Computer-implemented method for determining a decoupling matrix for a control system

Abstract

The invention relates to a computer-implemented method for determining a decoupling matrix D for a control system (52) of an electro-hydraulic drive network comprising n hydraulic cylinders (10, 12) each having two chambers (20, 22, 24, 26), n-1 chamber short-circuiting's between the cylinder's chambers, and n+1 displacement units (14, 16, 18), the method comprising the steps of: Determining the relations between the control volume pressures, the load pressures and the sum pressure (S12) within the electro-hydraulic drive network; Establishing load pressure dynamics and sum pressure dynamics by using dedicated matrices (S14); and Deriving the decoupling matrix D (S16) from the load pressure dynamics and the sum pressure dynamics.

Description

[0001]R. 412339 -1 -Description Title matrix for a control The invention relates to the field of designing control systems for electro- hydraulic drive networks, especially for excavators. State of the Art An electro-hydraulic drive network integrates electrical and hydraulic components to facilitate various tasks, including control, actuation, and power transmission. Structurally, it consists of electrical components such as power supplies, control devices like switches, relays, PLCs, and hydraulic components like hydraulic fluid, pumps, actuators, and valves. The electrical components, starting with a power supply, generate control signals through devices such as relays, timers, and PLCs based on input parameters. These parameters could include sensor readings or operator commands. On the hydraulic side, hydraulic fluid serves as the medium for energy transmission, with pumps generating flow and pressure, while actuators, such as cylinders and motors, convert hydraulic energy into mechanical motion. Usually, valves regulate the direction, pressure, and flow rate of the fluid. Control logic, ranging from simple on-off control to more sophisticated proportional control systems, adaptive control systems, or non-linear controlsystems , governs the operation of the electro-hydraulic network. This logicprocesses input signals and generates output commands to control hydraulic components. Communication interfaces, such as serial protocols or Ethernet, may also be present for integration with higher-level control systems or remote monitoring. In summary, an electro-hydraulic drive network combines electrical and hydraulic systems to deliver efficient, precise, and reliable control over mechanical R. 412339 -2 -processes, making it indispensable in numerous industrial and mobile applications. Valves play a crucial role in regulating the flow, within an electro-hydraulic drive network. However, they can also be a source of various problems that affect the performance, efficiency, and reliability of the system. However, the use of valves in an electro-hydraulic drive network leads to inherent losses and therefore to low-energy efficiency. An electro-hydraulic drive network without valves may comprise n hydraulic cylinders, wherein some chambers of the hydraulic cylinders are short-circuited with n-1 chamber short-circuiting’s, and wherein the electro-hydraulic drivenetwork contains n+1 displacement units, wherein n is equal to or greater than 2.Any displacement unit may be a fixed displacement unit or a variable displacement unit. The primary difference between fixed displacement units and variable displacement units lies in their methods of controlling hydraulic fluid flow and, consequently, output power. Fixed displacement units operate by delivering a consistent volume of hydraulic fluid per revolution or stroke, regardless of the load or demand placed on them. This consistency in output flow rate ensures that the speed of the hydraulic cylinder or actuator it powers remains constant, assuming the load remains steady. Examples of fixed displacement units include fixed displacement pumps and hydraulic motors, both of which maintain a constant output flow rate under varying conditions. On the other hand, variable displacement units offer the flexibility to adjust the volume of hydraulic fluid delivered per revolution or stroke. This adjustment can be achieved manually, hydraulically, or electronically, depending on the specific design and application requirements. By varying the displacement, variable displacement units can dynamically adjust the output flow rate and pressure of hydraulic fluid to match changing load or demand conditions. This adaptability enables more precise control over the speed and force of hydraulic actuators, leading to improved efficiency and performance across a range of applications. Variable displacement pumps and hydraulic motors are typical examples of such units. R. 412339 -3 -While both fixed displacement units and variable displacement units are essential components of electro-hydraulic systems, their fundamental distinction lies in their ability to provide either a constant or adjustable flow of hydraulic fluid. This distinction directly influences the system's capacity to regulate speed, force, and overall efficiency. However, the displacement units have to be controlled individually, but not independently. Because of the short-circuiting’s the pressures of the volumes connected to the displacement units is divided to all the chambers of these hydraulic cylinders that are short-circuited. This means that the coupling between the hydraulic cylinders must be considered when controlling the electro-hydraulic drive network. It is not possible to control individual cylinders without further ado. In other words, if a displacement unit is activated to increase the pressure in a chamber that is short-circuited to another