To determine the control complexity, it is necessary to quantify and classify the control dimensions, control accuracy, operating condition response, and hierarchy based on the decomposed trajectory requirements. Finally, the control complexity level that suits the trajectory requirements is determined to be low / medium / high. For example, the requirement for static orbit determination of a single component is low complexity, while the requirement for precise orbit determination of multiple components under changing operating conditions is high complexity.

[0046] The required smoothness of the process consists of three parts: the continuity of rotational speed change, the stability of the rate of change of rotational speed, and the fluctuation threshold of rotational speed acceleration. It is also related to the requirements of no sudden changes in motion trajectory, the requirements of equipment waterproofing and impact / component wear, and the requirements of process operation stability. If the required smoothness of the process is determined, it is necessary to quantify and define the maximum limit of the rate of change of rotational speed, the fluctuation range of acceleration, and the tolerance threshold of the step change of rotational speed based on the disassembled trajectory requirements. Finally, specific quantitative indicators of the smoothness of the process that match the trajectory requirements are determined. If both control complexity and the required smoothness of the process are determined at the same time, it is necessary to quantify and define the two types of indicators in the above manner to ensure that both types of indicators are highly adapted to the motion trajectory requirements.

[0047] To select a quartic polynomial based on control complexity and required process smoothness, it is necessary to review existing mainstream speed curve models. Currently, speed curve models include fixed ramp, S-curve, and low / high-order polynomial forms. Each model's mathematical structure, solution implementation difficulty, parameter adjustment flexibility, and speed smoothness performance will be analyzed to clarify its adaptability to different control complexity levels and different process smoothness indices. Then, using at least one of the control complexity and required process smoothness as selection criteria, targeted adaptability verification will be conducted on the quartic polynomial model to verify whether its number of mathematical parameters matches the predetermined control complexity level. Finally, the quartic polynomial will be selected as the target speed curve model to adapt to the motion trajectory requirements of the pump and turbine, and the general mathematical expression of this model will be clarified.

[0048] Furthermore, in the embodiments of this application, the expression for the target speed curve model is:

[0049] in, n ( t ( ) represents the target speed curve model. t For startup time, A , B , C , D , E Let be the coefficients of the fourth-degree polynomial to be determined.

[0050] It is understood that the embodiments of this application construct the target speed curve model with a quartic polynomial as the core, generate a curve with global high-order continuous smoothness, transform the complex curve generation problem into the problem of solving a standard linear equation system, achieve efficient calculation by relying on the mathematical characteristics of the quartic polynomial, avoid abrupt acceleration changes by using global high-order continuous smoothness, minimize the impact and vibration on mechanical components, effectively suppress the impact effect during the start-up process of water pumps and turbines, enable precise control of the start-up process for specific loads and process requirements, significantly reduce the amount of calculation and hardware requirements, and improve the stability, flexibility and safety of equipment start-up.

[0051] Specifically, in this application embodiment, based on the motion trajectory requirements, load characteristics and process requirements of the water pump and water turbine, the objectives of global high-order continuous smoothness, custom curve shape and efficient calculation are defined, and a fourth-order polynomial is selected as the target speed curve model.

[0052] The quartic polynomial has continuous first to third derivatives. Its first derivative corresponds to the rate of change of rotational speed, which corresponds to acceleration; the second derivative corresponds to jerk; and the third derivative corresponds to jerk. This global high-order continuity can avoid the acceleration abrupt change problem of traditional fixed slope curves and can also make up for the discontinuity of the third-order S-curve in high-order derivatives. It can eliminate the impact and vibration of mechanical parts from the source of rotational speed change and meet the needs of water pumps and turbines to prevent water pressure impact and reduce component wear during startup.

[0053] Solving a quartic polynomial can be transformed into solving a standard linear equation system with five variables. This method is computationally efficient, fast, and requires minimal processor performance. It can be implemented in embedded controllers without complex computing power, balancing algorithmic simplicity with practical engineering applications. Compared to higher-order polynomials, such as quintic and sixth-order polynomials, quartic polynomials avoid the problem of a sharp increase in computational complexity. Compared to lower-order polynomials, such as quadratic and cubic polynomials, quartic polynomials offer better smoothness and flexibility, achieving an optimal balance between smoothness, flexibility, and computational efficiency.

[0054] Furthermore, in the embodiments of this application, the boundary conditions of the target speed curve model include: the initial speed of the water pump and the water turbine are the first target speeds, the final speeds of the water pump and the water turbine are the second target speeds, the initial speed change rate of the water pump and the water turbine is the first target change rate, the final speed change rate is the second target change rate, and the midpoint speed of the water pump and the water turbine is the characteristic speed.

