Mountain cable car type gravity energy storage system dynamic modeling and sliding mode control method

Abstract

The invention discloses a dynamic modeling and sliding mode control method for a mountain cable car type gravity energy storage system, and relates to the technical field of gravity energy storage, and the method comprises the steps: constructing a nine-node closed-loop cable topological structure; performing dynamic modeling by using the nine-node closed-loop cable topology structure, and constructing a dynamic model of the nine-node closed-loop cable topology; and performing sliding mode control based on the dynamic model of the nine-node closed-loop cable topology to obtain a sliding mode control result. According to the invention, the response time of the acceleration stage of the system is shortened, the fluctuation amplitude of traction force is controlled within + / -3.5 * 10 <-3 > m / s < 2 >, and the cycle efficiency is improved. The MC-GES system can adapt to multi-period power requirements of a power grid through trapezoidal external power characteristics, has modular expansion capability based on state-of-charge dynamic evolution verification, and solves the problems that a gravity energy storage system is limited in geographical adaptability and insufficient in dynamic stability.

Description

Technical Field

[0001] This invention relates to the field of gravity energy storage technology, and in particular to a dynamic modeling and sliding mode control method for a mountain cable car-type gravity energy storage system. Background Technology

[0002] With the accelerated global energy transition, the penetration rate of renewable energy sources, represented by wind and solar power, in the power system continues to increase. my country has clearly stated that by 2030, the proportion of non-fossil energy consumption should reach approximately 25%, and the total installed capacity of wind and solar power will exceed 1.2 billion kilowatts. However, renewable energy generation is significantly affected by natural factors such as sunlight and wind speed, exhibiting significant intermittency, volatility, and uncertainty. This exacerbates the difficulty of real-time power balancing in the power grid, easily leading to frequency anomalies, voltage fluctuations, and even localized power outages. Energy storage technology, as a core means of solving the problem of renewable energy consumption, can achieve peak shaving and valley filling through the spatiotemporal transfer of energy, improving the stability and flexibility of the power system.

[0003] Among current mainstream energy storage technologies, pumped hydro storage, with its energy conversion efficiency of 80%–90% and long lifespan, has become the preferred solution for large-scale energy storage. However, its construction depends on specific terrain conditions (such as waterways with varying elevations) and has a construction cycle of 8–15 years, making it difficult to quickly respond to large-scale energy storage demands. While electrochemical energy storage offers advantages such as flexible site selection and short construction cycles, it faces core challenges including cycle life degradation, limited energy density, and the risk of thermal runaway. Against this backdrop, gravity energy storage technology, due to its advantages such as recyclable media, strong site adaptability, and long lifespan, has become a research hotspot in the field of physical energy storage.

[0004] Mountain cable car-type gravity energy storage systems achieve energy conversion by transporting heavy objects through cable loops. Deployment requires only a vertical elevation difference, significantly reducing terrain dependence compared to traditional track-based and shaft-based gravity energy storage technologies, thus offering greater versatility and economy. However, this system exhibits complex dynamic characteristics: time-varying mass distribution during loading and unloading, pulley friction nonlinearity, and multi-segment coupling effects result in a highly nonlinear, time-varying, and multivariable coupled dynamic model. Existing control strategies (such as traditional proportional-integral-derivative (PID) and linear quadratic regulator (LQR) control) rely on linearization assumptions, making it difficult to handle these complex dynamics and resulting in insufficient control accuracy and poor robustness. While traditional sliding mode control offers some adaptability to nonlinear systems, it does not fully consider the effects of time-varying inertia and sudden mass changes. Furthermore, the sliding surface design does not integrate the system's unique segmented gravity coupling and friction characteristics, leading to prominent high-frequency chattering, increased fatigue damage to mechanical components, and severely impacting system reliability and lifespan.

[0005] Therefore, there is an urgent need for a dynamic modeling and sliding mode control method for mountain cable car-type gravity energy storage systems to solve problems such as low control accuracy, weak chattering suppression capability, and poor engineering applicability in existing technologies. Summary of the Invention

[0006] The purpose of this invention is to propose a dynamic modeling and sliding mode control method for a mountain cable car-type gravity energy storage system, so as to solve the technical problem of control instability caused by insufficient modeling of multi-source nonlinear dynamic characteristics in existing mountain cable car-type gravity energy storage systems (MC-GES).

[0007] To achieve the above objectives, this invention provides a dynamic modeling and sliding mode control method for a mountain cable car-type gravity energy storage system, comprising the following steps:

[0008] Construct a nine-node closed-loop cable topology;

[0009] Dynamic modeling is performed using the nine-node closed-loop cable topology to construct a dynamic model of the nine-node closed-loop cable topology.

[0010] Sliding mode control is performed based on the dynamic model of the nine-node closed-loop cable topology to obtain the sliding mode control results.

[0011] Optionally, a nine-node closed-loop cable topology is constructed, including:

[0012] A unidirectional circulation loop is obtained by using a mountain cable car-type gravity energy storage system. The unidirectional circulation loop includes a horizontal loading section, an inclined transport section, a horizontal unloading section, a vertical descent section, a power drive section, an inclined acceleration section, a gravity descent section, a ground unloading section, and a vertical reset section.

[0013] Based on the single-loop combination and the spatial distribution pattern of nodes, a nine-node closed-loop cable topology is constructed.

[0014] Optionally, the total path length vector calculation formula for the nine-node closed-loop cable topology is as follows:

[0015]

[0016] Where L is the total path length vector of the nine-node closed-loop cable topology, l is the length of the horizontal baseline segment, and ΔH is the total height difference of the MC-GES system. H1 is the tilt angle, and H1 is the vertical height of the upper and lower stacking platforms.

