Ceso-based linear active disturbance rejection control method and system for electro-hydraulic servo system

Abstract

The present application relates to the technical field of valve control asymmetric cylinder electro-hydraulic servo system control, more specifically, to a linear active disturbance rejection control method and system for an electro-hydraulic servo system based on a CESCO.The present application provides a linear active disturbance rejection control method and system for an electro-hydraulic servo system based on a cascade extended state observer, which has a simple structure, is easy to implement in engineering, and has good suppression ability for uncertain disturbances of a system containing high-frequency measurement noise.The present application uses a linear cascade ESO instead of a traditional high-gain ESO observer, uses multiple layers to process the input voltage and output displacement of an EHSS obtained in real time, and cooperates with a state feedback controller to control the EHSS throughout the operation.The present application eliminates the restriction factor of sensor high-frequency measurement noise on the estimation accuracy of the overall disturbance of the system in the linear active disturbance rejection control of the traditional electro-hydraulic servo system, improves the disturbance estimation accuracy, and reduces the sensitivity of the observer bandwidth value to high-frequency measurement noise.

Description

Technical Field

[0001] This invention relates to the field of control technology for valve-controlled asymmetric cylinder electro-hydraulic servo systems, and more specifically, to a linear active disturbance rejection control method and system for electro-hydraulic servo systems based on CESO (Cascaded Extended State Observer). Background Technology

[0002] EHSS (valve-controlled asymmetric cylinder electro-hydraulic servo system) is inherently nonlinear, exhibiting multi-source uncertainties such as model uncertainty, time-varying load, and high-frequency sensor measurement noise, posing a significant challenge to high-performance displacement control. Current conventional methods typically employ high-gain ESO (extended state observer), but their effectiveness is generally limited. Therefore, improving its overall disturbance estimation / control performance is a major research direction. Summary of the Invention

[0003] Therefore, it is necessary to provide a linear active disturbance rejection control method and system for electro-hydraulic servo systems based on CESO to address the problem that the existing high-gain ESOs have only moderate performance.

[0004] This invention is achieved using the following technical solution:

[0005] In a first aspect, the present invention discloses a linear active disturbance rejection control method for an electro-hydraulic servo system based on CESO, which is used for disturbance suppression and displacement control of the EHSS.

[0006] The linear active disturbance rejection control method for the CESO-based electro-hydraulic servo system includes the following steps:

[0007] S1, real-time acquisition of the input voltage u and output displacement x of the EHSS at the current moment, and processing by CESO and state selector to obtain displacement estimate, velocity estimate and total disturbance estimate;

[0008] The CESO is composed of n layers of ESO connected in series, where 1 ≤ n ≤ 3; the displacement estimate of the output of the nth layer of the CESO. Speed ​​valuation Disruption valuation The state selector selects the final output based on the number n of the CESO layers; the displacement estimate is selected from the displacement estimate output of the nth layer ESO. The velocity estimate is selected from the velocity estimate output of the nth layer ESO. The total disturbance estimate is selected as the sum of the disturbance estimates from n layers.

[0009] S2, based on the displacement estimate, the velocity estimate, and the total disturbance estimate, the corrected voltage is obtained through control by the control law and used as the new input voltage u' of the EHSS. The new input voltage u' corresponds to the control of the EHSS to output a new displacement x'.

[0010] S3, repeats the process of steps S1 and S2, accompanies the EHSS operation, and performs real-time estimation and compensation for the total disturbance of the EHSS.

[0011] This CESO-based electro-hydraulic servo system linear active disturbance rejection control method implements the method or process according to embodiments of this disclosure.

[0012] Secondly, the present invention discloses a linear active disturbance rejection control system for an electro-hydraulic servo system based on CESO, which uses the linear active disturbance rejection control method for an electro-hydraulic servo system based on CESO from the first aspect.

[0013] The CESO-based electro-hydraulic servo system linear active disturbance rejection control system includes a cascaded extended state observer, a state selector, and a state feedback controller.

[0014] The cascaded extended state observer is used to process the input voltage u and output displacement x of the real-time acquired EHSS to obtain several different displacement estimates, velocity estimates, and disturbance estimates.

[0015] The state selector is used in conjunction with the cascaded extended state observer to select the final displacement estimate, velocity estimate, and total disturbance estimate;

[0016] The state feedback controller is used to calculate the corrected voltage based on the selected displacement estimate, velocity estimate and total disturbance estimate, as the new input voltage u' of the EHSS.