[0055] Among them, the initial speed refers to the actual rotational speed of the pump and turbine at the start-up moment; the first target speed is the target rotational speed of the pump and turbine at the start-up moment, preset to meet the motion trajectory requirements of the pump and turbine; the final speed is the actual rotational speed at the end of the pump and turbine speed control process; the second target speed is the target rotational speed at the end of the equipment speed control process, preset to meet the motion trajectory requirements of the pump and turbine; the initial speed change rate is the rate of change of the actual rotational speed at the start of the pump and turbine speed control process; the first target speed change rate is the target rotational speed of the pump and turbine at the end of the speed control process. The control requirements are as follows: the target speed change rate at the start of the equipment speed control is preset; the termination speed change rate is the actual speed change rate at the end of the pump and turbine speed control process; the second target speed change rate is the target speed change rate at the end of the equipment speed control process, preset to meet the pump and turbine speed control requirements; the intermediate point speed is the actual speed value of the preset moving parts at a certain intermediate time node during the pump and turbine speed control process; and the characteristic speed is the normal operating speed of the pump and turbine under the designed working conditions, preset for stable and safe operation.

[0056] It is understood that, in accordance with the requirements for pump and turbine startup or operating condition switching, this application embodiment sets multi-dimensional boundary conditions for the fourth-order polynomial target speed curve model. It explicitly limits the starting speed of the pump and turbine to a first target speed and the ending speed to a second target speed. Simultaneously, it constrains the rate of change of the starting speed of the pump and turbine to a first target rate of change and the rate of change of the ending speed of the pump and turbine to a second target rate of change. Furthermore, it sets the midpoint speed of each pump and turbine as a characteristic speed, forming a boundary constraint system from the control start point, intermediate transition stage to the end point. This provides mathematical constraints that fit the actual operating requirements of the equipment for solving the target speed curve model. It avoids abrupt changes in speed and acceleration at the start and end points of the target speed curve, while ensuring that the intermediate stage of the curve matches the speed requirements of the equipment's steady-state operation. This guarantees the high-order continuous smoothness of the fourth-order polynomial curve, making the trend of the entire speed curve match the precise control of the pump and turbine from startup / operating condition switching to steady-state operation, thus improving the stability, flexibility, and safety of equipment startup.

[0057] Specifically, based on the starting and control requirements of the water pump and turbine, system parameters, and the selected fourth-order polynomial target speed curve model, and referring to the general position (speed) constraints, acceleration (angular acceleration) constraints, jerk (angular jerk) constraints and internal point constraint logic, five independent boundary conditions are selected and set to fully constrain the fourth-order polynomial.

[0058] First, it's necessary to define the acceleration time range and the ratio of rated speed to the midpoint speed. Then, specifically set the boundary conditions and determine the starting speed; that is, the initial speed is 0, corresponding to the first target speed being 0. n (0) = 0, the rate of change of rotational speed at the initial moment is 0, which corresponds to the rate of change of the first target speed being 0. n '(0)=0, the rotational speed at the termination moment is the rated rotational speed, and the corresponding second target speed is a ,Right now n ( T )= a The rate of change of rotational speed at the termination moment is 0, which corresponds to the rate of change of the second target speed being 0. n '( T )=0, and at the same time, the midpoint speed during the startup process is set to a certain proportion of the rated speed, that is n ( T / 2)= k The entire process ensures that the five boundary conditions meet the general constraint requirements, conform to the process smoothness and speed control requirements of the pump and turbine start-up phase, and independently satisfy the mathematical requirements of the complete constraint of the fourth-order polynomial.

[0059] Furthermore, in the embodiments of this application, the process of solving the target speed curve model based on the boundary conditions of the target speed curve model to obtain the target speed curve includes: substituting the boundary conditions into the target speed curve model to establish a linear equation system; representing the linear equation system as a speed curve matrix; determining the coefficients of the target speed curve model based on the solution results of the speed curve matrix; and generating the target speed curve based on the coefficients of the target speed curve model.

[0060] Among them, the linear equation system is a set of linear equations containing the unknown coefficients of the model obtained by substituting the boundary conditions of the target speed curve model into the model and its derivative expression; the speed curve matrix is ​​the mathematical carrier after the linear equation system is transformed into standard matrix form; the coefficients of the target speed curve model are unknown parameters that determine the specific shape of the target speed curve model.

[0061] It is understood that this embodiment combines the operating conditions of the pump and turbine startup phase with five preset independent boundary conditions. Each boundary condition is substituted into the quartic polynomial target speed curve model and its first derivative expression to construct a system of linear equations containing unknown coefficients of the model. This ensures that each equation in the system corresponds to the boundary constraint requirements. Subsequently, the system of linear equations is transformed into a standard speed curve matrix form, clarifying the correspondence between the coefficient matrix, the unknown coefficient vector, and the constant term vector in the matrix. The speed curve matrix is ​​solved through linear algebra operations. Based on the solution results, all unknown coefficients of the quartic polynomial model are determined. Finally, the general expression of the quartic polynomial is used to generate the target speed curve that meets the startup and control requirements of the pump and turbine. This achieves a systematic transformation from boundary constraints to speed curves, ensuring that all constraint requirements of the boundary conditions are integrated into the generation process of the target speed curve. It also achieves the uniqueness and accuracy of the model coefficients obtained from the solution, enabling precise control of the speed operating conditions.