[0017] Optionally, dynamic modeling is performed using the nine-node closed-loop cable topology to construct a dynamic model of the nine-node closed-loop cable topology, including:

[0018] Based on the nine-node closed-loop cable topology, the tension information on both sides of the pulley is obtained using the Euler friction formula;

[0019] By combining the tension information on both sides of the pulley with the moment of inertia and the bearing friction torque, the dynamic equation of the pulley is established;

[0020] The mass mutation caused by loading and unloading is obtained by using a step function based on the piecewise gravity tilt angle and time-varying mass.

[0021] The dynamic equations of the cable segment are obtained by utilizing the mass mutation caused by loading and unloading.

[0022] Based on the pulley dynamics equation and the cable segment dynamics equation, combined with the external force term, a dynamic model of a nine-node closed-loop cable topology is constructed.

[0023] Optionally, the calculation formula for the pulley dynamics equation is as follows:

[0024]

[0025] Among them, M f,j Let μ be the frictional torque of the pulley j bearing. b K is the bearing friction coefficient. j I is the winch formula coefficient on pulley j. j Let ω be the moment of inertia of pulley j. j Let be the angular velocity of the pulley, t be the time, and b be the angular velocity of the pulley. j Here, v is the coefficient of viscous friction, and r is the velocity. j Let be the radius of pulley j.

[0026] Optionally, the formula for calculating the quality mutation caused by loading and unloading is as follows:

[0027]

[0028] Where, m ij (t) represents the mass of segment ij at time t. Let be the inherent mass of segment ij. For the quality of cable segment ij, Let m be the mass of the vehicle in segment ij. c Let n be the mass added to the heavy object, n be the number of vehicles in segment ij, H(·) be the unit step function, and t be the time interval. load,k This indicates that the k-th vehicle is loaded, t unload,k This indicates the time of the k-th uninstallation event.

[0029] Optionally, the dynamic equation for the cable segment is calculated as follows:

[0030]

[0031] Among them, T ij T represents the tension on cable segment ij. jiFor the tension on the cable segment, F ext,ij For external forces, m ij (t) represents the mass of segment ij at time t, a(t) represents the cable acceleration at time t, and g represents the acceleration due to gravity. The angle of inclination is the segmented gravity.

[0032] Optionally, the dynamic model calculation formula for the nine-node closed-loop cable topology is as follows:

[0033]

[0034] Among them, F m (t) represents the equivalent load force of the MC-GES system at time t, M eq (t) represents the equivalent inertial mass / moment of inertia at time t, a(t) represents the cable acceleration at time t, C represents the comprehensive damping coefficient, v(t) represents the velocity at time t, and G(t) represents the gravitational potential energy term at time t.

[0035] Optionally, sliding mode control is performed based on the dynamic model of the nine-node closed-loop cable topology to obtain the sliding mode control results, including:

[0036] Set speed error;

[0037] The velocity error is subjected to inertial coupling processing to construct a time-varying inertial coupling inertial sliding surface;

[0038] Based on the dynamic model of the time-varying inertial coupling inertial sliding surface combined with the nine-node closed-loop cable topology, the equivalent control term is obtained.

[0039] Based on the time-varying inertial coupling inertial sliding surface combined with the boundary layer fuzzy compensation mechanism, the switching control term is obtained;

[0040] The switching control term and the equivalent control term are combined to obtain the control rate;

[0041] Based on the control law and the Lyapunov function, the sliding mode control result is obtained.

[0042] Compared with the closest existing technology, the present invention has the following advantages:

[0043] Compared to traditional control methods, this invention reduces the system's acceleration phase response time by 8.6% and controls the traction force fluctuation amplitude within ±3.5 × 10⁻⁶. -3 m / s 2The internal cycle efficiency is improved to 88.54%. The MC-GES system, through its trapezoidal external power characteristics, can adapt to the power demand of the power grid at different times. Based on dynamic evolution of the state of charge, it demonstrates modular scalability, solving the problems of limited geographical adaptability and insufficient dynamic stability of gravity energy storage systems. This invention is suitable for large-scale, long-term energy storage scenarios, providing an efficient and robust control solution for large-scale grid energy storage in mountainous terrain. Attached Figure Description

[0044] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0045] Figure 1 This is a flowchart illustrating the dynamic modeling and sliding mode control method of a mountain cable car-type gravity energy storage system according to an embodiment of the present invention;

[0046] Figure 2 Here is a flowchart of the dynamic modeling and adaptive compensation control proposed in this embodiment of the invention:

[0047] Figure 3 This is a schematic diagram of a mountain cable car-type gravity energy storage system proposed in an embodiment of the present invention;

[0048] Figure 4 This is a comparison chart of speed tracking performance proposed in an embodiment of the present invention;

[0049] Figure 5 This is a comparison chart of acceleration dynamic characteristics proposed in the embodiments of the present invention;

[0050] Figure 6 This is a comparison diagram of the geometric characteristics of the sliding surface proposed in the embodiments of the present invention;

[0051] Figure 7 This is a comparison chart of traction force fluctuation suppression proposed in the embodiments of the present invention;

[0052] Figure 8 This is a comparison diagram of power characteristics proposed in an embodiment of the present invention;

[0053] Figure 9 This is a graph showing the storage capacity and actual cumulative energy of the upper and lower storage tanks of the MC-GES proposed in this embodiment of the invention. Detailed Implementation

[0054] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions in the embodiments of this invention will be clearly and completely described below with reference to specific embodiments and corresponding drawings. Obviously, the described embodiments are only a part of the embodiments of this invention, and not all of them. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0055] The terminology used in the embodiments section of this invention is for the purpose of explaining specific embodiments of the invention only, and is not intended to limit the invention.

[0056] Example 1

[0057] like Figure 1 As shown, this embodiment provides a dynamic modeling and sliding mode control method for a mountain cable car-type gravity energy storage system, including:

[0058] S1. Construct a nine-node closed-loop cable topology;

[0059] S2. Dynamic modeling is performed using the nine-node closed-loop cable topology to construct a dynamic model of the nine-node closed-loop cable topology.