[0017] This CESO-based electro-hydraulic servo system linear active disturbance rejection control method implements the method or process according to embodiments of this disclosure.

[0018] Thirdly, the present invention discloses a readable storage medium storing computer program instructions, which are read and executed by a processor to perform the above-described linear active disturbance rejection control method for an electro-hydraulic servo system based on CESO.

[0019] Compared with the prior art, the present invention has the following beneficial effects:

[0020] This invention, within the ADRC (Active Disturbance Rejection Control) framework, fully leverages the significant advantage of ADRC's independence from a precise mathematical model of the system. It proposes a linear active disturbance rejection control method and system for electro-hydraulic servo systems based on CESO (Continuous Electro-hydraulic Steering) noise, characterized by its simple structure, ease of implementation, and strong disturbance rejection capability. This invention replaces the traditional high-gain ESO observer with a cascaded ESO, utilizing its multi-level processing of the real-time acquired EHSS input voltage and output displacement to obtain the system state containing comprehensive disturbances in real time. A disturbance feedforward + state feedback control strategy is employed to control the EHSS throughout its operation. This invention eliminates the constraint of high-frequency sensor measurement noise on the accuracy of comprehensive disturbance estimation in traditional linear active disturbance rejection control of electro-hydraulic servo systems, improving disturbance estimation accuracy and reducing the sensitivity of the observer bandwidth to high-frequency measurement noise. Furthermore, simulation results demonstrate that the CESO-based linear active disturbance rejection control method for EHSS in this invention improves disturbance estimation / control performance and effectively suppresses the adverse effects of high-frequency measurement noise on the control performance of the electro-hydraulic servo system. Attached Figure Description

[0021] Figure 1 This is a structural diagram of the linear active disturbance rejection control system of the CESO-based electro-hydraulic servo system in Example 1;

[0022] Figure 2 for Figure 1 Structural diagram of the EHSS in China;

[0023] Figure 3 for Figure 1 Schematic diagram of the structure of CESO in China;

[0024] Figure 4 This is a structural diagram of the linear active disturbance rejection control system of the CESO-based electro-hydraulic servo system, which is a better design in Example 2.

[0025] Figure 5 This is the displacement tracking response curve under simulation experiment with a step signal as the reference signal and no measurement noise.

[0026] Figure 6 This is the displacement tracking error under simulation experiment with a step signal as the reference signal and no measurement noise.

[0027] Figure 7 This is the displacement estimation error under simulation experiment with a step signal as the reference signal and no measurement noise.

[0028] Figure 8 This is the estimation error of velocity in simulation experiments when the reference signal is a step signal and there is no measurement noise.

[0029] Figure 9This is the estimation error of the total disturbance under simulation experiment with a step signal as the reference signal and no measurement noise.

[0030] Figure 10 This is the control signal curve under simulation experiment with a step signal as the reference signal and no measurement noise.

[0031] Figure 11 This is the estimated curve of the total disturbance under simulation experiment with a step signal as the reference signal and no measurement noise.

[0032] Figure 12 In the simulation experiment, when the reference signal is a step signal, there is a tracking response curve of displacement under measurement noise;

[0033] Figure 13 In the simulation experiment, when the reference signal is a step signal, there is a tracking error in displacement under measurement noise;

[0034] Figure 14 In the simulation experiment, when the reference signal is a step signal, there is an estimation error in displacement under measurement noise.

[0035] Figure 15 In the simulation experiment, when the reference signal is a step signal, there is an estimation error in velocity under measurement noise.

[0036] Figure 16 In the simulation experiment, when the reference signal is a step signal, there is an estimation error of the total disturbance under measurement noise.

[0037] Figure 17 For simulation experiments, when the reference signal is a step signal, there is a control signal curve under measurement noise;

[0038] Figure 18 For simulation experiments, when the reference signal is a step signal, there is an estimated curve of the total disturbance under measurement noise;

[0039] Figure 19 This is the displacement tracking response curve under simulation experiment with a sinusoidal reference signal and no measurement noise.

[0040] Figure 20 This is the displacement tracking error under simulation experiment with a sinusoidal reference signal and no measurement noise.

[0041] Figure 21 This is the displacement estimation error under simulation experiment with a sinusoidal reference signal and no measurement noise.

[0042] Figure 22 This is the estimation error of velocity under simulation experiment with a sinusoidal reference signal and no measurement noise.