[0062] Specifically, this embodiment of the application uses five independent boundary conditions as a basis, substituting each boundary condition into the expression of a fourth-order polynomial and its derivatives, transforming it into a system of linear equations containing five unknown coefficients. This ensures that each equation in the system strictly matches the constraints of the starting speed, ending speed, the rate of change of the starting and ending speeds, and the speed at the intermediate point. Subsequently, a linear algebraic solution method is used to systematically solve the system of linear equations, obtaining a unique set of fourth-order polynomial coefficients, thereby obtaining the mathematical expression of the target speed curve. After completing the coefficient solution and establishing the mathematical expression, the speed command generation and execution stage begins. The processing software analyzes the solved fourth-order polynomial expression, and within a preset start-up time range, the speed setpoint is calculated point by point in a discretized manner. Finally, the speed setpoint is sent to a waveform generator, which converts the speed setpoint into a corresponding analog voltage signal, which is then transmitted to the servo driver in real time. After receiving the speed command, the servo driver precisely adjusts its output to generate variable voltage and variable frequency AC power to drive the motor, ensuring that the motor starts smoothly according to the designed target speed curve.

[0063] Furthermore, in an embodiment of this application, the expression for the rotational speed curve matrix is:

[0064] in, α For time in each boundary condition t The coefficient matrix consisting of the powers of and their derivatives. x For the coefficients to be determined A , B , C , D , E The unknown vector formed β This is the result vector consisting of the starting boundary conditions; The expression for the coefficients of the target speed curve model is: A= B= C= D=0 E=0 in, A , B , C , D , E Let be the coefficients of the fourth-degree polynomial to be determined. T To accelerate startup time, k For a certain percentage of the rated speed, a The second target speed.

[0065] It is understood that this application embodiment, focusing on the starting speed control requirements of water pumps and turbines, transforms the preset multi-dimensional boundary conditions into a standard speed curve matrix form. By performing linear algebraic solutions on the speed curve matrix, uniquely determined fourth-order polynomial coefficients are directly obtained. The boundary constraints are transformed into standardized matrix operations, realizing the mapping from boundary conditions to the coefficients of the target speed curve model. The solved coefficients can accurately restore the preset boundary constraints, ensuring the uniqueness and accuracy of the fourth-order polynomial coefficient solution. The generated fourth-order polynomial speed curve has high-order continuous smoothness, effectively avoiding acceleration abrupt changes and mechanical shocks. The matrix-based solution logic has the advantages of high computational efficiency and low hardware computing power requirements, and is easy to implement in embedded controllers, greatly improving the stability, flexibility, and economy of engineering implementation.

[0066] Specifically, the application itself constructs a matrix equation for the rotational speed curve, wherein... α The matrix consists of time values ​​from each boundary condition. t The powers and their derivatives constitute the equation. x The vector contains the coefficients of the fourth-degree polynomial to be determined. A , B , C , D , E , β The vector is composed of the specific values ​​of the starting boundary conditions, and the coefficients are then obtained by calculating the ratios of the determinants. A , B , C , D , E ,in D =0, E =0, A , B , C Startup acceleration time T Rated speed a and a certain proportion of the rated speed k The speed curve model was finally constructed through matrix operations.

[0067] This application embodiment selects a target speed curve model based on the motion trajectory requirements of the water pump and turbine. Then, it clarifies the boundary conditions corresponding to the target speed curve model, considering the equipment's mechanical performance, actual operating conditions, industry safety standards, and trajectory control requirements. Finally, it solves the boundary conditions of the target speed curve model through mathematical solutions and algorithm derivations, obtaining a target speed curve that fits the trajectory requirements and practical application requirements. The scientific setting of the boundary conditions defines a reasonable range for model solving that conforms to the actual equipment and adapts to the operating conditions. This ensures that the selection of the target speed curve model is always anchored to the motion trajectory requirements, transforming the abstract mathematical model and constraints into a concrete target speed curve. This ensures that the obtained target speed curve meets the requirements of motion trajectory for equipment speed control and conforms to various actual constraints of equipment operation. From model selection to setting dynamic boundary conditions and then to the solution process, everything revolves around the trajectory requirements and actual equipment operation, minimizing the impact and vibration on mechanical components and effectively suppressing the impact effect during the start-up process of the water pump and turbine, achieving smoothness and flexibility in the start-up of the water pump and turbine.

[0068] In step S103, the target speed curve is converted into an analog voltage setpoint signal, and the analog voltage setpoint signal is input to the servo drive to control the start of the water pump and turbine according to the analog voltage setpoint signal.

[0069] Among them, the analog voltage setpoint signal is a continuously changing analog voltage signal converted from the target speed curve; the servo drive is a control device that connects an arbitrary waveform generator to the water pump and water turbine. It receives electrical energy signals from the drive and synchronously converts them into mechanical energy to drive the operation of the water pump system with precise torque and speed.

