Analytical modeling of hydraulic on-off switching system considering throttling and switching nonlinearities

Abstract

The present application relates to a kind of analytical modeling method of hydraulic switching conversion system considering throttling and switching nonlinearity, belong to the field of hydraulic switching conversion system.The method steps of the present application are:1) establish the input-output relationship of hydraulic switching conversion system element;2) system topology lumped parameter equivalence;3) system processing is single topology form without switching element, structure is invariable, and the nonlinearity characteristics of throttling and switching are retained;4) establish system nonlinear static model and the neighborhood linear dynamic model related to static operating point.This method can reflect the output of system under different parameter configurations and different inputs through analytical expression, and the solving speed is fast.The influence law of system parameters on output is determined, the parameter adjustment range is reduced, and the optimization objective function of system dynamic response is given, which can be applied to solve the output evaluation and parameter configuration difficulty of hydraulic switching conversion system under multiple working conditions.The present application provides guidance for the design and optimization of hydraulic switching conversion system.

Description

Technical Field

[0001] This invention relates to the field of hydraulic switching systems (digital hydraulics), and specifically to an analytical modeling method for hydraulic switching systems that considers throttling and switching nonlinearities. Background Technology

[0002] Breakthroughs in electro-hydraulic proportional and servo technologies have enabled hydraulic systems to achieve rapid response and precise control through valve manipulation of fluids. However, valve control is an impedance control method, which suffers from energy dissipation and low efficiency. In contrast to impedance control, a more efficient switching control concept is widely used in the field of power electronics. Switching control replaces valve opening control with topology changes, theoretically achieving 100% energy conversion efficiency, providing a completely new approach to hydraulic technology.

[0003] Hydraulic switching converter systems are a direct analogue to switching control, consisting of switching elements and energy storage elements. The energy storage elements are divided into fluid sensing elements and fluid capacitive elements, respectively realizing the conversion between hydraulic energy and kinetic and potential energy. The system utilizes the on / off switching of valves to complete topology switching, and by controlling the switching time to change the charging and discharging time of the energy storage elements, it achieves the conversion and control of hydraulic energy. Because it fundamentally changes the valve control method that relies on dissipated energy, it is a potential replacement for high-efficiency hydraulic drive devices, with broad application prospects in high-efficiency hydraulic drives and single-source multi-drive applications. However, because hydraulic switching converter systems simultaneously involve throttling and switching nonlinearities, modeling the system is difficult, making it hard to accurately estimate the output of the actual system. The numerous parameters of hydraulic components and the complex operating mechanism of switching control make it difficult to adjust parameters to achieve ideal static and dynamic output characteristics without a suitable model. This makes it very difficult to predict the output of existing systems, optimize system components and loop structures, and select parameters that can achieve excellent output in practical applications under multiple working conditions. Among the publicly available modeling methods, the Time-Frequency Domain Numerical Iteration (TFDI) method represented by Manhartsgruber, the simultaneous solution method of differential equations represented by Negri and Wang, and the conclusions of power electronics modeling for switching nonlinearity represented by Rannow have all established models of hydraulic switching converter systems. They have evaluated the output of different topologies of hydraulic switching converter systems under certain conditions and have a certain degree of accuracy. However, some shortcomings or other limitations still exist, mainly manifested in the following ways:

[0004] (1) The numerical iterative method (TFDI) is slow and requires a lot of computation and pattern summarization to obtain the output performance of the actual system under different operating conditions. Optimizing system parameters requires the use of intelligent algorithms to select the best parameters from a large number of parameters, which is time-consuming and complicated.

[0005] (2) The method of solving differential equations and deriving analytical models is complex. In order to ensure that the differential equations are solvable, it is also necessary to ignore the higher-order behavior generated by the two energy storage elements, which makes the accuracy of the established model in predicting the actual system insufficient.

[0006] (3) When solving differential equations or directly applying the conclusions of power electronic state-space averaging to deal with switching nonlinearity, the throttling nonlinearity of the switching elements in the system cannot be considered, resulting in poor accuracy of the derived model when the system has low power input or large load fluctuations. Summary of the Invention

[0007] The purpose of this invention is to provide an analytical modeling method for hydraulic switch conversion systems that considers throttling and switching nonlinearity. This method can accurately evaluate the output of the hydraulic switch conversion system under multiple operating conditions, provide an optimization objective function, and achieve optimal parameter configuration for dynamic and static outputs.