chamber, another displacement unit must be used to equalize the pressure in the second chamber and compensate for the actuation of the second hydraulic cylinder. The problem to be solved by the invention is to provide a method for designing a control system for a highly efficient electro-hydraulic drive network having multiple hydraulic cylinders with short-circuited chambers. The problem is solved by the objects of the independent claims. Disclosure of the invention According to a first aspect of the invention, the problem is solved by a computer- implemented method for determining a decoupling matrix D for a control system of an electro-hydraulic drive network comprising n hydraulic cylinders each having two chambers, n-1 chamber short-circuiting’s between the cylinder’s chambers, and n+1 displacement units. The method comprises the steps of:- Determining the relations between the control volume pressures, the loadpressures and the sum pressure within the electro-hydraulic drive network;- Establishing load pressure dynamics and sum pressure dynamics by usingdedicated matrices; and R. 412339 -4 -- Deriving the decoupling matrix D from the load pressure dynamics and thesum pressure dynamics. In the following, different pressures are considered for the provided method. Control volume pressure refers to the pressure level within a specific volume of hydraulic fluid that is actively controlled or regulated by the system's control mechanisms. This designated volume typically encompasses the area where critical control components such as valves, actuators, and sensors are located. The control system continuously monitors and adjusts the pressure within this volume to maintain desired system performance, such as precise control over the speed, force, or position of hydraulic actuators. By managing the pressure within the control volume, the control system can optimize the operation of the hydraulic system, ensuring efficient and responsive performance. Load pressure, on the other hand, refers to the pressure exerted by the hydraulic system on the load being acted upon by hydraulic actuators. This pressure level is directly related to the force required to move or manipulate the load and is influenced by factors such as the size of the load, the resistance encountered, and the hydraulic system's operating conditions. Load pressure is typically measured at the point where the hydraulic actuator interfaces with the load, such as at the cylinder piston or hydraulic motor output shaft. In applications such as lifting, pushing, or pulling heavy loads, the hydraulic system must generate sufficient load pressure to overcome resistance and perform the desired work effectively. Finally, the sum pressure is a sum of all pressures of the hydraulic cylinders, orthe weighted sum of all pressures of the hydraulic system.As mentioned at the beginning, the aim of this invention is to decouple the relationships between different pressures in the electro-hydraulic drive network. It is therefore particularly important for the first step to determine the relationship between the pressures in the electro-hydraulic drive network. Based on this, the dynamics between the pressures are determined. A dynamic can be expressed in particular by a change in the respective variable over time. A decoupling matrix is derived from these dedicated matrices, which describes the relationship between the pressures in each chamber of each hydraulic cylinder of the given electro-hydraulic drive network. R. 412339 -5 -The decoupling matrix D can now be used to map the desired piston speed of each hydraulic cylinder of the electro-hydraulic drive network to the required signal input into the displacement units for increasing, decreasing or maintaining the current pressure within the connected volume. Thus, the provided method may be used for designing a control system for an electro-hydraulic drive network as described in the beginning. In an embodiment, the method comprises the following step prior to determining the relations between the physical pressures, the load pressures and the sum pressures: -Determining a flow continuity model for the electro-hydraulic drivenetwork according to the given number of cylinders, short-circuiting’s and displacement units. The flow continuity model for the electro-hydraulic drive network may especially consist of flow continuity equations. Thus, the pressure dynamics may be described as ^̇ = ^(^, ^̇, ^^),wherein p = [p1, p2, …, pn+1]Trepresents the vector of the control volume pressures of the displacement units, x = [x1, x2, …, xn]Trepresents the positions of each hydraulic cylinder and ω = [ω1, ω2, …, ωn+1]Tthe speeds of thedisplacement units’ shafts.In an embodiment, the flow losses and pressure losses within the electro- hydraulic drive network are neglected for determining the flow continuity model. In the context of the invention, “neglected” is considered as being equal to zero. Neglecting the losses reduces the complexity of the flow continuity model, thus, the decoupling matrix D is easier to determine. In an embodiment, the step of determining the sum pressures comprises summarizing the weighted control volume pressures. By weighting the control volume pressures, the decoupling matrix D determined in the end may become more precise to the need or the framework conditions of the electro-hydraulic drive network. R. 412339 -6 -In an embodiment, the step of determining the relations between the control volume pressures, the load pressures and the sum pressure comprises determining virtual pressures dynamics for each volume from the load pressures, the sum pressures and the control volume pressures. Using the virtual pressure dynamics gives conditions, which may be used for deriving