[0043] Figure 23This is the estimation error of the total disturbance under simulation experiment with a sinusoidal reference signal and no measurement noise.

[0044] Figure 24 This is the control signal curve under simulation experiment with a sinusoidal reference signal and no measurement noise.

[0045] Figure 25 This is the estimated curve of the total disturbance under simulation experiment with a sinusoidal reference signal and no measurement noise.

[0046] Figure 26 In the simulation experiment, when the reference signal is a sinusoidal signal, there is a tracking response curve of displacement under measurement noise;

[0047] Figure 27 In the simulation experiment, when the reference signal is a sinusoidal signal, there is a tracking error in displacement under measurement noise;

[0048] Figure 28 In the simulation experiment, when the reference signal is a sinusoidal signal, there is an estimation error in displacement under measurement noise.

[0049] Figure 29 In the simulation experiment, when the reference signal is a sinusoidal signal, there is an estimation error in velocity under measurement noise.

[0050] Figure 30 In the simulation experiment, when the reference signal is a sinusoidal signal, there is an estimation error of the total disturbance under measurement noise;

[0051] Figure 31 For simulation experiments, when the reference signal is a sinusoidal signal, there is a control signal curve under measurement noise;

[0052] Figure 32 For simulation experiments, when the reference signal is a sinusoidal signal, there is an estimated curve of the total disturbance under measurement noise.

[0053] The attached diagram lists the components represented by each number as follows:

[0054] 1. Filter, 2. Motor, 3. Hydraulic pump, 4. Three-position four-way electro-hydraulic proportional valve, 5. Relief valve, 6. Single-outlet hydraulic cylinder, 7. Load, 8. Controller, 9. Linear displacement sensor, 10. Analog-to-digital converter, 11. Digital-to-analog converter. Detailed Implementation

[0055] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0056] It should be noted that when a component is said to be "installed on" another component, it can be directly on the other component or it may be in a component that is centered on it. When a component is said to be "set on" another component, it can be directly set on the other component or it may also be in a component that is centered on it. When a component is said to be "fixed to" another component, it can be directly fixed to the other component or it may also be in a component that is centered on it.

[0057] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. The terminology used herein in the specification of this invention is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. The term "or / and" as used herein includes any and all combinations of one or more of the associated listed items.

[0058] Example 1

[0059] Please see Figure 1 , Figure 2 , Figure 1 This is a structural diagram of the self-disturbance rejection control system of the CESO-based electro-hydraulic servo system in Example 1. Figure 2 This is a structural diagram of the EHSS.

[0060] The following is combined Figure 2 A brief explanation of EHSS: EHSS includes filter 1, motor 2, hydraulic pump 3, electro-hydraulic proportional valve 4, relief valve 5, hydraulic cylinder 6, load 7, controller 8, linear displacement sensor 9, analog-to-digital converter 10, and digital-to-analog converter 11.

[0061] Among them, the electro-hydraulic proportional valve 4 is a three-position four-way valve, and the hydraulic cylinder 6 is a single-rod valve.

[0062] Specifically, motor 2 is connected to hydraulic pump 3, and motor 2 drives hydraulic pump 3 to work. Hydraulic pump 3 is equipped with filter 1 to protect it. Hydraulic pump 3 is connected to relief valve 5, which serves to regulate pressure, relieve pressure, unload the system, and provide safety protection. Electro-hydraulic proportional valve 4, as the control component of EHSS, has four ports (P, T, A, B): port P is connected to the oil source Ps, and port T is connected to the return oil tank. Hydraulic cylinder 6 is divided into rod chamber and rodless chamber by a piston; port A is connected to the rod chamber, and port B is connected to the rodless chamber. Hydraulic cylinder 6 is connected to load 7, so that the movement of the piston in hydraulic cylinder 6 drives the load 7 to move synchronously, and the displacements of the two are the same. Load 7 is equipped with linear displacement sensor 9 to collect its displacement. Linear displacement sensor 9 is electrically connected to controller 8 through analog-to-digital converter 10. Controller 8 is in turn electrically connected to electro-hydraulic proportional valve 4 through digital-to-analog converter 11.

[0063] The EHSS is a single-input single-output system. The input is a voltage signal u (|u|≤10V), and the output is displacement x. A linear displacement sensor 9 with a resolution of 0.5μm is used to acquire the displacement.