[0008] To achieve the above objectives, the technical solution of the present invention is: an analytical modeling method for a hydraulic switching conversion system considering throttling and switching nonlinearity. The hydraulic switching conversion system includes an energy storage element, a switching element, hydraulic pipelines, and an output load. The energy storage element includes a liquid storage element and a liquid sensing element. The liquid storage element includes an accumulator and an oil chamber. The liquid sensing element includes an inertial tube and a hydraulic motor. The switching element includes a switching valve and a check valve. The volume of the hydraulic pipelines between the switching valve, check valve, and liquid sensing element that contains the hydraulic fluid is described as the switching volume. The output load includes a throttle valve. The hydraulic switching conversion system includes a boost topology, a depressurization topology, and a boost-depressurization topology. The function of the switching element in the hydraulic switching conversion system causes intermittent and alternating flow in the hydraulic pipelines containing the switching valve and the check valve, referred to as an alternating topology. The alternating flow branches are described as switching branches in the hydraulic switching conversion system, and the nodes where the switching branches intersect are described as switching nodes. The analytical modeling method for the hydraulic switching conversion system includes the following steps:

[0009] Step S1: Establish the input-output relationship of the components of the hydraulic switch conversion system, and make equivalent connections based on the lumped parameter approach;

[0010] Step S2: Based on the lumped parameter approach, transform the lumped parameters of the hydraulic switch conversion system into an equivalent topology.

[0011] Step S3: While retaining the throttling and switching nonlinear characteristics of the hydraulic switch conversion system, the alternating topology of the hydraulic switch conversion system caused by the switching of switching elements is processed into a single topology without switching elements and with unchanged structure.

[0012] Step S4: Establish a nonlinear static model of the hydraulic switch conversion system and a neighborhood linear dynamic model related to the static point.

[0013] In one embodiment of the present invention, for components other than switching elements, the method of lumped parameter equivalence is to define the integral, differential, and proportional components of the component's transfer function as the component's own liquid capacitance part, liquid sensing part, and linear liquid resistance part, respectively, with the series and parallel relationships of each part following the transfer function; the method of lumped parameter equivalence for switching elements and throttle valves with nonlinear input-output relationships is to define the constant term in the nonlinear equation as the nonlinear liquid resistance part R:

[0014]

[0015] In the formula, q orifice C represents the throttling flow rate of switching elements and throttle valves. d ρ is the flow coefficient, A is the equivalent flow area of ​​the switching element / throttle valve, ρ is the density of the flowing oil, and Δp is the flow coefficient. orifice This refers to the pressure drop during the flow of switching elements and throttle valves.

[0016] In one embodiment of the present invention, the method for lumped parameter equivalence of buck topology is to consider the liquid capacitor element, liquid sensor element, switching element and output load in buck topology, and lumped parameterize and connect each part; the method for lumped parameter equivalence of boost topology and buck-boost topology is to consider the liquid capacitor element, liquid sensor element, switching element, output load and switching volume in boost and buck-boost topology, and lumped parameterize and connect each part.

[0017] In one embodiment of the present invention, the variables of the hydraulic switchgear system include state variables and input variables. Before processing the single topology of the hydraulic switchgear system, the following assumptions need to be made about the variables of the hydraulic switchgear system: 1) It is assumed that the energy storage capacity of the energy storage element of the hydraulic switchgear system is sufficient to make the ripple of the state variables of the hydraulic switchgear system much smaller than its average value; 2) External disturbances are much smaller than the average value of the input variables of the hydraulic switchgear system itself. The mean value of each variable of the hydraulic switchgear system is calculated over one switching cycle, replacing its time-varying value over one cycle. The mean value is the sum of the static part and the dynamic fluctuation part of the hydraulic switchgear system variable.

[0018]

[0019] In the formula, x(t) is a variable of the hydraulic switch conversion system. The variable is in a switching cycle T S The mean of the variable, where X is the static part of the variable. It refers to the dynamic fluctuation of the variable.

[0020] In one embodiment of the present invention, the method for processing a hydraulic switchgear system from an alternating topology to a single topology without switching elements and with unchanged structure is as follows: The variables in the hydraulic switchgear system that exhibit step signals due to topology switching are processed into continuous variables, including the flow rate q of the switching branch. bran (t) and the fluid pressure p at the switching node node (t).

[0021] In one embodiment of the present invention, in a step-down topology, if the flow rate q of the switching branch... bran (t) is cut off when the switching valve is on and flows when the switching valve is off, with a flow rate q. bran (t) is:

[0022]

[0023] Then the segmented flow q bran (t) is treated as a continuous variable The method is as follows:

[0024]

[0025] In the formula, d(t) is the proportion of the valve's on-time to the switching cycle, and d'(t) = 1 - d(t) is the proportion of the valve's off-time to the switching cycle. This refers to the flow rate variable delivered to the switching branch in the step-down topology.