[0060] S3. Perform sliding mode control based on the dynamic model of the nine-node closed-loop cable topology and obtain the sliding mode control results.

[0061] As one possible implementation, in the above embodiments, step S1 may specifically include the following steps:

[0062] A unidirectional circulation loop is obtained by using a mountain cable car-type gravity energy storage system. The unidirectional circulation loop includes a horizontal loading section, an inclined transport section, a horizontal unloading section, a vertical descent section, a power drive section, an inclined acceleration section, a gravity descent section, a ground unloading section, and a vertical reset section.

[0063] Based on the single-loop combination and the spatial distribution pattern of nodes, a nine-node closed-loop cable topology is constructed.

[0064] Furthermore, the formula for calculating the total path length vector of the nine-node closed-loop cable topology is as follows:

[0065]

[0066] Where L is the total path length vector of the nine-node closed-loop cable topology, l is the length of the horizontal baseline segment, and ΔH is the total height difference of the MC-GES system. H1 is the tilt angle, and H1 is the vertical height of the upper and lower stacking platforms.

[0067] As one possible implementation, in the above embodiments, step S2 may specifically include the following steps:

[0068] Based on the aforementioned nine-node closed-loop cable topology, the tension information on both sides of the pulley is obtained using Euler's friction formula, as follows:

[0069]

[0070] Among them, T jk For the tension on the JK segment cable, T ij Let μ be the tension on cable segment ij. a Let θ be the coefficient of friction between the pulley and the cable. j The angle of wrap of the cable on pulley j;

[0071] By combining the tension information on both sides of the pulley with the moment of inertia and the bearing friction torque, the dynamic equation of the pulley is established;

[0072] The formula for calculating the moment of inertia is as follows:

[0073]

[0074] The formula for calculating the bearing friction torque is as follows:

[0075]

[0076] Among them, T jk For the tension on the JK segment cable, T ij Let r be the tension on cable segment ij. j Let M be the radius of pulley j. f,j For the frictional torque of the pulley j bearing, I j Let ω be the moment of inertia of pulley j. j Let μ be the angular velocity of the pulley, t be the time, and μ be the angular velocity of the pulley. b b is the bearing friction coefficient. j Where v is the coefficient of viscous friction and v is the velocity.

[0077] The mass mutation caused by loading and unloading is obtained by using a step function based on the piecewise gravity tilt angle and time-varying mass.

[0078] The dynamic equations of the cable segment are obtained by utilizing the mass mutation caused by loading and unloading.

[0079] Based on the pulley dynamics equation and the cable segment dynamics equation, combined with the external force term, a dynamic model of a nine-node closed-loop cable topology is constructed.

[0080] The formula for calculating the external force term is as follows:

[0081]

[0082] Among them, F ext,ij The external force term is M(t), where M(t) is the load torque of the motor, and r is the torque of the load. m This represents the motor transmission ratio.

[0083] Furthermore, the calculation formula for the pulley dynamics equation is as follows:

[0084]

[0085] Among them, M f,j Let μ be the frictional torque of the pulley j bearing. b K is the bearing friction coefficient. j The winch formula coefficient on pulley j is derived from the coefficient of friction μ between the pulley and the cable. a The angle of wrap θ of the cable on pulley j j Decide, I j Let ω be the moment of inertia of pulley j. j Let be the angular velocity of the pulley, t be the time, and b be the angular velocity of the pulley. j Here, v is the coefficient of viscous friction, and r is the velocity. j Let be the radius of pulley j.

[0086] Furthermore, the calculation method for the quality mutation caused by loading and unloading is as follows:

[0087]

[0088] Where, m ij (t) represents the mass of segment ij at time t. Let be the inherent mass of segment ij. For the quality of cable segment ij, Let m be the mass of the vehicle in segment ij. c Let n be the mass added to the heavy object, n be the number of vehicles in segment ij, H(·) be the unit step function, and t be the time interval. load,k This indicates that the k-th vehicle is loaded, t unload,k This indicates the time of the k-th uninstallation event.

[0089] Furthermore, the dynamic equation for the cable segment is calculated as follows:

[0090]

[0091] Among them, T ij T represents the tension on cable segment ij. ji For the tension on the cable segment, F ext,ij For external forces, m ij (t) represents the mass of segment ij at time t, a(t) represents the cable acceleration at time t, and g represents the acceleration due to gravity. The angle of inclination is the segmented gravity.

[0092] Furthermore, the dynamic model calculation formula for the nine-node closed-loop cable topology is as follows:

[0093]

[0094] Among them, F m (t) represents the equivalent load force of the MC-GES system at time t, M eq (t) represents the equivalent inertial mass / moment of inertia at time t, a(t) represents the cable acceleration at time t, C represents the comprehensive damping coefficient, v(t) represents the velocity at time t, and G(t) represents the gravitational potential energy term at time t.

[0095] As one possible implementation, in the above embodiments, step S3 may specifically include the following steps:

[0096] Set speed error;

[0097] The velocity error is subjected to inertial coupling processing to construct a time-varying inertial coupling inertial sliding surface;

[0098] Based on the dynamic model of the time-varying inertial coupling inertial sliding surface combined with the nine-node closed-loop cable topology, the equivalent control term is obtained.

[0099] Based on the time-varying inertial coupling inertial sliding surface combined with the boundary layer fuzzy compensation mechanism, the switching control term is obtained;

[0100] The switching control term and the equivalent control term are combined to obtain the control rate;

[0101] Based on the control law and the Lyapunov function, the sliding mode control result is obtained.