[0070] It is understood that the embodiments of this application convert the preset target speed curve into an analog voltage command signal that is recognized by the servo driver, and then input the analog voltage signal into the servo driver. The driver parses the signal and outputs the appropriate drive command, thereby controlling the water pump and water turbine to complete the start-up action according to the target speed curve. This avoids sudden speed changes or shocks during the start-up process of the water pump and water turbine, and achieves precise control of the actual speed of the water pump and water turbine according to the preset speed curve, thereby improving the stability, flexibility and safety of equipment start-up.

[0071] Specifically, in this embodiment, a three-phase AC power grid provides power to the main circuit of the servo system. The power supply undergoes voltage variation and electrical isolation processing through a dedicated transformer to provide a stable power source for the servo driver. Subsequently, the servo driver needs to be set to analog voltage input mode, and an analog voltage input signal generated by an arbitrary waveform generator is input to the driver. The driver interprets the analog voltage signal in real time through its internal control logic and converts the analog voltage signal into three-phase AC power with variable voltage and variable frequency (VVVF) power. The power is then delivered to the servo motor. After receiving the electrical energy from the driver, the servo motor converts it into mechanical energy, which drives the water pump and turbine to run with torque and speed. Finally, the speed curve preset by the host computer is reproduced, realizing the regulation of the speed conditions during the startup of the water pump and turbine system.

[0072] Furthermore, in the embodiments of this application, converting the target speed curve into an analog voltage setpoint signal includes: determining a speed setpoint based on the target speed curve; loading the speed setpoint into an arbitrary waveform generator; and generating an analog voltage setpoint signal through the arbitrary waveform generator.

[0073] The speed setpoint is the desired motor speed value determined at each time point based on the target speed curve; the arbitrary waveform generator is an electronic device that receives the loaded speed setpoint data and converts these digital speed targets into a continuous analog voltage command signal.

[0074] It is understood that the embodiments of this application determine the speed setpoint corresponding to each moment based on a preset dynamic target speed curve, and then load the speed value that changes with time into an arbitrary waveform generator. The arbitrary waveform generator converts the digital speed target into a continuous analog voltage command signal proportional to the speed, which allows the motor control system to obtain an analog voltage command that accurately matches the preset acceleration law, and drives the motor to strictly follow the target speed curve to complete the start-up and acceleration, ensuring the smoothness of speed change and the accuracy of dynamic response, and improving the stability, flexibility and safety of equipment start-up.

[0075] Specifically, based on the solved fourth-order polynomial expression, the corresponding software is used to process it and calculate a series of speed setpoints in a discretized manner during the startup time. These setpoints are then sent to the waveform generator to generate corresponding analog voltage signals. These voltage signals are then sent to the servo driver in real time. The driver precisely controls its output of variable voltage and variable frequency AC power according to the received speed command, and synchronously drives the motor to start strictly according to the designed target speed curve.

[0076] This embodiment converts a preset target speed curve into an analog voltage command signal that is recognized by the servo driver. The analog voltage signal is then input into the servo driver, which analyzes the signal and outputs an appropriate drive command. This controls the water pump and turbine to complete the start-up action according to the target speed curve, avoiding sudden speed changes or shocks during the start-up process. It achieves precise control of the actual speed of the water pump and turbine according to the preset speed curve, improving the stability, flexibility, and safety of equipment startup.

[0077] To better understand the solution of this application, the following specific embodiment describes the low-vibration and high-stability startup process method or execution flow of the water pump and turbine based on fourth-order polynomial speed control, as follows: like Figure 2 As shown, the main components and functions of the system for realizing the low-vibration and high-stability start-up process of water pumps and turbines based on fourth-order polynomial speed control include: control and command section, power drive section, and execution and feedback section.

[0078] Control and command section: Implemented on a host computer, its core is the parametric design and rapid generation of the S-shaped fourth-order polynomial speed curve. The entire process follows a rigorous five-step mathematical modeling and execution framework, with the specific operation steps as follows: (1) Choose a fourth-degree polynomial as the mathematical model.

[0079] Based on the expected control complexity and the required smoothness of the process, a fourth-order polynomial is first selected. n ( t As the mathematical model for the target speed curve, the general form of the fourth-order polynomial is:

[0080] in, A , B , C , D , E Let be the coefficients of the fourth-degree polynomial to be determined.

[0081] A quartic polynomial has five independent coefficients, therefore five independent boundary conditions are required to solve for and determine the unique coefficients.

[0082] (2) Set the start boundary conditions.

[0083] Based on the selected speed curve in step (1), as well as the specific operating conditions and system parameters, five boundary conditions are set to fully constrain the quartic polynomial. n ( t The boundary conditions can be freely selected from the following types: Position (speed) constraint: at a specific time point t i The required rotational speed is to reach a specific value. n ( t i ).