[0026] In one embodiment of the present invention, the segmented flow q of the switching branch between the boost topology and the buck-boost topology is processed. bran (t) is a continuous variable At this time, it is necessary to increase the shunt flow rate q to take into account the switching volume. sv The effect of (t); on the diversion flow rate q sv (t) is processed:

[0027] Step S01: Divert the traffic q sv (t) Flow averaging during valve on-off and off-off:

[0028]

[0029] Step S02: Obtain the segmented flow q of the switched branch. bran (t) is:

[0030]

[0031] In the formula, d(t) is the proportion of the valve's on-time to the switching cycle, d'(t) = 1 - d(t) is the proportion of the valve's off-time to the switching cycle, and C sv To switch the volumetric liquid capacity section, sv ​> represents the average shunting result of the switching volume when the switching element is on or off, p tar To switch the highest pressure that the oil in the volume can reach, This refers to the flow rate variable delivered to the switching branch in the boost topology and boost-buck topology.

[0032] In one embodiment of the present invention, the segmented fluid pressure p at the switching node is processed. node When (t), the pressure drop Δp(t) of all lumped parameter parts in the switching branch needs to be considered, including three cases: (1) constant pressure drop part p or node p where the pressure value is a state variable. i (t); (2) Linear liquid resistance part; (3) Nonlinear liquid resistance part;

[0033] The handling method for situation (1) is as follows:

[0034]

[0035]

[0036] The handling method for situation (2) is as follows:

[0037]

[0038] The handling method for situation (3) is as follows:

[0039]

[0040] In the formula, d(t) is the proportion of the valve's on-time to the switching cycle. R represents the flow rate variable delivered to the switching branch in the buck topology, boost topology, and buck-boost topology, and R is the nonlinear liquid resistance component.

[0041] In one embodiment of the present invention, the method for establishing a nonlinear static model of a hydraulic switch conversion system is as follows: ignoring the dynamic fluctuation part of the mean value of the hydraulic switch conversion system variables, retaining only the static part of the mean value, and establishing the relationship between the static values ​​of the variables based on the processed single topology.

[0042] In one embodiment of the present invention, the method for establishing the dynamic model of the hydraulic switch conversion system is as follows: the mean value of the hydraulic switch conversion system variable is decomposed into the sum of dynamic fluctuation part and static part, and substituted into the static model to obtain a nonlinear dynamic model related to the static operating point of the variable. Higher-order dynamic terms are ignored, and the nonlinear dynamic terms are expanded in the neighborhood of its static point to obtain a linear dynamic model in the neighborhood of the static value of the hydraulic switch conversion system variable.

[0043] Compared with the prior art, the present invention has the following beneficial effects:

[0044] (1) This invention solves the problems of slow solution speed and difficult parameter optimization in numerical iterative methods. The proposed method can provide analytical expressions for the static and dynamic behavior of the hydraulic switch conversion system. Under different system parameter configurations and different inputs, the expressions reflect the system output law, and the solution speed is fast. When optimizing system parameters, the influence law of system parameters on output is clarified, the parameter adjustment range is narrowed, and the optimization objectives of system dynamic response are also given: damping ratio function and natural frequency function.

[0045] (2) This invention solves the problems of complex calculations and inaccurate models in the method of solving differential equations. The proposed method derives the model based on the average behavior of the system state variables over a period of time, abandoning the time-axis-based differential equation differentiation method. As long as algebraic operations are performed, higher-order differentials of multiple energy storage elements can also be considered.

[0046] (3) This invention solves the problem of poor model accuracy when the system has low power input or large load fluctuations. The proposed method is based on the basic theory of state-space averaging in power electronics. It derives a method for handling the segmented voltage drop variable caused by switching when considering the nonlinearity of hydraulic throttling. The derived model includes both throttling nonlinearity and switching nonlinearity characteristics. It has been verified that it can accurately estimate the system behavior over a wide range of operating conditions. Attached Figure Description

[0047] Figure 1 The following are the basic topologies of the hydraulic switch conversion system according to an embodiment of the present invention.

[0048] Figure 2 This is a flowchart of an embodiment of the present invention.

[0049] Figure 3 This is a schematic diagram illustrating the specific implementation process of an embodiment of the present invention.

[0050] Figure 4 This is a schematic diagram of a single topology of the hydraulic switch conversion system according to an embodiment of the present invention.

[0051] Figure 5 The method of this invention evaluates the output of a hydraulic switch conversion system under different duty cycle conditions.