[0064] The controller 8 receives two input signals: a displacement reference signal and a digital signal obtained by converting the analog electrical signal of the displacement measurement acquired by the linear displacement sensor 9 into a digital signal. The displacement measurement signal needs to be converted into a digital signal using an analog-to-digital converter 10. The output of the controller 8 is a digital signal, which needs to be converted into an analog voltage signal with an amplitude not exceeding 10V (i.e., the input voltage signal of the EHSS) using a digital-to-analog converter 11, thereby controlling the valve core displacement of the electro-hydraulic proportional valve 4. When the valve core moves, the valve orifice is opened, and fluid flows into the hydraulic cylinder 6 through one port of the electro-hydraulic proportional valve 4, and then flows back through the other port. P1 and P2 are the corresponding pressures on the piston side and rod side, respectively, which act as driving forces for the load on the piston.

[0065] The goal of EHSS control is to ensure that the controlled object can stably, quickly, and accurately track the desired trajectory even when the system is subject to time-varying, nonlinear, or uncertain disturbances, especially when the load changes.

[0066] To achieve the above control objectives, this embodiment 1 provides a linear active disturbance rejection control method for an electro-hydraulic servo system based on CESO, which is used to suppress disturbances and control displacement of the EHSS.

[0067] Prior to this, the inventors established a dynamic structural mathematical model for EHSS:

[0068] Since the operating frequency bandwidth of the hydraulic cylinder 6 is much lower than the dynamic response speed of the electro-hydraulic proportional valve 4, the linear model of the electro-hydraulic proportional valve 4 can be expressed as:

[0069] xv =k v u(|u|≤10) (1)

[0070] Where, x v It is the valve core displacement, k v is the gain of the proportional valve, and u is the input voltage.

[0071] According to Newton's second law, the dynamics of a piston can be described as follows:

[0072]

[0073] Where M is the total mass of the piston and rod, and B p c is the viscous damping coefficient corresponding to the actuator and load rigidity, d is the external disturbance, P1 and P2 are the corresponding pressures on the piston side and rod side, A1 and A2 are the areas on the piston side and rod side, and x, and These are the corresponding piston displacement, velocity, and acceleration.

[0074] Neglecting external leakage from the cylinder, the continuity equation for the flow in the two chambers can be described as follows:

[0075]

[0076]

[0077] Where, V1 = V 10 +A1x is the total volume of the piston chamber, V2=V 20 -A2x is the total volume of the rod cell, V 10 and V 20 These are the initial volumes of the piston side and the rod side, respectively, C. t It is the internal leakage coefficient of the hydraulic cylinder, β e Q1 is the effective bulk modulus of the oil, and Q2 is the flow rate supplied into the piston chamber and the return flow rate from the rod chamber, respectively.

[0078] Define the switching function S(·) as:

[0079]

[0080] The fluid equation for an electro-hydraulic proportional valve can be described as follows:

[0081]

[0082]

[0083] in, C d ω and ρ are the flow coefficient and area gradient of the electro-hydraulic proportional valve 4, respectively; ρ is the oil density, P s and Pr These are supply pressure and return pressure, respectively.

[0084] Substituting formula (1) into formula (5) simplifies to:

[0085]

[0086]

[0087] For greater brevity, the following definition is given:

[0088] γ=k q k v (7)

[0089]

[0090] Substituting formulas (7) and (8) into (6), formula (6) can be simplified to:

[0091] Q1=γR1u (9a)

[0092] Q2=γR2u (9b)

[0093] Substituting formula (9) into (3), we get:

[0094]

[0095]

[0096] Piston driving force can be described as:

[0097] F = P1A1 - P2A2 (11)

[0098] According to formulas (2), (9), (10) and (11), the dynamic equation of motor 2 can be described as:

[0099]

[0100] From the above formula (12), it can be seen that EHSS is clearly a high-order uncertain nonlinear system. For ease of subsequent analysis and design, formula (12) is roughly transformed into a second-order system model in the time domain, which can be described as:

[0101]

[0102] in It is the total disturbance, which includes nonlinear uncertain dynamics and external disturbances.

[0103] a2 = -M / B p ,

[0104] Δ represents the uncertain model dynamics. The constant coefficient b0 is an estimate of the control gain b, where b = γβ. e (R1 A1 / V1+R2 A2 / V2) / B p .