[0102] Example 2

[0103] like Figure 2 As shown, this embodiment provides a dynamic modeling and sliding mode control method for a mountain cable car-type gravity energy storage system, including: constructing a dynamic model of a nine-node closed-loop cable topology; quantifying the equivalent inertial step characteristics and frictional damping evolution law of the loading and unloading process; designing an inertial sliding mode surface reconstruction strategy; achieving adaptive compensation for mass jumps and frictional disturbances through Newton-Euler dynamic constraint embedding; and suppressing high-frequency chattering in sliding mode control by combining a fuzzy boundary layer mechanism. Details are as follows:

[0104] Step 1: Nine-node closed-loop cable topology of the mountain cable car-type gravity energy storage system, specifically:

[0105] The MC-GES system employs a nine-node closed-loop cable topology, such as... Figure 3As shown, nodes 1-9 are equipped with directional pulleys, forming a unidirectional circular transport loop consisting of 9 segments. The functions of each segment are defined as follows:

[0106] Horizontal loading section (section 12): Loading station in the stacking area at the bottom of the hill; Inclined transport section (section 23): Inclined angle The ramp leads to the following sections: 1. Sloping uphill passage; 2. Horizontal unloading section (section 34): unloading station in the mountaintop stacking area; 3. Vertical descent section (section 45): vertical passage from the mountaintop to the loading platform; 4. Power-driven section (section 56): parallel loading buffer and power drive at the mountaintop, combining loading, driving, and energy release functions; 5. Inclined acceleration section (section 67): secondary climbing power compensation section, with an inclination angle of [missing information]. Gravity descent section (segment 78): Potential energy recovery-dominated descent channel; Ground unloading section (segment 89): Mountain bottom stacking unloading buffer zone; Vertical reset section (segment 91): Vehicle vertical reset channel.

[0107] The spatial distribution of nodes satisfies the following rules: {1,2}∈L1, {5,6}∈L2, {3,4,7}∈L3, {8,9}∈L4, where L... i This represents the i-th horizontal layer. The carrier is fixed to the cable at equal intervals via coupling devices, forming a quasi-continuous mass flow.

[0108] The total path length vector L of a nine-node closed-loop cable topology is L = [l 12 ,l 23 ,l 34 ,l 45 ,l 56 ,l 67 ,l 78 ,l 89 ,l 91 The calculation formula is as follows:

[0109]

[0110] Among them, l 12 l is the length of the horizontal loading section. 23 l is the length of the inclined transport section. 34 l is the length of the horizontal unloading section. 45 l is the length of the vertical descent segment. 56 l is the length of the power drive section. 67 l is the length of the oblique acceleration segment. 78 Let l be the length of the downward gravitational segment. 89 l is the length of the ground unloading section. 91 Let l be the length of the vertical reset segment, l be the length of the horizontal baseline segment, H1 be the vertical height of the upper and lower stacking platforms (i.e., the height difference between L1 and L4, and L2 and L3), and ΔH be the total height difference of the MC-GES system, used to characterize the vertical distance between L1 and L3, i.e., the height difference between L1 and L3. The angle of inclination is denoted as 'tilt'.

[0111] Step 2: Construct a dynamic model of the nine-node closed-loop cable topology, considering pulley friction nonlinearity, time-varying mass distribution, and segmented gravity coupling, and establish Newton-Euler equations to describe the system's dynamic behavior. Specifically:

[0112] Construction of unified equations for dynamics

[0113] The dynamic behavior of the MC-GES system is described by the piecewise coupled Newton-Euler equations, defining the tension T of each cable segment in the global coordinate system. ij Cable acceleration a and mass distribution m ij The constraints of (t):

[0114] Dynamic equations at each pulley node

[0115] When considering the contact friction between the pulley and the cable, the cable tensions on both sides of the pulley are no longer equal. This relationship can be described by the Euler-Eytelwein formula. This formula is applicable to scenarios where a flexible cable slides or tends to slide along the surface of a rigid pulley. It assumes that the frictional force between the cable and the pulley obeys Coulomb's law of friction, and that the friction is uniformly distributed within the wrap angle.

[0116] For the pulley at the node, let the cable turn from segment ij around the pulley to segment jk, and the angle of wrap of the cable on the pulley be θ. j (i.e., the central angle corresponding to the arc of contact between the cable and the pulley, in radians), the coefficient of friction between the pulley and the cable is μ. a Then the tension on both sides of the pulley satisfies:

[0117]

[0118] Among them, T jk For the tension on the JK segment cable, T ij Let be the tension on the cable segment ij, that is, the tension from i to j.

[0119] Physical meaning: When the cable travels clockwise around the pulley (from i→j to j→k), the tension increases along the direction of motion (T). jk >T ji The degree of increase is determined by the friction coefficient μ. a and the wrap angle θ j Decide.

[0120] Definition of the wrap angle: θ j ∈(0,π], when the pulley is semi-circular (commonly seen in 90° turns), θ j =π / 2; if it is a fully enclosed pulley (such as a circular winding method), θ j=2πn, where n is the number of wrapping rings.

[0121] For pulley j, the following dynamic equations apply:

[0122]

[0123] Where, r j Let I be the radius of pulley j. j Let ω be the moment of inertia of pulley j. j Let ω be the angular velocity of the pulley, and t be the time. Assuming there is no slippage between the pulleys and the transmission mechanism and the cable, we have ω j =v / r j v is velocity, M f,j The friction torque of pulley j bearing is calculated using the following formula:

[0124]

[0125] Where, μ b b is the bearing friction coefficient, which is related to the material and lubrication. j It is the viscous friction coefficient, which is related to the lubricant viscosity and bearing geometry.

[0126] From (2)-(4), the equations for pulley dynamics are obtained, and the calculation formulas are as follows:

[0127]

[0128] Among them, K j The winch formula coefficient on pulley j is derived from the coefficient of friction μ between the pulley and the cable. a The angle of wrap θ of the cable on pulley j j Decide, It is a hyperbolic cotangent function.