[0052] Figure 6 This embodiment demonstrates the parameter optimization effect of the method on the dynamic response of the hydraulic switch boosting system. Detailed Implementation

[0053] The technical solution of the present invention will now be described in detail with reference to the accompanying drawings.

[0054] Figure 1 The following are the basic topologies of the hydraulic switch conversion system according to an embodiment of the present invention. Figure 1(a) is the step-down topology of the hydraulic switch conversion system. Figure 1 (b) is the boost topology of the hydraulic switch conversion system. Figure 1 (c) is the boost / deboost topology of a hydraulic switch conversion system. The hydraulic switch conversion system comprises: an energy storage element, a switching element, a switching volume, hydraulic lines, and an output load. The energy storage element includes a liquid storage element and a liquid sensing element. The liquid storage element includes an accumulator and an oil chamber. The liquid sensing element includes an inertial tube and a hydraulic motor. The switching element includes a switching valve and a check valve. The switching volume is the volume of hydraulic fluid contained in the hydraulic lines between the switching valve, the check valve, and the liquid sensing element. The output load includes a throttle valve. The hydraulic switch conversion system includes boost topology, deboost topology, and boost / deboost topology. The function of the switching element in the hydraulic switch conversion system allows the hydraulic lines containing the switching valve and the check valve to flow intermittently and alternately. This is called an alternating topology. The alternating branches are described as switching branches in the system, and the nodes where the switching branches intersect are described as switching nodes.

[0055] like Figure 2 and Figure 3 This embodiment provides a method for analytical modeling of a hydraulic switching system that includes throttling and switching nonlinearities, comprising the following steps:

[0056] Step S1: Establish the input-output relationship of the components of the hydraulic switch conversion system, and make equivalent connections based on the lumped parameter approach;

[0057] Step S2: Based on the lumped parameter equivalent components, the lumped parameter of the hydraulic switch conversion system is transformed into an equivalent topology;

[0058] Step S3: While preserving the throttling and switching nonlinear characteristics of the hydraulic switch conversion system, the alternating topology caused by the switching of switching elements is processed into a single topology without switching elements and with unchanged structure.

[0059] Step S4: Establish a nonlinear static model of the hydraulic switch conversion system and a neighborhood linear dynamic model related to the static point.

[0060] In step S1, the input and output of the hydraulic components are pressure drop and flow rate, respectively. Based on the flow continuity equation and force balance equation, the relationship between pressure drop and flow rate of each component in the hydraulic switching system can be established. For components other than the switching element, including the accumulator, oil chamber, hydraulic motor, inertial tube, hydraulic pipeline, and switching volume, a linear relationship between pressure drop (pressure) and flow rate can be obtained. After Laplace transformation, the transfer function of the output with respect to the input is obtained. The integral, differential, and proportional components are decomposed and named the liquid capacity part, liquid sensing part, and linear liquid resistance part, respectively. Based on lumped parameter theory, the corresponding components can be equivalent to series / parallel connections of the liquid capacity part, liquid sensing part, and linear liquid resistance part. The series / parallel connection relationship of each part follows the transfer function. The following uses the more complex accumulator component as an example to demonstrate its lumped parameter equivalence.

[0061] A bladder accumulator structure consists of a gas section and a mechanical section. The gas section is characterized by stiffness K. a Acting on the mechanical parts, the gas stiffness is derived below. It is assumed that the accumulator gas does not exchange heat with the outside environment during operation; therefore, at a certain moment, the gas pressure p... a and volume V a follow,

[0062] f(p a V a ) = p a V a n =p0V0 n

[0063] In the formula, p0 = p pre +p atm V0 is the initial absolute pressure of the accumulator gas; V0 is the volume of the accumulator (initial gas). Since the accumulator operating frequency is higher than 5Hz, the process is considered adiabatic, and therefore the gas polytropic index n = 1.4 is taken. Then the gas stiffness K... a This is manifested as the working point (p) a0 V a0 The function is δ(p). For local linearization, the bivariate function (2-1) in the neighborhood δ(p) is linearized. a0 V a0 First-order Taylor expansion,

[0064] f(p a V a ) = p a0 V a0 n +V a0 n ·dp a +np a0 V a0 n-1 dV a

[0065] The gas stiffness can be obtained.

[0066]

[0067] In the mechanical part of the accumulator, the forces acting on it can be simplified to the balance between hydraulic pressure passing through a gas spring and damping, and the mass of the moving part. The equation is as follows:

[0068]

[0069] In the formula, M is the equivalent mass of the oil and diaphragm inside the accumulator, A is the oil contact area at the bottom of the diaphragm, and k B k is the viscous drag coefficient. B =B b +C a B b C is the damping coefficient of the oil in the liquid cavity. a denoted as ρ, where ρ is the gas damping coefficient in the airbag. x represents the equivalent displacement of the accumulator diaphragm moving element. The equivalent displacement and net flow rate q are also considered. c Relationships such as,

[0070]

[0071] The input and output relationship of the accumulator can be obtained.