[0105] Thus, based on the second-order nonlinear differential equation (13), u and x are the corresponding input and output of the EHSS, and the function f(x,d,P1,P2,u) represents the total perturbation. Therefore, equation (13) can be described as follows:

[0106]

[0107] in w represents the measurement noise, and the system output is affected by the measurement noise.

[0108] The first layer of the cascaded extended state observer (CESO) is a standard ESO, which can be represented as:

[0109]

[0110] in, It is the state estimation vector of x1, L1=[l 11 l 12 l 13 ] T It is the gain vector of the standard ESO. w' represents the noise margin after the measurement noise w is filtered by the first layer of ESO.

[0111] When choosing L, the principle should be that all eigenvalues ​​of the observer are located at -ω. o ,Right now

[0112]

[0113] The second layer ESO of CESO can be represented as

[0114]

[0115] in, This is the state estimation vector for x2; the coefficients q = [0 1 0]. T L2 = [l 21 l 22 l 23 ] T It is the gain vector of the second-layer ESO, and

[0116]

[0117] The third layer ESO of CESO can be represented as:

[0118]

[0119] in It is the state estimation vector of x3. It is the gain vector of the third-layer ESO.

[0120] When the number of cascaded ESO layers n=1, its working mechanism is equivalent to that of a conventional ESO. For a conventional ESO, a higher bandwidth value results in more accurate disturbance estimation, but a higher bandwidth also amplifies measurement noise more severely, ultimately leading to increased disturbance estimation error. Therefore, the bandwidth value of a conventional ESO usually needs to be a trade-off between disturbance estimation accuracy and the adverse effects of measurement noise. However, increasing the number of cascaded ESO layers n, thus forming a CESO structure, not only reduces the bandwidth value but also improves the disturbance estimation accuracy.

[0121] When the number of CESO layers n > 1, the second-layer ESO directly uses the output of the first-layer ESO, which is independent of the system output y, and is therefore unaffected by measurement noise. Simultaneously, in the CESO structure, because the bandwidth of the first-layer ESO decreases, it possesses high-frequency filtering characteristics, effectively reducing the adverse effects of high-frequency measurement noise. If n = 2, the disturbance estimation error generated by the first-layer ESO can be further estimated in the second-layer ESO. (Right now This is because ω o2 >ω o1 Similarly, if n=3, then after the first and second layer ESO estimations, the remaining disturbance residuals can be estimated in the third layer ESO as follows: (Right now The final estimated total disturbance can be expressed as: This enables high-performance estimation of the combined uncertain disturbance f, which includes measurement noise and different frequencies.

[0122] Specifically, the inventors analyzed n=1, n=2, and n=3 respectively, and selected ω on =α n-1 ω o1 Where α is an adjustable parameter.

[0123] From equations (15) and (17), it can be seen that only the output of the first layer is related to the measurement noise. Since the second-layer ESO directly uses the output of the first-layer ESO, it is not affected by the measurement noise. The perturbations estimated by the second and third-layer ESOs are actually the residuals of the perturbation estimates of the first-layer ESO. With a well-designed observer, the estimate of the total perturbation should be taken from the new extended state estimate:

[0124]

[0125] If the controller is designed as follows:

[0126]

[0127] Therefore, disturbances and uncertainties are eliminated from the input signal before they affect the state variables.

[0128] Based on the above principle analysis, see Figure 1 The linear active disturbance rejection control method for the CESO-based electro-hydraulic servo system includes the following steps:

[0129] S1 acquires the input voltage u and output displacement x of EHSS in real time, and processes them through CESO and state selector to obtain displacement estimate, velocity (i.e., the derivative of displacement) estimate, and total disturbance estimate.

[0130] Among them, CESO is composed of n layers of ESO connected in series, where 1≤n≤3.

[0131] ESO output displacement estimate of the nth layer of CESO Speed ​​valuation Disruption valuation In other words, each layer of ESO outputs a set of values, including displacement estimate, velocity estimate, and disturbance estimate; n layers of ESO output a total of n sets of values.

[0132] The state selector selects the final output based on the number of CESO layers n; specifically, the displacement estimate is taken from the displacement estimate of the nth layer ESO. The velocity estimate is taken from the velocity estimate of the nth layer ESO. The total disturbance estimate is the sum of the disturbance estimates from n layers.

[0133] It should be noted that both displacement and velocity estimates are taken from the last layer (i.e., the nth layer), because noise can affect them, especially the velocity estimate. This can be verified through simulation experiments later. Figure 15 .