the decoupling matrix D. Basically, the virtual pressure can be equated to a target state for which the certain conditions apply. These conditions are the same for different system states, so that the decoupling matrix D can be easily determined. In an embodiment, the load pressure dynamics and sum pressure dynamics are derived from the dynamic virtual pressures, wherein the dynamic virtual pressures are derived from the sum of a first dedicated matrix A multiplied withthe piston positions and a second dedicated matrix B multiplied with the speedsof the electric motors driving the displacement units. The virtual pressure dynamics may be derived as a vector from wherein A and B are the dedicated matrices, which may be determined with In an embodiment, the decoupling matrix D is derived from the inverse of the second dedicated matrix B and the first dedicated matrix A. With the boundary condition that the virtual pressure dynamics should be zero, the equation from above can be converted into the following form. ^= −^^^^^ = −^^, ^ = ^^^^wherein B-1is the inverse of the second dedicated matrix B. R. 412339 -7 -The aim of the control system is to obtain a signal for the displacement units from a predefined system state, i.e., defined piston velocities z. The decoupling matrix D is to be used for this purpose. This makes it easy to determine D. In another aspect, the invention relates to a method for operating an electro-hydraulic drive network comprising n hydraulic cylinders each having twochambers, n-1 chamber short-circuiting’s between the cylinder’s chambers, and n+1 displacement units. Each cylinder comprises a piston rod which is extendable from the corresponding cylinder, wherein the rod velocity is controlled by the angular velocity of the displacement units. The angular velocity ω of each displacement unit is controlled by a signal to an electric motor driving the displacement units, wherein the signals to the electric motors are derived from a representation of the aimed rod velocity and a decoupling matrix, wherein the decoupling matrix D is determined by using a method as described above. In yet another aspect, the invention relates to an excavator comprising an electro-hydraulic drive network, wherein the electro-hydraulic drive network is operated with a method as described above. In yet another aspect, the invention relates to a computer program comprising program code, for executing a method as described above when the computer program is executed on a computer. In yet another aspect, the invention relates to a computer-readable medium containing program code of a computer program to execute a method as described above when the computer program is executed on a computer. In yet another aspect, the invention relates to a system for determining a decoupling matrix D for a control system of an electro-hydraulic drive network, wherein the system is configured to execute a method as described above. In summary, a computer-implemented method for determining a decoupling matrix D for a control system of an electro-hydraulic drive network, a method for operating an electro-hydraulic drive network, an excavator comprising said electro-hydraulic drive network, a computer program comprising program code and a computer-readable medium containing program code are presented. R. 412339 -8 -The described embodiments and further developments can be combined with each other as desired. Further possible embodiments, further developments and implementations of the invention also include combinations of features of the invention described above or below with respect to the embodiments that are not explicitly mentioned. Brief description of the drawings The accompanying drawings are intended to provide a further understanding of embodiments of the invention. They illustrate embodiments and, in connection with the description, serve to explain principles and concepts of the invention. Other embodiments and many of the advantages mentioned will be apparent with reference to the drawings. The elements shown in the drawings are not necessarily shown to scale with respect to each other. The figures show:Fig. 1 a schematic flow chart of the method for determining adecoupling matrix D for a control system of an electro-hydraulic drive network; andFig. 2 a schematic view of an exemplary electro-hydraulic drivenetwork. In the figures of the drawings, identical reference signs denote identical or functionally identical elements, parts, or components, unless otherwise indicated. Fig.1 shows a schematic flow chart of the method for determining a decoupling matrix D for a control system of an electro-hydraulic drive network. In a first step S10, the flow continuity equations for the given electro-hydraulic drive network are determined. This includes for example determining the exact number of hydraulic cylinders, displacement units and short-circuiting’s between the hydraulic cylinder’s chambers. The pressure dynamics, i.e. the time derivatives of the electro-hydraulic units control volume pressures, are established from its flow continuity equations while R. 412339 -9 -ignoring flow and pressure losses. Under these conditions the electro-hydraulicunits pressure dynamics may be described as Eq. (1), where ^ = [^1 ^2 ⋯ ^^+1]T,^ = [^1 ^2 ⋯ ^^]T, ^ = [^1 ^2 ⋯ ^^+1]T represent vectors of the control volumepressures, axis positions and electro-hydraulic unit shaft speeds, respectively,and • denotes the time derivative of some vector •. In step S12, the relations between the control volume pressures, the load pressures and the sum pressures are determined. The control volume pressures are mapped into virtual pressure states consisting of the load pressures ^L = [pL1 pL2 ⋯ pLn]^ and a weighted system sum