[0072]

[0073] The Laplace transform yields the transfer function.

[0074]

[0075] Therefore, the bladder-type accumulator can be parameterized as the liquid capacity C. c Liquid sensing part L c and linear liquid resistance part R c The series connection is used. Other energy storage elements can be lumped together and parameterized equivalent by repeating the above steps.

[0076] For switching elements and output throttling valves, including switching valves, check valves, and throttling valves, whose pressure drop and flow rate follow a nonlinear orifice throttling equation, the constant term in the nonlinear equation is defined as the nonlinear liquid resistance R:

[0077]

[0078] In the formula, q orifice C represents the throttling flow rate of switching elements and throttle valves. d ρ is the flow coefficient, A is the equivalent flow area of ​​the switching element / throttle valve, ρ is the density of the flowing oil, and Δp is the flow coefficient. orificeThe pressure drop during the flow of the switching element and the throttle valve is considered. Therefore, the switching element and the output throttle valve can be lumped into a nonlinear hydraulic resistance component.

[0079] In step S2, based on the components after lumped parameter equivalence, when lumped parameter equivalence is applied to the hydraulic switching conversion system, the step-down topology considers the liquid capacity element, liquid sensing element, switching element, and output load; the step-up and step-down topologies consider the liquid capacity element, liquid sensing element, switching element, output load, and switching volume in the step-up and step-down topologies. Therefore, the impact of the switching volume on the system in the step-up and step-down topologies cannot be ignored.

[0080] In step S3, before processing the system topology switching, assumptions are made about the system's state and input variables. The variables of the hydraulic switchgear system include state variables and input variables, specifically including the flow rate of the hydraulic sensing element, the system output pressure, the system input pressure, and the duty cycle of the switching element. The assumptions are as follows: 1) It is assumed that the energy storage capacity of the system's energy storage element will make the ripple of the system state variables much smaller than their average value; 2) External disturbances are much smaller than the average value of the system's input variables themselves. Furthermore, the mean value of each system variable over one switching cycle is calculated to replace its time-varying value over one cycle. The mean value is the sum of the static and dynamic fluctuation components of the system variables.

[0081]

[0082] In the formula, x(t) is the system variable. The variable is in a switching cycle T S The mean of the variable, where X is the static value of the variable. It refers to the dynamic fluctuation of variables.

[0083] To transform the alternating topology caused by switching elements in a hydraulic switch-changing system based on variable mean values ​​into a single, structurally unchanged topology without switching elements, while preserving the throttling and switching nonlinear characteristics of the system, it is necessary to handle two piecewise variables resulting from the switching: the flow rate q of the switching branch. bran (t) and the fluid pressure p at the switching node node (t). First, process the segmented flow q. bran (t).

[0084] for Figure 1 (a) In the step-down topology, the switching of the switching element results in a step signal in the flow rate of the switching valve branch and the check valve branch.

[0085]

[0086] In the formula, q switch (t) represents the flow rate of the on / off valve, q check (t) represents the flow rate of the check valve. Let d(t) represent the flow rate of the liquid sensing element. d(t) is the proportion of the valve's on-time to the switching cycle, and d'(t) = 1 - d(t) is the proportion of the valve's off-time to the switching cycle. The segmented flow rates of these two branches are treated as continuous variables.

[0087]

[0088]

[0089] In the formula, The segmented flow rate q of the on / off valve branch switch (t) The continuous flow rate after processing; The segmented flow rate q of the one-way valve branch check (t) Continuous flow rate after processing.

[0090] for Figure 1 (b) In the boost topology, the switching of the switching element also results in a step signal in the flow of the switching valve branch and the check valve branch. However, when dealing with segmented flow, it is also necessary to add the shunt flow q that takes into account the switching volume. sv (t). First, the flow rate is averaged across the open and closed states of the switching valve.

[0091]

[0092] In the formula, C sv To switch the volumetric liquid capacity section, the maximum charging pressure of the additional liquid capacity element is the system output pressure p. load Then, the traffic will be split. sv Considering the segmented flow rate q in the boost topology bran In the processing of (t),

[0093]

[0094] In the formula, The segmented flow rate q of the on / off valve branch switch (t) The continuous flow rate after processing; The segmented flow rate q of the one-way valve branch check (t) Continuous flow rate after processing.