[0084] Acceleration (angular acceleration) constraint: at a specific time point t i The rate of change of rotational speed is required to reach a specific value. n '( t i ).

[0085] Angular jerk constraint: at a specific time point t i The rate of change of acceleration is required to reach a specific value. n ''( t i ).

[0086] Internal point constraints: Allows setting any intermediate point of the curve during the startup process. t z The position, velocity, or acceleration can be used to customize the shape of the curve.

[0087] The boundary conditions for the S-type quartic polynomial speed curve proposed in this application embodiment are as follows: (a) Initial velocity, n (0) = 0; (b) Termination velocity, n d (T)= a (c) Initial velocity change rate, n '(0)=0; (d) Termination rate of change, n '( T (e) Velocity at the midpoint, =0; n z ( T / 2)= k .

[0088] Among them, 0- T To accelerate startup time, a Rated speed, k It is a certain percentage of the rated speed.

[0089] (3) Construct a system of linear equations.

[0090] Substitute the five boundary conditions set in step (2) into the fourth-degree polynomial. n ( t ) and its derivatives n '( t i ),n ''( t i In the expression, a structure is created containing five unknowns. A , B , C , D , E A system of linear equations, which can be represented in matrix form.

[0091] in: x For the coefficients to be determined A , B , C , D , E The unknown vector formed α For time in each boundary condition t The coefficient matrix consisting of the powers of and their derivatives. β The target value is determined by each boundary condition (e.g.) n ( t i ), n '( t i ), n ''( t i The result vector is composed of (etc.).

[0092] (4) Solve for the coefficients of the fourth-degree polynomial.

[0093] Solving this system of equations using standard linear algebraic methods (such as Gaussian elimination or matrix inversion) yields a unique set of quartic polynomial coefficients. A , B , C , D , E Thus, the mathematical expression for the target speed curve is obtained. n ( t ).

[0094] The coefficients obtained by solving the S-type quartic polynomial speed curve proposed in this embodiment are as follows: A= B= C= D=0 E=0 (5) Generate speed command and execute it.

[0095] Based on the solved quartic polynomial expression, the corresponding software is used to process it, calculating a series of speed setpoints in a discretized manner during the startup time. These setpoints are then sent to a waveform generator to generate corresponding analog voltage signals. These voltage signals are then sent to the servo driver in real time. The driver, based on the received speed command, precisely controls its output of variable voltage and variable frequency AC power, synchronously driving the motor to strictly follow the designed target speed curve. n ( t )start up.

[0096] This acceleration curve exhibits significant advantages in smoothness, shock suppression, and stable system startup, unlike the fixed "S"-shaped acceleration curve of traditional frequency converters. The S-curve based on the quartic polynomial can generate speed curves with various growth trends by controlling the constraints of the intermediate internal points.

[0097] The dimensionless boundary condition for the intermediate speed curve in this embodiment is: n (0)=0、 n d (1) = 1、 n '(0)=0、 n '(1)=0、 n z (0.5) = 0.5( n d (1) This curve is the most classic and basic form. The time spent in its acceleration and deceleration phases is exactly equal. The acceleration curve is axially symmetric about the midpoint of time, while the jerk curve is centrally symmetric about the midpoint of time. It is the preferred trajectory planning scheme in applications with high requirements for vibration suppression, positioning accuracy, protection systems, and smooth start-up.

[0098] By modifying the value of the internal intermediate point: n z (0.5) = 0.35 n d (1)) or n z (0.5) = 0.425 n d(1) An asymmetric S-shaped fourth-order polynomial speed curve with "slow start and quick stop" characteristics can be constructed. This curve differs significantly from the symmetric S-shaped fourth-order polynomial curve: First, it exhibits lower acceleration in the initial stage of startup. Due to the smaller initial acceleration and its gradual increase, it more effectively suppresses the initial impact on the system. Second, the acceleration curve shows a significant asymmetric shape and a "peak shift" phenomenon. In order to compensate for the slow increase in speed in the early stage in the second half of the process, the acceleration peak will shift to after the midpoint of the startup time. This scheme of "trading initial stability for end-stage dynamic performance" makes it uniquely valuable in specific engineering applications.

[0099] By setting a middle path constraint point with a reverse offset: n z (0.5) = 0.65 n d (1)) or n z (0.5) = 0.575 n d (1)) can construct an asymmetric S-shaped fourth-order polynomial speed curve with the characteristics of "rapid start and slow stop". This speed curve has the following significant advantages: First, the core advantage lies in the combination of rapid response capability in the early stage of start-up and end stability. The system starts with a high acceleration gradient in the first half of the process, so as to reach a high speed in the shortest time. The second half of the process is a relatively long and smoother acceleration process, which ensures that the system can achieve stable operation with minimal impact and vibration when approaching the target, and can effectively suppress overshoot. Second, the acceleration curve of this curve shows significant "peak forward shift" and asymmetric attenuation characteristics. This trajectory planning strategy is suitable for engineering scenarios with dual requirements for time efficiency and terminal positioning accuracy.