[0129] Dynamic equations of each cable segment

[0130] For any segment ij, its kinematic equations can be expressed as:

[0131]

[0132] Among them, T ji The tension on segment ji of the cable, i.e., the tension from j to i, is m. ij (t) represents the mass of segment ij at time t, a(t) represents the cable acceleration at time t, and g represents the acceleration due to gravity. The segmented gravity inclination angle is defined as the inclination angle between the velocity vector of segment ij and the positive horizontal direction. In equation (6), the external force term F ext,ij Defined as:

[0133]

[0134] Where M(t) is the load torque of the motor, r m The motor transmission ratio is given. The gravity tilt angles of each segment are shown in Table 1.

[0135] Table 1

[0136]

[0137] Motor dynamics model

[0138]

[0139] Among them, M e (t) represents the electromagnetic torque of the motor, I m Let ω be the moment of inertia of the motor. m This represents the angular velocity of the motor.

[0140] The entire system, i.e., all segments, runs at the same speed v, as calculated below:

[0141]

[0142] Where v(t) is the velocity at time t, and v(t-1) is the velocity at time t-1.

[0143] Analysis of characteristics of time-varying mass systems

[0144] The loading and unloading process causes instantaneous changes in mass distribution, which need to be described using a piecewise constant function, calculated as follows:

[0145]

[0146] In the formula, m ij (t) represents the mass of segment ij at time t. Let m be the inherent mass of segment ij. c Add mass to the object, H(·) is the unit step function, t load,k This indicates that the k-th vehicle is loaded, t unload,k This indicates the time of the k-th unloading event. For the quality of cable segment ij, Let denot be the mass of the vehicle in segment ij, and n be the number of vehicles in segment ij.

[0147] System dynamics behavior

[0148] Based on the analysis of (5)-(7) and the formula structure and physical dimensions, the original formula can be simplified to the following form:

[0149]

[0150] Among them, F m(t) represents the equivalent load force of the MC-GES system at time t, provided by the motor, M eq G(t) represents the equivalent inertial mass / moment of inertia at time t, C is the comprehensive damping coefficient, and G(t) is the gravitational potential energy term at time t. The specific expression is as follows:

[0151]

[0152] Among them, K i Let i be the winch formula coefficient. r i Let b be the radius of pulley i. i Let be the coefficient of viscous friction of pulley i.

[0153] Energy Analysis

[0154] Energy storage capacity E store The calculation formula is as follows:

[0155] E store =∑m up g△H(14)

[0156] Where, ∑m up It represents the sum of the masses of the heavy objects stored in the stack.

[0157] Energy storage efficiency η charge The calculation formula is as follows:

[0158]

[0159] Energy release efficiency η discharge The calculation formula is as follows:

[0160]

[0161] Among them, E in The work done by E for the energy storage equivalent load force out The work done by M for the equivalent load force during the energy release phase eq Equivalent inertial mass / moment of inertia.

[0162] Step 3: Designing an inertial sliding surface reconstruction strategy – Proposing an adaptive compensation control method, namely, the inertial sliding control system achieves robust tracking of the rated speed by integrating time-varying inertial terms and mass jump terms in the sliding surface design. Specifically:

[0163] The dynamic model of the MC-GES system exhibits typical multi-source nonlinearity and time-varying characteristics. Its complex dynamic behavior mainly stems from the time-varying mass distribution caused by loading and unloading operations, pulley friction nonlinearity, and the coupling effect of the power drive section. The MC-GES system utilizes the equivalent load force F... mTo achieve the transport of heavy objects and the flow of energy, the following nonlinear characteristics must be overcome when operating at rated speed: loading and unloading events cause the equivalent inertial mass / moment of inertia M to be affected. eq The step jump (described by the unit step function H(t) at time t, describing the mass term m) ij (t) sudden change), pulley tension relationship The exponential frictional characteristics lead to nonlinear tension transmission, and the frictional torque M of the pulley j bearing. f,j The combined nonlinear damping effect of velocity-related terms and tension-related terms. These nonlinear factors are related to the equivalent inertial mass / moment of inertia M of the dynamic segment. eq The combined superposition of these factors constitutes multimodal dynamic coupling, making it difficult for traditional linear control methods to achieve stable regulation.

[0164] For such complex systems, typical control methods have limitations: PID control, while simple in structure, lacks robustness to time-varying parameters and nonlinear friction, and frequent loading and unloading-induced mass mutations easily lead to integral saturation; Model predictive control (MPC), while capable of handling constraints, has a high computational burden for real-time solving of nonlinear optimization problems and is difficult to adapt to high-frequency disturbances in mountainous environments; Adaptive control, while capable of online parameter adjustment, relies on accurate dynamic models and lags in response to step parameter jumps during loading and unloading events. In contrast, sliding mode control exhibits significant advantages due to its unique structural adaptability and strong robustness: by designing a sliding surface containing system nonlinear terms, it directly handles complex dynamics such as time-varying mass and exponential friction using Lyapunov functions; it achieves finite-time convergence using an improved quasi-sliding mode reaching law, maintaining dynamic compensation capability even during mass mutations caused by loading and unloading; its switching characteristics naturally adapt to piecewise smooth discontinuous dynamics of the system, effectively suppressing the impact of external disturbances such as mountainous wind resistance and vehicle vibration on the F-axis. m The cumulative effect of the items.

[0165] This embodiment addresses the multi-source nonlinear characteristics (time-varying inertia, exponential friction, and piecewise gravity coupling) and uncertainties of the MC-GES system, selecting sliding mode control as the core strategy. By constructing a sliding surface that integrates the mass jump term H(t) and the friction nonlinearity term, and combining it with boundary layer fuzzy compensation to suppress chattering, robust tracking of the rated speed is achieved. This scheme not only avoids the dependence of traditional methods on precise linearization, but also coordinates the parameter differences of multi-node pulleys through the design of a dynamic sliding surface, ensuring the global stability of the system in the Lyapunov sense.