[0095] for Figure 1 (c) The buck-boost topology is the same as the boost topology, and the result after continuous processing is as follows.

[0096]

[0097] In the formula, The segmented flow rate q of the on / off valve branch switch (t) The continuous flow rate after processing;​ The segmented flow rate q of the one-way valve branch check (t) Continuous flow rate after processing.

[0098] In step S3, while preserving the throttling and switching nonlinear characteristics of the hydraulic switch conversion system, the alternating topology caused by the switching of switching elements is processed into a single topology without switching elements and with unchanged structure. This process addresses the segmented flow rate q of the switching branch. bran After (t), the segmented fluid pressure p at the switching node also needs to be addressed. node (t). When processing, the voltage drop Δp(t) of all components in the switching branch needs to be considered, including three cases: (1) constant voltage drop part p or node p where the pressure value is a state variable. i (t); (2) linear liquid resistance part; (3) nonlinear liquid resistance part.

[0099] exist Figure 1 In a hydraulic switching system, case (1) includes the one-way valve conduction pressure drop p cr State variable p rail (t), p load (t) Switching node p node The pressure contribution of (t). Due to the switch switching, case (1) for p node The pressure contribution of (t) is a piecewise variable, which can be made continuous as follows:

[0100]

[0101]

[0102] In the formula, Δp(t) is the voltage drop contribution of case 1) in the system topology to the switching node, and is a piecewise variable; This is a continuous result.

[0103] Case (2) includes linear liquid resistance R of the liquid sensing element. m Partially, the linear liquid resistance R of the connecting pipeline t Partial. Its continuum is:

[0104]

[0105] In the formula, For the continuous flow results of the corresponding segmented branches, This is a continuation of the voltage drop contribution of case (2) to the switching node.

[0106] Case (3) includes the nonlinear liquid resistance R of the switching element. s R ch The part, and the nonlinear liquid resistance R part of the output throttle valve. Its continuity is as follows:

[0107]

[0108] In the formula, This represents the continuous flow result for the corresponding segmented branch, where d(t) represents the conduction stage of the corresponding branch. This is a continuation of the voltage drop contribution of case (3) to the switching node.

[0109] The segmented traffic q from the two branches behind the switching node will be switched. bran (t) and segmented fluid pressure p node (t) After continuous transformation, the hydraulic switch conversion system is transformed from the alternating topology caused by switch switching into a single topology without switching elements and with unchanged structure.

[0110] Figure 4 This is a schematic diagram of a single topology of the hydraulic switch conversion system according to an embodiment of the present invention.

[0111] In step S4, based on the single topology of the hydraulic switch conversion system, the state variable equation of the step-down topology can be established as follows:

[0112]

[0113] In the formula,

[0114] The state variable equations for the boost topology can be established as follows:

[0115]

[0116] In the formula,

[0117] The state variable equations for the boost-boost topology can be established as follows:

[0118]

[0119] In the formula,

[0120] Treating the state variables as static values, the above equation represents the static model of the hydraulic switch conversion system, showing the relationship between the static values ​​of the system's state variables. Taking the booster topology as an example, its derived static model is as follows:

[0121]

[0122] In the formula,

[0123]

[0124] The state variable is written as the sum of its static value and the small ripple dynamic component.

[0125]

[0126] Substitute into the system state variable equations. Ignore the product terms of static variables, such as P. load D. Ignore higher-order dynamic terms, such as... etc. For nonlinear terms and Linear expansion at their respective static points

[0127]

[0128] Simplification yields a linear dynamic model of the hydraulic switch conversion system related to the static values ​​of state variables. Taking a booster topology as an example...

[0129]

[0130]

[0131] The dynamic response index of the hydraulic switch conversion system, related to the static values ​​of state variables, can be obtained from the linear dynamic model.

[0132]

[0133] In the formula,

[0134] This invention provides an analytical modeling method for hydraulic switch conversion systems that considers throttling and switching nonlinearities. This method simultaneously considers the throttling and switching nonlinearities of the hydraulic switch conversion system and can be applied to the rapid and accurate evaluation of the system's output under multiple operating conditions. The method clarifies the influence of system parameters on the output, narrows the parameter adjustment range, and also provides the damping ratio and natural frequency as the optimization objective functions for the system's dynamic response. It can be applied to parameter optimization under multiple operating conditions.