[0134] Due to the design characteristics of CESO, the inputs of the first-level ESO of CESO include the real-time acquired output displacement x and the real-time acquired input voltage u after processing by the control gain estimate b0, which is u*b0.

[0135] The input to the nth layer ESO in CESO includes the displacement estimate of the output of the (n-1)th layer ESO. Speed ​​estimate of the ESO output at layer n-1 The sum of the perturbation estimates of the first n-1 layers The value of u*b0 is obtained by processing the real-time input voltage u with the control gain estimate b0.

[0136] S2, based on the displacement estimate, velocity estimate and total disturbance estimate obtained from S1, is controlled by a control law to obtain the corrected voltage as the new input voltage u' of the EHSS. The new input voltage u' corresponds to the control of the EHSS to output a new displacement x'.

[0137] The calculation formula for the control law in this embodiment 1 is as follows:

[0138]

[0139] r is the reference signal, k1 and k2 are the feedback gains, and b0 is the estimated control gain.

[0140] S3, repeats the process of steps S1 and S2, accompanies the EHSS operation, and performs real-time estimation and compensation for the total disturbance of the EHSS.

[0141] Of course, this embodiment also provides a linear active disturbance rejection control system for an electro-hydraulic servo system based on CESO, which uses the above-mentioned control method.

[0142] The CESO-based electro-hydraulic servo system linear active disturbance rejection control system includes a cascaded extended state observer, a state selector, and a state feedback controller. The cascaded extended state observer obtains the real-time input voltage u from the electro-hydraulic proportional valve 4 and the real-time output displacement x from the linear displacement sensor 9. The cascaded extended state observer processes the real-time acquired EHSS input voltage u and output displacement x to obtain n sets of displacement estimates, velocity estimates, and disturbance estimates. The state selector, in conjunction with the cascaded extended state observer, selects the displacement estimate, velocity estimate, and total disturbance estimate.

[0143] Based on the selected displacement estimate, velocity estimate, and total disturbance estimate, the state feedback controller calculates the corrected voltage as the new input voltage u' of the EHSS. Thus, the EHSS outputs a new displacement x' according to the new input voltage u'.

[0144] The calculation formula of the state feedback controller is based on formula (22). According to formula (22), the state feedback controller needs to input a reference signal r to calculate the displacement error with the displacement estimate.

[0145] like Figure 1 As shown, n=3, meaning CESO has 3 layers. Based on the number of layers, the final displacement estimate is... Speed ​​estimate is The total disturbance estimate is also, Figure 1 middle

[0146] This CESO-based electro-hydraulic servo system linear active disturbance rejection control system acquires and processes the input voltage and output displacement of the EHSS in real time, i.e., it performs cyclic operation, accompanies the EHSS in operation, and estimates and compensates for the total disturbance of the EHSS in real time until the EHSS ends.

[0147] Example 2

[0148] This embodiment 2 also provides a linear active disturbance rejection control method for an electro-hydraulic servo system based on CESO and a control system using this control method.

[0149] See Figure 4 The difference between this embodiment 2 and embodiment 1 is that the calculation formula used in the control method of embodiment 2 is different. The control system adds a tracking differentiator, which can achieve high-performance tracking and avoid overshoot.

[0150] This embodiment 2 is based on the principle that, in order to achieve high-performance tracking, in addition to the state feedback controller, a tracking differentiator is needed to become part of the control law and improve tracking performance. The tracking differentiator can filter out spikes and avoid overshoot. The tracking differentiator is essentially a transition process for step signals, allowing the signal to smoothly transition to the target value rather than abruptly.

[0151] Therefore, the calculation formula for the control law in this embodiment 2 is as follows:

[0152]

[0153] r1 and r2 are reference signals, specifically transient process reference signals arranged according to control performance indicators. k1 and k2 are feedback gains, and b0 is the estimated control gain.

[0154] The control system in this embodiment 2 includes a tracking differentiator, a cascaded extended state observer, a state selector, and a state feedback controller.

[0155] The cascaded extended state observer obtains the real-time input voltage u from the electro-hydraulic proportional valve 4 and the real-time output displacement x from the linear displacement sensor 9. The cascaded extended state observer processes the real-time acquired input voltage u and output displacement x of the EHSS to obtain n sets of displacement estimates, velocity estimates, and disturbance estimates. The state selector, in conjunction with the cascaded extended state observer, selects the final displacement estimate, velocity estimate, and total disturbance estimate.