[0166] Robust sliding mode control based on mountain cable car-type gravity energy storage system

[0167] To address the multi-source nonlinear characteristics (time-varying inertia, exponential friction, piecewise gravity coupling) and uncertainties (loading and unloading disturbances, environmental interference) of the MC-GES system, this embodiment selects sliding mode control as the core strategy to achieve robust tracking at rated speed. The following is the complete process of implementing this sliding mode control strategy, including the design of the sliding surface integrating the mass jump term H(t) and the frictional nonlinear term, boundary layer fuzzy compensation, and dynamic sliding surface adjustment, ultimately ensuring the system's global stability in the Lyapunov sense.

[0168] Sliding surface design

[0169] The sliding surface is the core component of sliding mode control, used to define the desired dynamics of the system. In sliding mode control, the system state "slides" along the sliding surface until it reaches the target state. The design of the sliding surface ensures that the system state converges towards the target state and can accommodate uncertainties and nonlinear behavior in the system.

[0170] Speed ​​error and basic sliding surface

[0171] The speed error e is defined as the difference between the actual speed and the target speed, and is calculated as follows:

[0172] e = vv d (17)

[0173] Among them, v d This is the reference value for the system's rated speed.

[0174] The basic sliding surface s is calculated as follows:

[0175] s=e+c∫edt (18)

[0176] Here, c>0 is the convergence rate coefficient, ensuring error convergence. However, considering M... eq The time-varying nature of (t) requires adjustment of the sliding surface to accommodate changes in mass.

[0177] s=M eq (t)e+c∫edt (19)

[0178] This allows for a dynamic reflection of the impact of inertia changes on the first derivative e of the velocity error, ensuring that the control system adapts to dynamically changing inertia.

[0179] The fusion mass jump term H(t):

[0180] Changes in mass can cause abrupt changes in the system's inertia, meaning that the system's response capability will also change. Therefore, the sliding surface needs to be dynamically adjusted according to these changes to ensure that the system can still operate stably after a sudden change in mass. The mass jump term H(t) represents the abrupt change caused by the loading and unloading event, and can be modeled as:

[0181] M eq (t)=M0+m c ·H(tt event (20)

[0182] Where M0 is the basic inertia, t event H(tt) represents the time when the event occurs. event ) for tt event The step function at time t, when t≥t event The value is 1 if the condition is met, and 0 otherwise. Substituting this mass jump term into the sliding surface equation:

[0183] s=[M0+ΔM·H(tt event )]e+c∫edt(21)

[0184] Where ΔM is the change in mass.

[0185] In this way, the sliding surface can adaptively adjust according to sudden changes in quality, so as to ensure that the system can continue to operate stably after the sudden change.

[0186] Control Law Design

[0187] Control rate F m Equivalent control term F eq With switching control item F sw Composite composition:

[0188] F m =F eq +F sw (twenty two)

[0189] Equivalent control term design:

[0190] To ensure the dynamic satisfaction of the sliding surface The equivalent control term can be obtained:

[0191]

[0192] in, It is the first derivative of the basic sliding surface.

[0193] By combining the system dynamics equations (12), the equivalent control term is derived:

[0194]

[0195] The equivalent control term is derived from the dynamic equation of the system and helps the system to operate stably in the absence of external disturbances.

[0196] Switching control item design:

[0197] To suppress parameter perturbations and disturbances, a boundary layer fuzzy compensation mechanism is introduced:

[0198]

[0199] Where k>0 is the switching gain; sat(·) is the saturation function. The saturation function is used to control the nonlinear characteristics during the switching process and avoid frequent high-frequency switching; ε>0 is the adjustable boundary layer thickness, and the value of ε needs to be matched with the unmodeled dynamics of the system, the range of parameter perturbations, and the amplitude of external disturbances. For high-frequency disturbances or rapidly changing systems, a smaller ε should be selected to improve the response speed; for low-frequency disturbances or slowly changing systems, ε can be appropriately increased to enhance smoothness.

[0200] Stability analysis

[0201] The Lyapunov function is a mathematical tool used to prove whether a dynamic system is stable under a specific control strategy. Stability analysis uses the Lyapunov function to verify the stability of the system; the Lyapunov function V is chosen as follows:

[0202]

[0203] Differentiating with respect to V, we get:

[0204]

[0205] By simplifying equations (12) and (23)-(25), we can obtain:

[0206]

[0207] When |s|>ε The system state converges to the boundary layer in a finite time; when |s|≤ε, the system enters the quasi-sliding mode. According to Lyapunov's stability theorem, the designed controller can guarantee the global asymptotic stability of the closed-loop system.

[0208] Step 4: Dynamic characteristics of inertial sliding surfaces based on time-varying inertial coupling and traditional sliding surfaces, specifically:

[0209] The MC-GES system operates in an intermittent, two-stage cyclic mode, achieving energy conversion through a sequential operation of "shutdown → energy storage → shutdown → energy release → shutdown". This mechanism provides infrastructure support for future multi-cable collaborative operation through the dynamic scheduling of single-cable units. This embodiment proposes an innovative design paradigm of modular single-cable architecture: based on the dynamic model construction of a single-cable unit, a scalable array-type energy storage system is formed, laying the technical foundation for the large-scale deployment of GW-level power plants. At the level of control strategy optimization, the differences in dynamic characteristics between the traditional sliding surface type (18) and the improved inertial sliding surface type (19) are compared.

[0210] like Figure 4 As shown, the speed tracking comparison between traditional sliding mode control and inertial sliding mode control is illustrated. Simulation results show that during the acceleration phase, inertial sliding mode control reaches 90% of the target value (1.8 m / s) in just 16.9 s, a reduction of 8.6% in response time compared to the traditional method's 18.6 s. During the deceleration phase, inertial sliding mode control reduces the speed to 10% of the initial value (0.2 m / s) in 24.1 s, a reduction of 26.07% compared to the traditional sliding mode control's 32.6 s. The steady-state error of inertial sliding mode control approaches zero, while the traditional method exhibits a 5% steady-state error. The inertial sliding surface is connected via M... eq The time-varying compensation of (t) embeds the Newton-Euler dynamics equations into the control law design, avoiding the conflict between control force and inertial force, and fundamentally suppressing high-frequency switching energy.