pressurepΣ = [^ 1]^ ^where^ = [k₁ k₂ ⋯ k^]^is a weight vector. The load pressures ^L are proportional to the hydraulic cylinder forces ^cyl = [Fcyl1 Fcyl2 ⋯ Fcyln]^. As an example, the hydraulic cylinder force for cylinder 1 of Figure 1 is given by Fcyl1 = A₁·p₁ − A₂·p₂ where A₁ and A₂ are the piston and rod side piston areas, respectively.This mapping of the control volume pressures ^ into the virtual pressure vector ^vcan be described using the transformation matrix as described by Eq. (2). R. 412339 -10 - In step S14, the load pressure dynamics and the sum pressure dynamics are represented in dedicated matrices. Thus, these dedicated matrices represent the dynamic behavior of the given electro-hydraulic drive network. The virtual pressure dynamics are described in Eq. (3), where A and B are (n+1) ×(n+1) matrices, and ^=[^ 0]T.The virtual pressure dynamics are given by: In step S16, the decoupling matrix D is derived from the dedicated matrices representing the load pressure dynamics and the sum pressure dynamics. While the dedicated matrices predict the pressures in the electro-hydraulic drive network for a given system state, the decoupling matrix D may be used for deriving a set of commands for achieving said system state and pressures within the electro-hydraulic drive network.The n weights of the weight vector ^ are obtained by solving Eq. (4) for ^1, ^2, …, ^^,resulting in Eq. (5). R. 412339 -11 - Finally, in step S18, the decoupling matrix D may be used for actually controlling the displacement units of the electro-hydraulic drive network. The decoupling control structure is established by taking the left-hand side of Eq. (3)and substituting z and ω with their reference values:z* = [ ẋ* ; ṗΣ* ], ω* = [ ω₁* ω₂* ⋯ ω^₊₁* ]^By setting z = z* and ω = ω*, the reference virtual pressure dynamics are given by: Assuming steady-state conditions (i.e., ṗ_v* = 0), the decoupling control law is derived as: Assuming negligible electro-hydraulic unit dynamics such that ω = ω*, the resultingdecoupled virtual pressure dynamics are: R. 412339 -12 -Fig.2 shows an electro-hydraulic drive network with two hydraulic cylinders 10, 12 and three displacement units 14, 16, 18. Each of the hydraulic cylinders 10, 12 comprises a first chamber 20, 22 and a second chamber 24, 26, a piston 28, 30 and a piston rod 32, 34. The piston rods 32, 34 are moved by a pressure difference in the two chambers 20, 22, 24, 26 of the hydraulic cylinders 10, 12. The second chamber 24 of the first hydraulic cylinder 10 is fluidically connected to the first chamber 22 of the second hydraulic cylinder 12 and thus short- circuited. These two chambers 24 and 22 together form a common volume 36. The first displacement unit 14 is fluidically connected to the first chamber 20 of the first hydraulic cylinder 10 and the volume 36. When the first displacement unit is activated, the piston 28 in the first hydraulic cylinder moves. However, the pressure also changes in the second chamber 24 of the same hydraulic cylinder and thus also in the first chamber 22 of the second hydraulic cylinder 12. The second displacement unit 16 is arranged between the volume 36 and the second chamber 26 of the second hydraulic cylinder 12. When the first displacement unit 14 is activated, the second displacement unit 16 must be controlled in such a way that it compensates for the pressure increase in the first chamber 22 of the second hydraulic cylinder 12, provided that the piston 30 of the second hydraulic cylinder 12 is not to move as well. The third displacement unit 18 is arranged between the second chamber 26 and a flexible fluid volume 38. The further the piston rods 32, 34 are pushed out of the hydraulic cylinders 10, 12, the less fluid within the first chambers 20, 22 is displaced by them. The entire electro-hydraulic drive network must therefore be supplied with fluid from the flexible fluid volume 38 via the third displacement unit 18. Conversely, fluid must be removed from the electro-hydraulic drive network when the pistons 28, 30 are retracted and the piston rods 32, 34 displace fluid. The electro-hydraulic drive network also has various sensors. The position sensors 40, 42 continuously determine the position of the pistons 28, 30 within the hydraulic cylinders 10, 12. The speed of the pistons 28, 30 can be derived from the change in position over time. The pressure sensors 44, 46, 48 measure the pressures that are present in the first chamber 20 of the first hydraulic cylinder 10, the volume 36 shared by both hydraulic cylinders 10, 12 and the second chamber 26 of the second hydraulic R. 412339 -13 -cylinder 12. The pressure dynamics can be derived from the change in pressure over time. The data from all sensors 40, 42, 44, 46, 48 are transmitted to hardware interfaces 50 of the control system 52. The control software 54 generates control signals for the displacement units 14, 16, 18 from the sensor values and setpoint values 56, which it receives, for example, via an input from a user or from other software, etc. The generated signals are sent to the control units 58, 60, 62, which each control the displacement units 14, 16, 18 assigned to them.Since the displacement units 14, 16, 18 are coupled to each other via the shortcircuit of the second chamber 24 of the first hydraulic cylinder 10 and the first chamber 22 of the second hydraulic cylinder 12, the signals for the displacementunits 14, 16, 18 must be generated in a decoupled manner. This is done usingthe decoupling matrix D. A control signal for the displacement units 14, 16, 18 is thus generated within the control software from the setpoint values 56 and the sensor values of the sensors 40, 42, 44, 46, 48, with which the pistons 28, 30 are moved into the desired position.