[0100] The power drive section mainly consists of a transformer and a servo driver. The operation is as follows: the main circuit power supply for the servo system is provided by a three-phase AC power grid. After voltage variation and electrical isolation by a dedicated transformer, a stable power source is provided to the servo driver. The driver is set to analog voltage input mode. In this mode, it receives analog voltage input signals from an arbitrary waveform generator. Through its internal control logic, it interprets and converts these signals in real time into a set of variable voltage and variable frequency three-phase AC power, and then supplies the VVVF power to the servo motor as its direct driving force.

[0101] The execution and feedback section includes equipment such as the water pump and turbine circulation system, and servo motors. The servo motor, as the system's end effector, is mechanically connected to the water pump's drive shaft via a rigid coupling. It receives electrical signals from the driver and synchronously converts them into mechanical energy, driving the water pump system with precise torque and speed control. In this way, the preset speed curve in the host computer can be reproduced with high fidelity, thus achieving precise control of the water pump and turbine system's speed and operating conditions throughout the entire transient process.

[0102] like Figure 3 As shown, the design speed and the experimentally measured speed are compared at a start-up time of 0.5s. Figure 3 The design speed curves and test speed curves corresponding to different speed ratios almost completely overlap, showing that the speed change measured in the test is basically consistent with the speed change process of the design. It can reproduce the preset speed curve with high fidelity. This not only verifies the accuracy and effectiveness of the control method in speed tracking, but also reflects its ability to precisely control the speed conditions. The speed under different speed ratios can quickly rise to a stable value in a short time and the process is smooth with no obvious fluctuations or deviations.

[0103] like Figure 4 As shown, the head changes of the water pump and the centrifugal pump of the turbine during a 0.5s start-up time. Figure 4 The head curves corresponding to different speed ratios all showed a rapid rise followed by a stabilization trend. The measured head changes with time exhibited a significant lag effect. The curves with higher speed ratios showed a faster head rise during the startup phase. Furthermore, it was observed that at the end of startup, the smoother the acceleration change, the smaller the transient impact head. This phenomenon reflects that changes in speed and acceleration are the main factors affecting the transient impact of centrifugal pumps, and also verifies the role of speed curve design in controlling transient impact.

[0104] In summary, the low-vibration and high-stability startup method for water pumps and turbines based on fourth-order polynomial speed control proposed in this application obtains the motion trajectory requirements of the water pump and turbine, selects a target speed curve model based on these requirements, solves the specific target speed curve by combining the model boundary conditions, and then converts the target speed curve into an analog voltage command signal that is recognized by the servo driver. The analog voltage command signal is input to the servo driver, which analyzes the signal and drives the water pump and turbine to start. This achieves control over the startup process of the water pump and turbine, ensuring that the water pump and turbine start up and operate strictly according to the preset motion trajectory requirements. It also precisely controls the actual speed of the water pump and turbine to change with the preset speed curve, improving the stability, flexibility, and operational safety of the water pump and turbine startup.

[0105] Next, referring to the accompanying drawings, a low-vibration and high-stability start-up system for a water pump and turbine based on fourth-order polynomial speed control, according to an embodiment of this application, is described.

[0106] Figure 5 This is a block diagram of a low-vibration, high-stability start-up system 500 for a water pump and turbine based on fourth-order polynomial speed control, according to an embodiment of this application.

[0107] like Figure 5 As shown, the low-vibration and high-stability start-up system 500 for water pumps and turbines based on fourth-order polynomial speed control includes: an acquisition module 501, a solution module 502, and a start-up module 503.

[0108] The module 501 is used to acquire the motion trajectory requirements of the water pump and the turbine; the solution module 502 is used to select a fourth-order polynomial target speed curve model according to the motion trajectory requirements, set boundary conditions according to the target speed curve model, and solve the coefficients of the target speed curve model according to the boundary conditions to obtain the target speed curve; the start module 503 is used to convert the target speed curve into an analog voltage given signal, and the servo driver controls the water pump and turbine to start according to the analog voltage given signal.

[0109] Furthermore, in this embodiment of the application, the solving module 502 is further configured to: determine at least one of the control complexity and the required smoothness of the process according to the motion trajectory requirements; select a quartic polynomial according to at least one of the control complexity and the required smoothness of the process, and use the quartic polynomial as the target speed curve model.

[0110] Furthermore, in this embodiment, the expression for the target speed curve model is:

[0111] in, n ( t ( ) represents the target speed curve model. t For startup time, A , B , C , D , E Let be the coefficients of the fourth-degree polynomial to be determined.

[0112] Furthermore, in the embodiments of this application, the boundary conditions of the target speed curve model include: the initial speed of the water pump and the water turbine are the first target speeds, the final speeds of the water pump and the water turbine are the second target speeds, the initial speed change rate of the water pump and the water turbine is the first target change rate, the final speed change rate is the second target change rate, and the midpoint speed of the water pump and the water turbine is the characteristic speed.