[0135] In the verification of this embodiment, the parameters of each component of the hydraulic switch conversion system were selected as follows:

[0136]

[0137] Figure 5 This embodiment demonstrates the effectiveness of the method in evaluating the output of a hydraulic switch conversion system under different duty cycle conditions. Figure 5 (a) is the output estimate for the buck topology. Figure 5 (b) is the output estimate for the boost topology. Figure 5 (c) Output estimation for the boost / buck topology. It can be seen that, under different duty cycles of the switching elements, the model calculation results of the hydraulic switch conversion system without considering the throttling nonlinearity of the switching elements deviate significantly from the accurate numerical simulation results of the corresponding topology. By considering the throttling nonlinearity of the system switching elements according to this method, the system output can be accurately estimated.

[0138] Figure 6 This embodiment demonstrates the parameter optimization effect of the method on the dynamic response of the hydraulic switch boosting system. The energy storage element's liquid capacity parameter C... c And the liquid sensing parameter L m It will affect the dynamic response process of the output pressure of the hydraulic switch conversion system. Figure 6 (a) Inappropriate parameters cause severe oscillations in the system output, resulting in poor system accuracy in regulating the input pressure. Figure 6 (b) represents the damping ratio objective function in the dynamic model with respect to parameter C. c L m The optimization effect. Figure 6 (b) Empirical adjustment parameter C c L m Numerous trials and optimizations are required; otherwise, finding the optimal parameter ratio is difficult. While the system's output accuracy improves, its dynamic response remains slow. Optimization using the damping ratio function provided in this method can quickly find suitable parameter configurations, enabling the system to achieve better dynamic output.

[0139] The above are preferred embodiments of the present invention. Any changes made to the technical solution of the present invention that do not exceed the scope of the technical solution of the present invention shall fall within the protection scope of the present invention.

Claims

1. An analytical modeling method for a hydraulic switching conversion system considering throttling and switching nonlinearities, wherein the hydraulic switching conversion system includes an energy storage element, a switching element, hydraulic lines, and an output load; the energy storage element includes a liquid storage element and a liquid sensing element, the liquid storage element includes an accumulator and an oil chamber, the liquid sensing element includes an inertial tube and a hydraulic motor, the switching element includes a switching valve and a check valve, the volume of the hydraulic lines between the switching valve, the check valve, and the liquid sensing element that contains the hydraulic fluid is described as the switching volume, and the output load includes a throttle valve; the hydraulic switching conversion system includes a boost topology, a depressurization topology, and a boost-depressurization topology, the function of the switching element in the hydraulic switching conversion system causes the hydraulic lines containing the switching valve and the hydraulic lines containing the check valve to flow intermittently and alternately, which is called an alternating topology, the alternating flow branches are described as switching branches in the hydraulic switching conversion system, and the nodes where the switching branches intersect are described as switching nodes; characterized in that, The analytical modeling method for the hydraulic switch conversion system includes the following steps: Step S1: Establish the input-output relationship of the components of the hydraulic switch conversion system, and make equivalent connections based on the lumped parameter approach; Step S2: Based on the lumped parameter approach, transform the lumped parameters of the hydraulic switch conversion system into an equivalent topology. Step S3: While retaining the throttling and switching nonlinear characteristics of the hydraulic switch conversion system, the alternating topology of the hydraulic switch conversion system caused by the switching of switching elements is processed into a single topology without switching elements and with unchanged structure. Step S4: Establish a nonlinear static model of the hydraulic switch conversion system and a neighborhood linear dynamic model related to the static point.

2. The analytical modeling method for a hydraulic switching system considering throttling and switching nonlinearity according to claim 1, characterized in that, For components other than switching elements, the lumped parameter equivalence method is to define the integral, differential, and proportional components of the component's transfer function as the component's own capacitive, inductive, and linear resistive components, respectively, with the series and parallel relationships of each component following the transfer function. The lumped parameter equivalence method for switching elements and throttle valves with nonlinear input-output relationships is to define the constant term in the nonlinear equation as the nonlinear resistive component R. In the formula, q orifice C represents the throttling flow rate of switching elements and throttle valves. d ρ is the flow coefficient, A is the equivalent flow area of ​​the switching element / throttle valve, ρ is the density of the flowing oil, and Δp is the flow coefficient. orifice This refers to the pressure drop during the flow of switching elements and throttle valves.

3. The analytical modeling method for a hydraulic switching system considering throttling and switching nonlinearity according to claim 1, characterized in that, The method for lumped parameter equivalence of buck topology is to consider the liquid capacitor element, liquid inductor element, switching element and output load in buck topology, and lumped parameterize and connect each part. The method for lumped parameter equivalence of boost and buck-boost topologies is to consider the liquid capacitors, liquid inductors, switching elements, output loads, and switching volumes in the boost and buck-boost topologies, and then lumped parameterize and connect each part.