[0156] The tracking differentiator provides two reference signals. See details... Figure 4The tracking differentiator takes a reference signal r as input and outputs two signals: one is r1, which is the result of processing r, and the other is r2, the derivative of r1. r1 is used to calculate the displacement error with the displacement estimate, and r2 is used to calculate the velocity error with the velocity estimate.

[0157] Based on the selected displacement estimate, velocity estimate, and total disturbance estimate, the state feedback controller calculates the corrected voltage as the new input voltage u' of the EHSS. Thus, the EHSS outputs a new displacement x' according to the new input voltage u'.

[0158] The calculation formula for the state feedback controller is based on formula (23). According to formula (23), the tracking differentiator inputs two reference signals r1 and r2 to the state feedback controller, which are then used to calculate the displacement estimate and velocity estimate, respectively.

[0159] like Figure 4 As shown, n=3, meaning CESO has 3 layers. Based on the number of layers, the final displacement estimate is... Speed ​​estimate is The total disturbance estimate is also, Figure 4 middle

[0160] This CESO-based electro-hydraulic servo system linear active disturbance rejection control system acquires and processes the input voltage and output displacement of the EHSS in real time, i.e., performs cyclic operation, thereby realizing disturbance rejection and displacement control of the EHSS until the EHSS finishes working.

[0161] Example 3

[0162] To demonstrate the flexibility and effectiveness of the proposed control method, tracking control of the EHSS was conducted through simulation experiments based on Examples 1 and 2. The physical parameters of the EHSS, according to the actual working environment, are shown in Table 1.

[0163] Table 1 Physical parameters of EHSS

[0164]

[0165] It should be noted that the internal disturbance of EHSS is mainly manifested in the uncertainty of internal parameters. As shown in Table 1, the parameters change around time t = 5 seconds. If the system can remain stable under this condition, it indicates that the designed system has strong robustness.

[0166] Based on Example 2, a dynamic model of the EHSS and a LADRC controller were established in MATLAB / Simulink. The simulation parameters were configured as follows: ode45 (Bogacki-Shampine) was selected as the solver. The fixed step size was set to 0.001 seconds. The sampling period was 0.001 seconds, the same as the actual experimental system. The CESO control parameters are shown in Table 2.

[0167] Table 2 CESO Control Parameters

[0168]

[0169] The ESO obtained with p=1 is taken as the standard ESO. For different ESO structures, the controller ultimately achieves the given objective.

[0170] The nonlinear dynamic equation of model (13) is subject to an external, nonlinear disturbance. The control objective is to make the output y track the ideal trajectory r in the presence of measurement noise w and disturbance d. The signal r can be either a step signal or a sinusoidal signal, both of which are analyzed in this paper. The peak value of the step signal is filtered out by a differential tracker. The measurement noise is 1e -9 White noise. The control law chosen is equation (21), and the controller used is a well-known design. Comparative analysis is performed on the following cases.

[0171] It should be noted that the tracking differentiator in Example 2 only applies to step signals. Sinusoidal signals do not require a transition process, therefore Example 1 is used.

[0172] (i) When the reference signal is a step signal, the method of Example 2 was used, and trajectory tracking without measurement noise was as follows: Figures 5-11 As shown; trajectory tracking with measurement noise is as follows Figures 12-18 As shown.

[0173] in Figure 5 , Figure 12 It is the displacement tracking response curve; Figure 6 , Figure 13 It is the tracking error of the displacement; Figure 7 , Figure 14 It is the estimation error of the displacement; Figure 8 , Figure 15 It is the speed estimation error; Figure 9 , Figure 16 It is the estimation error of the total disturbance; Figure 10 , Figure 17 It is a control signal; Figure 11 , Figure 18 It is an estimate of the total disturbance.

[0174] It can be seen that the control performance in the absence of noise is slightly improved compared to the standard ESO. When measurement noise is present, the well-known negative impact of high-gain observers can be observed in the standard ESO, i.e., as the observer bandwidth ω... o1 As the number of levels (n) increases, noise is significantly amplified. With increasing n levels, both tracking accuracy and noise suppression capabilities improve. A cascaded ESO with n=3 provides the lowest measurement noise, followed by a cascaded ESO with n=2, and finally a standard ESO. This is because as the value of n increases, ω... o1 With a lower value compared to the standard ESO, the transmission of signals from the sensor to the control signal is also weakened.