[0113] Furthermore, in this embodiment, the solver module 502 is further configured to: substitute boundary conditions into the target speed curve model to establish a linear equation system; represent the linear equation system as a speed curve matrix; determine the coefficients of the target speed curve model based on the solution results of the speed curve matrix; and generate the target speed curve based on the coefficients of the target speed curve model.

[0114] Furthermore, in this embodiment, the expression for the rotational speed curve matrix is:

[0115] in, α For time in each boundary condition t The coefficient matrix consisting of the powers of and their derivatives. x For the coefficients to be determined A , B , C , D , E The unknown vector formed β This is the result vector consisting of the starting boundary conditions; The expression for the coefficients of the target speed curve model is: A= B= C= D=0 E=0 in, A , B , C , D , E Let be the coefficients of the fourth-degree polynomial to be determined. T To accelerate startup time, k For a certain percentage of the rated speed, a The second target speed.

[0116] Furthermore, in this embodiment of the application, the startup module 503 is further configured to: convert the target speed curve into an analog voltage setpoint signal, including: determining a speed setpoint based on the target speed curve; loading the speed setpoint into an arbitrary waveform generator; and generating an analog voltage setpoint signal through the arbitrary waveform generator.

[0117] It should be noted that the foregoing explanation of the method embodiment for low-vibration and high-stability start-up of water pumps and turbines based on fourth-order polynomial speed control also applies to the low-vibration and high-stability start-up system of water pumps and turbines based on fourth-order polynomial speed control in this embodiment, and will not be repeated here.

[0118] In summary, the low-vibration and high-stability starting system for water pumps and turbines based on fourth-order polynomial speed control proposed in this application obtains the motion trajectory requirements of the water pumps and turbines, selects a target speed curve model based on these requirements, and solves the specific target speed curve by combining the model's boundary conditions. Subsequently, the target speed curve is converted into an analog voltage command signal that is recognized by the servo driver. The analog voltage command signal is input to the servo driver, which analyzes the signal and drives the water pump and turbine to start. This achieves control over the starting process of the water pump and turbine, ensuring that the water pump and turbine start and operate strictly according to the preset motion trajectory requirements. It also precisely controls the actual speed of the water pump and turbine to change with the preset speed curve, improving the smoothness, flexibility, and operational safety of the water pump and turbine starting process.

[0119] Figure 6 A schematic diagram of an electronic device provided in an embodiment of this application. The electronic device may include: The memory 601, the processor 602, and the computer program stored on the memory 601 and capable of running on the processor 602.

[0120] When the processor 602 executes the program, it implements the low-vibration and high-stability start-up process method for water pumps and turbines based on fourth-order polynomial speed control provided in the above embodiments.

[0121] Furthermore, electronic devices also include: Communication interface 603 is used for communication between memory 601 and processor 602.

[0122] The memory 601 is used to store computer programs that can run on the processor 602.

[0123] The memory 601 may include high-speed RAM memory, and may also include non-volatile memory, such as at least one disk storage device.

[0124] If the memory 601, processor 602, and communication interface 603 are implemented independently, then the communication interface 603, memory 601, and processor 602 can be interconnected via a bus to complete communication between them. The bus can be an Industry Standard Architecture (ISA) bus, a Peripheral Component Interconnect (PCI) bus, or an Extended Industry Standard Architecture (EISA) bus, etc. The bus can be divided into address bus, data bus, control bus, etc. For ease of representation, Figure 6 The bus is represented by a single thick line, but this does not mean that there is only one bus or one type of bus.

[0125] Optionally, in a specific implementation, if the memory 601, processor 602, and communication interface 603 are integrated on a single chip, then the memory 601, processor 602, and communication interface 603 can communicate with each other through an internal interface.

[0126] The processor 602 may be a central processing unit (CPU), an application specific integrated circuit (ASIC), or one or more integrated circuits configured to implement the embodiments of this application.

[0127] This application also provides a computer-readable storage medium storing a computer program or instructions thereon, which, when executed by a processor, implements the above-described method for low-vibration and high-stability start-up of a water pump and turbine based on fourth-order polynomial speed control.

[0128] This application also provides a computer program product, including a computer program or instructions, which, when executed, implement the above-described method for low-vibration and high-stability start-up of a water pump and turbine based on fourth-order polynomial speed control.

[0129] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of this application. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of different embodiments or examples.

[0130] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of that feature. In the description of this application, "N" means at least two, such as two, three, etc., unless otherwise explicitly specified.

[0131] Any process or method described in the flowchart or otherwise herein can be understood as representing a module, segment, or portion of code comprising one or N executable instructions for implementing custom logic functions or processes, and the scope of the preferred embodiments of this application includes additional implementations in which functions may be performed not in the order shown or discussed, including substantially simultaneously or in reverse order depending on the functions involved, as should be understood by those skilled in the art to which embodiments of this application pertain.