Claims

R. 412339 -14 -Claims1. Computer-implemented method for determining a decoupling matrix D for acontrol system (52) of an electro-hydraulic drive network comprising nhydraulic cylinders (10, 12) each having two chambers (20, 22, 24, 26), n-1chamber short-circuiting’s between the cylinder’s chambers, and n+1displacement units (14, 16, 18), wherein n is equal to or greater than 2,the method comprising the steps of: -Determining the relations between the control volume pressures, the loadpressures and the sum pressure (S12) within the electro-hydraulic drivenetwork; -Establishing load pressure dynamics and sum pressure dynamics byusing dedicated matrices (S14); and- Deriving the decoupling matrix D (S16) from the load pressure dynamicsand the sum pressure dynamics.

2. Computer-implemented method according to claim 1, wherein the methodcomprises the following step prior to determining the relations between the physical pressures, the load pressures and the sum pressures:- Determining a flow continuity model (S10) for the electro-hydraulic drivenetwork according to the given number of cylinders, short-circuiting’s and displacement units.

3. Computer-implemented method according to one of the previous claims,wherein the flow losses and pressure losses within the electro-hydraulic drive network are neglected for determining the flow continuity model.

4. Computer-implemented method according to one of the previous claims,wherein the step of determining the sum pressures comprises summarizing the weighted control volume pressures.

5. Computer-implemented method according to one of the previous claims,wherein the step of determining the relations between the control volume pressures, the load pressures and the sum pressure comprises determining virtual pressure dynamics for each volume from the load pressures, the sumpressures and the control volume pressures.R. 412339 -15 -6. Computer-implemented method according to claim 5, wherein the loadpressure dynamics and sum pressure dynamics are derived from the dynamic virtual pressures, wherein the dynamic virtual pressures are derived from the sum of a first dedicated matrix A multiplied with the piston positions and a second dedicated matrix B multiplied with the speeds of the electric motors driving the displacement units.

7. Computer-implemented method according to claim 6, wherein the decouplingmatrix D is derived from the inverse of the second dedicated matrix B and the first dedicated matrix A.

8. Method for operating an electro-hydraulic drive network comprising nhydraulic cylinders (10, 12) each having two chambers (20, 22, 24, 26), n-1chamber short-circuiting’s between the cylinder’s chambers, and n+1 displacement units (14, 16, 18), wherein each cylinder comprises a pistonrod (32, 34) which is extendable from the corresponding hydraulic cylinder (10, 12), wherein the piston rod velocity is controlled by the angular velocity of the displacement units (14, 16, 18), wherein the angular velocity of eachdisplacement unit (14, 16, 18) is controlled by a signal to an electric motor driving the displacement units (14, 16, 18), wherein the signals to the electricmotors are derived from a representation of the aimed rod velocity and a decoupling matrix D,wherein the decoupling matrix D is determined according to one of the previous claims.

9. Excavator comprising an electro-hydraulic drive network, wherein theelectro-hydraulic drive network is operated with a method according to claim 8.

10. Computer program comprising program code, for executing a methodaccording to one of the claims 1 to 7 when the computer program isexecuted on a computer.

11. Computer-readable medium containing program code of a computerprogram to execute a method according to one of the claims 1 to 7 when thecomputer program is executed on a computer.R. 412339 -16 -12. System for determining a decoupling matrix D for a control system (52) of anelectro-hydraulic drive network, wherein the system is configured to execute amethod according to one of the claims 1 to 7.

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