4. The analytical modeling method for a hydraulic switching system considering throttling and switching nonlinearity according to claim 1, characterized in that, The variables of a hydraulic switchgear system include state variables and input variables. Before processing a single topology of the hydraulic switchgear system, the following assumptions need to be made about the variables: 1) It is assumed that the energy storage capacity of the energy storage element in the hydraulic switchgear system is sufficient to make the ripple of the state variables much smaller than their average value; 2) External disturbances are much smaller than the average value of the input variables themselves. The mean value of each variable in the hydraulic switchgear system over one switching cycle is used to replace its time-varying value over one cycle. The mean value is the sum of the static and dynamic fluctuation components of the hydraulic switchgear system variables. In the formula, x(t) is a variable of the hydraulic switch conversion system. The variable is in a switching cycle T S The mean of the variable, where X is the static part of the variable. It refers to the dynamic fluctuation of the variable.

5. The analytical modeling method for a hydraulic switching system considering throttling and switching nonlinearity according to claim 4, characterized in that, The method for transforming a hydraulic switchgear system from an alternating topology to a single topology without switching elements and with an unchanged structure is as follows: The variables in the hydraulic switchgear system that exhibit step signals due to topology switching are treated as continuous variables, including the flow rate q of the switching branch. bran (t) and the fluid pressure p at the switching node node (t).

6. The analytical modeling method for a hydraulic switching system considering throttling and switching nonlinearity according to claim 5, characterized in that, In a step-down topology, if the flow q of the switching branch... bran (t) is cut off when the switching valve is on and flows when the switching valve is off, with a flow rate q. bran (t) is: Then the segmented flow q bran (t) is treated as a continuous variable q bran (t) TS The method is as follows: In the formula, d(t) is the proportion of the valve's on-time to the switching cycle, and d'(t) = 1 - d(t) is the proportion of the valve's off-time to the switching cycle. This refers to the flow rate variable delivered to the switching branch in the step-down topology.

7. The analytical modeling method for a hydraulic switching system considering throttling and switching nonlinearity according to claim 5, characterized in that, Handling segmented flow q in the switching branch between boost and buck-boost topologies bran (t) is a continuous variable At this time, it is necessary to increase the shunt flow rate q to take into account the switching volume. sv The effect of (t); on the diversion flow rate q sv (t) is processed: Step S01: Divert the traffic q sv (t) Flow averaging during valve on-off and off-off: Step S02: Obtain the segmented flow q of the switched branch. bran (t) is: In the formula, d(t) is the proportion of the valve's on-time to the switching cycle, d'(t) = 1 - d(t) is the proportion of the valve's off-time to the switching cycle, and C sv To switch the volumetric liquid capacity section, q sv p represents the average shunting result of the switching volume in the on or off state of the switching element. tar To switch the highest pressure that the oil in the volume can reach, This refers to the flow rate variable delivered to the switching branch in the boost topology and boost-buck topology.

8. The analytical modeling method for a hydraulic switching system considering throttling and switching nonlinearity according to claim 5, characterized in that, Handling segmented fluid pressure p at the switching node node When (t), the pressure drop Δp(t) of all lumped parameter parts in the switching branch needs to be considered, including three cases: (1) constant pressure drop part p or node p where the pressure value is a state variable. i (t); (2) Linear liquid resistance part; (3) Nonlinear liquid resistance part; The handling method for scenario (1) is as follows: The handling method for scenario (2) is as follows: The handling method for situation (3) is as follows: In the formula, d(t) is the proportion of the valve's on-time to the switching cycle. R represents the flow rate variable delivered to the switching branch in the buck topology, boost topology, and buck-boost topology, and R is the nonlinear liquid resistance component.

9. An analytical modeling method for a hydraulic switching system considering throttling and switching nonlinearities according to any one of claims 1 to 4, characterized in that, The method for establishing the nonlinear static model of the hydraulic switch conversion system is as follows: ignore the dynamic fluctuation part in the mean of the hydraulic switch conversion system variables, retain only the static part in the mean, and establish the relationship between the static values ​​of the variables based on the processed single topology.

10. An analytical modeling method for a hydraulic switching system considering throttling and switching nonlinearities according to any one of claims 1 to 4, characterized in that, The method for establishing the dynamic model of the hydraulic switch conversion system is as follows: the mean value of the hydraulic switch conversion system variable is decomposed into the sum of dynamic fluctuation part and static part, and substituted into the static model to obtain the nonlinear dynamic model related to the static operating point of the variable. Higher-order dynamic terms are ignored, and the nonlinear dynamic terms are expanded in the neighborhood of its static point to obtain the linear dynamic model in the neighborhood of the static value of the hydraulic switch conversion system variable.

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