[0132] It should be understood that the various parts of this application can be implemented using hardware, software, firmware, or a combination thereof. In the above embodiments, the N steps or methods can be implemented using software or firmware stored in memory and executed by a suitable instruction execution system. For example, if implemented in hardware, as in another embodiment, it can be implemented using any one or more of the following techniques known in the art: discrete logic circuits having logic gates for implementing logical functions on data signals, application-specific integrated circuits (ASICs) having suitable combinational logic gates, programmable gate arrays (FPGAs), field-programmable gate arrays (FPGAs), etc.

[0133] Those skilled in the art will understand that all or part of the steps of the methods in the above embodiments can be implemented by a program instructing related hardware. The program can be stored in a computer-readable storage medium, and when executed, the program includes one or a combination of the steps of the method embodiments.

Claims

1. A method for low-vibration and high-stability start-up of water pumps and turbines based on fourth-order polynomial speed control, characterized in that, Includes the following steps: The required motion trajectories of the water pump and water turbine are obtained; The target rotational speed curve model is selected based on the required motion trajectory, and the target rotational speed curve is obtained by solving the target rotational speed curve model according to the boundary conditions of the target rotational speed curve model. The target speed curve is converted into an analog voltage command signal, and the analog voltage command signal is input to the servo driver to control the start of the water pump and turbine according to the analog voltage command signal.

2. The pump and turbine starting method according to claim 1, characterized in that, The step of selecting a fourth-order polynomial target rotational speed curve model based on the motion trajectory requirements includes: Determine at least one of the control complexity and the required smoothness of the process based on the motion trajectory requirements; A quartic polynomial is selected based on at least one of the control complexity and the required smoothness of the process, and the quartic polynomial is used as the target speed curve model.

3. The method for starting a water pump and a water turbine according to claim 1 or 2, characterized in that, The expression for the target speed curve model is: in, n ( t ( ) represents the target speed curve model. t For startup time, A , B , C , D , E Let be the coefficients of the fourth-degree polynomial to be determined.

4. The method for starting a water pump and a water turbine according to claim 1, characterized in that, The boundary conditions of the target speed curve model include: the initial speed of the water pump and the water turbine are the first target speeds, the final speeds of the water pump and the water turbine are the second target speeds, the initial speed change rate of the water pump and the water turbine is the first target change rate, the final speed change rate is the second target change rate, and the midpoint speed of the water pump and the water turbine is the characteristic speed.

5. The method for starting a water pump and a water turbine according to claim 1 or 4, characterized in that, The step of solving the target speed curve model based on the boundary conditions of the target speed curve model to obtain the target speed curve includes: The boundary conditions are then substituted into the target rotational speed curve model to establish a system of linear equations. The linear equation system is represented as a speed curve matrix, and the coefficients of the target speed curve model are determined based on the solution results of the speed curve matrix. The target speed curve is generated based on the coefficients of the target speed curve model.

6. The method for starting a water pump and a water turbine according to claim 5, characterized in that, The expression for the rotational speed curve matrix is: in, α For time in each boundary condition t The coefficient matrix consisting of the powers of and their derivatives. x For the coefficients to be determined A , B , C , D , E The unknown vector formed β This is the result vector consisting of the starting boundary conditions; The expression for the coefficients of the target speed curve model is as follows: A= B= C= D=0 E=0 in, A , B , C , D , E Let be the coefficients of the fourth-degree polynomial to be determined. T To accelerate startup time, k For a certain percentage of the rated speed, a The second target speed.

7. The method for starting a water pump and a water turbine according to claim 1, characterized in that, The step of converting the target speed curve into an analog voltage command signal includes: Determine the speed setpoint based on the target speed curve; The speed setting value is applied to an arbitrary waveform generator; The analog voltage given signal is generated by the arbitrary waveform generator.

8. A low-vibration, high-stability starting system for water pumps and turbines based on fourth-order polynomial speed control, characterized in that, include: The acquisition module is used to acquire the motion trajectory requirements of the water pump and water turbine; The solution module is used to select a fourth-order polynomial target speed curve model according to the motion trajectory requirements, set boundary conditions according to the target speed curve model, and solve the coefficients of the target speed curve model according to the boundary conditions to obtain the target speed curve. The starting module is used to convert the target speed curve into an analog voltage setpoint signal, and the servo driver controls the water pump and water turbine to start according to the analog voltage setpoint signal.

9. An electronic device, characterized in that, include: The memory, the processor, and the computer program stored in the memory and executable on the processor, the processor executing the program to implement the low-vibration, high-stability start-up method for water pumps and turbines based on fourth-order polynomial speed control as described in any one of claims 1-7.

10. A computer program product, comprising a computer program or instructions, characterized in that, When the computer program or instructions are executed, they implement the low-vibration and high-stability start-up process method for water pumps and turbines based on fourth-order polynomial speed control as described in any one of claims 1-7.

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