[0211] like Figure 5 As shown, by comparing the acceleration dynamic characteristics of traditional sliding mode control and inertial sliding mode control, the mechanism by which sliding surface geometric reconstruction suppresses high-frequency chattering is revealed. Traditional sliding mode control uses a fixed gradient vector. Basic sliding surface Its normal vector direction tan -1 (1 / c) forces the state trajectory to cut into the sliding surface at an acute angle. This geometric characteristic necessitates that the control law use high-frequency switching terms. Forcibly resisting the system's inertial force This excites a mechanical resonant mode, resulting in an amplitude of ±3.5 × 10⁻⁶. -3 m / s 2 The jagged fluctuations. Inertial sliding mode control introduces an equivalent inertial term M. eq Reconstruct the sliding surface as Make the gradient vector become When M eq When >>1, the normal vector direction tan -1 (M eq / c)→90°, the driving trajectory smoothly converges to the sliding surface at a near-vertical angle. This design utilizes the dynamic constraints implicit in the sliding surface equations. Achieve dynamic alignment of acceleration response with Newton-Euler equations, while simultaneously adjusting M... eq As a low-pass filter embedded in the control loop, it suppresses the energy surge during high-frequency switching. Simulation results show that the inertial sliding mode maintains the same peak acceleration (0.2976 m / s²). 2 At the same time, it significantly reduced the fluctuation amplitude, verifying the synergistic optimization effect of geometric characteristics and physical mechanisms.

[0212] like Figure 6As shown, by comparing the dynamic response characteristics of traditional sliding surfaces and inertial sliding surfaces, the essential differences between the two control strategies in terms of energy dissipation paths are revealed. Traditional sliding surfaces rely on a rigid switching mechanism, which can converge rapidly within 0.2s, but the instantaneous peak energy of the sliding surface reaches ±400 (the amplitudes are the same, but the high-frequency switching of traditional sliding surfaces causes energy to be repeatedly injected into the system in an oscillating manner, triggering subsequent continuous oscillations). Inertial sliding surfaces reshape the energy dissipation path through a two-pronged strategy: firstly, the equivalent inertial term M... eq As a low-pass filter, it directionally absorbs concentrated impact energy in the early stages of disturbances (no subsequent oscillations at the same peak value ±400); secondly, the verticalization design of the sliding surface normal vector shortens the residence time of the state trajectory in the switching layer |s|<ε, and combined with the saturation function softening control switching, it allows energy to pass through M eq The coupling effect with system damping leads to gradient release. Although the approach time is extended to 20s, the control energy waveform of the inertial sliding mode exhibits a smooth decay characteristic, avoiding the accumulation of high-frequency components. This design significantly suppresses high-frequency chattering in MC-GES through the synergistic effect of geometric characteristics (vertical convergence angle) and physical mechanisms (dynamic adaptation of inertial forces).

[0213] like Figure 7 As shown, by comparing the dynamic response characteristics of traditional sliding mode surfaces and inertial sliding mode surfaces, the suppression effect of inertial sliding mode design on high-frequency traction force oscillation is revealed. Simulation results show that traditional sliding mode control exhibits significant chattering (traction force fluctuation ±20N) under 0.5kHz high-frequency interference due to the limitation of fixed switching gain. This high-frequency torque pulsation, transmitted through the transmission chain, will cause multiple hazards: firstly, mechanical transmission components will suffer accelerated fatigue damage under 500Hz alternating stress; secondly, high-frequency oscillations, amplified by transmission gaps, will increase the speed tracking error of the servo system and reduce the measured positioning accuracy; and thirdly, cable tension will be subject to sudden changes under periodic impacts. The inertial sliding mode surface design introduced in this embodiment, through the equivalent inertial mass / moment of inertia M... eq This method achieves pre-compensation for load surge energy. Simulation results show that it effectively suppresses the 500Hz high-frequency chattering component and significantly reduces the amplitude of traction force fluctuations. Through a dynamic gain adaptation mechanism, this improved scheme significantly enhances mechanical reliability while maintaining system robustness.

[0214] like Figure 8As shown, this diagram compares the power curves of MC-GES under two control strategies. Simulation results indicate that MC-GES exhibits typical trapezoidal power characteristics during energy storage / release: the oblique transition segment originates from the dynamic adjustment phase of loading / unloading the vehicle queues of segments 23 (oblique transport segment) and 78 (gravity descent segment) of the working cable during the switching between shutdown and operating states; the horizontal steady-state segment corresponds to the stable operating state of power output or absorption after the vehicle queue is fully loaded. The drop and rise characteristics of the power curve are directly related to the loading and unloading sequence of MC-GES, and its dynamic process can be clearly identified through locally magnified waveforms. It is worth noting that due to the limitations of fixed switching gain, traditional sliding mode control still exhibits a high-frequency chattering component with an amplitude of approximately ±0.172% in the power level segment (fluctuation details in the locally magnified diagram). Such high-frequency power fluctuations may affect converter lifespan and grid power quality through electromechanical coupling paths. In contrast, inertial sliding mode control reconstructs the power regulation mechanism through dynamic damping terms, effectively suppressing high-frequency components while maintaining trapezoidal power characteristics.

[0215] like Figure 9 As shown, it displays the dynamic response curves of the upper and lower reservoir mass storage capacity (SOC) and actual cumulative energy of the MC-GES system. It is worth noting that at the instant the system switches to the working mode, both the upper and lower reservoir SOC curves exhibit significant step characteristics. This phenomenon originates from the transient characteristics of the synchronous loading of the working section mass of the gravity energy storage device during mode switching. Among them, the upper reservoir SOC characterizes the stored mass of the energy storage medium (weight), and its physical meaning is the potential energy that the system can release; while the lower reservoir SOC reflects the effective capacity of the energy storage system to absorb energy. By coupling the cumulative energy curve and the dual reservoir SOC curves, and combining the dynamic energy balance equations established by equations (14)-(15), the energy conversion efficiency of the system for a complete charge and discharge cycle can be accurately calculated. The research results show that under the current design parameters, the cycle efficiency of the MC-GES system reaches 88.54%.

[0216] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0217] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0218] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0219] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0220] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of the present invention. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention should be covered within the scope of protection of the claims of the present invention.

Claims

1. A dynamic modeling and sliding mode control method for a mountain cable car-type gravity energy storage system, characterized in that, include: Construct a nine-node closed-loop cable topology; Dynamic modeling is performed using the nine-node closed-loop cable topology to construct a dynamic model of the nine-node closed-loop cable topology. Sliding mode control is performed based on the dynamic model of the nine-node closed-loop cable topology to obtain the sliding mode control results.

2. The dynamic modeling and sliding mode control method for a mountain cable car-type gravity energy storage system according to claim 1, characterized in that, Constructing a nine-node closed-loop cable topology includes: A unidirectional circulation loop is obtained by using a mountain cable car-type gravity energy storage system. The unidirectional circulation loop includes a horizontal loading section, an inclined transport section, a horizontal unloading section, a vertical descent section, a power drive section, an inclined acceleration section, a gravity descent section, a ground unloading section, and a vertical reset section. Based on the single-loop combination and the spatial distribution pattern of nodes, a nine-node closed-loop cable topology is constructed.

3. The dynamic modeling and sliding mode control method for a mountain cable car-type gravity energy storage system according to claim 2, characterized in that, The formula for calculating the total path length vector of the nine-node closed-loop cable topology is as follows: Where L is the total path length vector of the nine-node closed-loop cable topology, l is the length of the horizontal baseline segment, and ΔH is the total height difference of the MC-GES system. H1 is the tilt angle, and H1 is the vertical height of the upper and lower stacking platforms.

4. The dynamic modeling and sliding mode control method for a mountain cable car-type gravity energy storage system according to claim 1, characterized in that, Dynamic modeling is performed using the aforementioned nine-node closed-loop cable topology, constructing a dynamic model of the nine-node closed-loop cable topology, including: Based on the nine-node closed-loop cable topology, the tension information on both sides of the pulley is obtained using the Euler friction formula; By combining the tension information on both sides of the pulley with the moment of inertia and the bearing friction torque, the dynamic equation of the pulley is established; The mass mutation caused by loading and unloading is obtained by using a step function based on the piecewise gravity tilt angle and time-varying mass. The dynamic equations of the cable segment are obtained by utilizing the mass mutation caused by loading and unloading. Based on the pulley dynamics equation and the cable segment dynamics equation, combined with the external force term, a dynamic model of a nine-node closed-loop cable topology is constructed.

5. The dynamic modeling and sliding mode control method for a mountain cable car-type gravity energy storage system according to claim 4, characterized in that, The formula for calculating the pulley dynamics is as follows: Among them, M f,j Let μ be the frictional torque of the pulley j bearing. b K is the bearing friction coefficient. j I is the winch formula coefficient on pulley j. j Let ω be the moment of inertia of pulley j. j Let be the angular velocity of the pulley, t be the time, and b be the angular velocity of the pulley. j Here, v is the coefficient of viscous friction, and r is the velocity. j Let be the radius of pulley j.

6. The dynamic modeling and sliding mode control method for a mountain cable car-type gravity energy storage system according to claim 4, characterized in that, The formula for calculating the quality mutation caused by loading and unloading is as follows: Where, m ij (t) represents the mass of segment ij at time t. Let be the inherent mass of segment ij. For the quality of cable segment ij, Let m be the mass of the vehicle in segment ij. c Let n be the mass added to the heavy object, n be the number of vehicles in segment ij, H(·) be the unit step function, and t be the time interval. load,k This indicates that the k-th vehicle is loaded, t unload,k This indicates the time of the k-th uninstallation event.

7. The dynamic modeling and sliding mode control method for a mountain cable car-type gravity energy storage system according to claim 4, characterized in that, The dynamic equation for the cable segment is calculated as follows: Among them, T ij T represents the tension on cable segment ij. ji For the tension on the cable segment, F ext,ij For external forces, m ij (t) represents the mass of segment ij at time t, a(t) represents the cable acceleration at time t, and g represents the acceleration due to gravity. The angle of inclination is the segmented gravity.

8. The dynamic modeling and sliding mode control method for a mountain cable car-type gravity energy storage system according to claim 4, characterized in that, The dynamic model calculation formula for the nine-node closed-loop cable topology is as follows: Among them, F m (t) represents the equivalent load force of the MC-GES system at time t, M eq (t) represents the equivalent inertial mass / moment of inertia at time t, a(t) represents the cable acceleration at time t, C represents the comprehensive damping coefficient, v(t) represents the velocity at time t, and G(t) represents the gravitational potential energy term at time t.

9. The dynamic modeling and sliding mode control method for a mountain cable car-type gravity energy storage system according to claim 1, characterized in that, Sliding mode control is performed based on the dynamic model of the nine-node closed-loop cable topology, and the sliding mode control results are obtained, including: Set speed error; The velocity error is subjected to inertial coupling processing to construct a time-varying inertial coupling inertial sliding surface; Based on the dynamic model of the time-varying inertial coupling inertial sliding surface combined with the nine-node closed-loop cable topology, the equivalent control term is obtained. Based on the time-varying inertial coupling inertial sliding surface combined with the boundary layer fuzzy compensation mechanism, the switching control term is obtained; The switching control term and the equivalent control term are combined to obtain the control rate; Based on the control law and the Lyapunov function, the sliding mode control result is obtained.

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