[0175] (ii) When the reference signal is a sinusoidal signal, the method of Example 1 was used, and the trajectory tracking without measurement noise was as follows: Figures 19-25 As shown; trajectory tracking with measurement noise is as follows Figures 26-32 As shown.

[0176] in Figure 19 , Figure 26 It is the displacement tracking response curve; Figure 20 , Figure 27 It is the tracking error of the displacement; Figure 21 , Figure 28 It is the estimation error of the displacement; Figure 22 , Figure 29 It is the speed estimation error; Figure 23 , Figure 30 It is the estimation error of the total disturbance; Figure 24 , Figure 31 It is a control signal; Figure 25 , Figure 32 It is an estimate of the total disturbance.

[0177] It can be seen that, under the standard ESO case, increasing the controller bandwidth ω c (in, k2=2ω c It can improve the control error caused by phase lag, but the control signal and noise levels are not ideal. In the case of cascaded ESOs with n=2 and n=3, the influence of measurement noise can be effectively suppressed.

[0178] In summary, a CESO layer number n of 3 can achieve better results. Therefore, it is recommended to set the CESO layer number to 3 in both Examples 1 and 2.

[0179] This invention proposes a linear active disturbance rejection control method and system for a valve-controlled asymmetric cylinder electro-hydraulic servo system based on CESO. This method effectively improves the accuracy of the system's uncertain comprehensive disturbance estimation and eliminates the constraint of high-frequency sensor measurement noise on the accuracy of comprehensive disturbance estimation in traditional electro-hydraulic servo linear ADRC. Simulation results show that, compared with traditional ADRC, the CESO-based linear active disturbance rejection control for the valve-controlled asymmetric cylinder electro-hydraulic servo system has advantages such as strong robustness, high control performance, independence from a precise mathematical model of the system, ease of implementation, and strong disturbance rejection capability.

[0180] Example 4

[0181] This embodiment also discloses a readable storage medium storing computer program instructions. When the computer program instructions are read and executed by a processor, the above-described linear active disturbance rejection control method for an electro-hydraulic servo system based on CESO is performed.

[0182] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0183] The embodiments described above are merely illustrative of several implementations of the present invention, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these all fall within the protection scope of the present invention. Therefore, the protection scope of this invention patent should be determined by the appended claims.

Claims

1. A linear active disturbance rejection control method for electro-hydraulic servo systems based on CESO, which performs disturbance suppression and displacement control on valve-controlled asymmetric cylinder electro-hydraulic servo systems (EHSS), characterized in that... The linear active disturbance rejection control method for the CESO-based electro-hydraulic servo system includes the following steps: S1, Real-time acquisition of the input voltage of the EHSS at the current moment. u Output displacement x The displacement estimate, velocity estimate, and total disturbance estimate are obtained through CESO and state selector processing. Wherein, CESO is n The CESO is composed of three interconnected ESO layers, n=3; the first ESO layer... n Layer ESO output displacement estimation Speed ​​estimation Disruptions to valuation The state selector is based on the number of CESO layers. n Select the final output; the displacement estimate is selected from the [number]th [value]. n Displacement estimate of layer ESO output The speed estimate is selected from the first... n Speed ​​estimation of layer ESO output The total disturbance estimate is selected n The sum of the perturbation estimates of the layers ; S2, based on the displacement estimate, the velocity estimate, and the total disturbance estimate, the corrected voltage is obtained through control by a control law and used as the new input voltage of the EHSS. New input voltage The corresponding control EHSS outputs a new displacement. ; The calculation formula for the control law is as follows: ； in, r For reference signal, k 1 and k 2 represents the state feedback gain. b 0 Estimated value of EHSS process control gain; S3, repeats the process of steps S1 and S2, accompanies the EHSS operation, and performs real-time estimation and compensation for the total disturbance of the EHSS.

2. The linear active disturbance rejection control method for an electro-hydraulic servo system based on CESO according to claim 1, characterized in that, In S1, the input of the first layer ESO of the CESO includes the output displacement acquired in real time. x ; as well as Real-time acquired input voltage u After control gain estimation b 0 Processed value u*b 0 .

3. The linear active disturbance rejection control method for an electro-hydraulic servo system based on CESO according to claim 2, characterized in that, In S1, the CESO's first n The input of the layer ESO includes the first n Displacement estimation of ESO output at layer -1 , No. n -1 Layer ESO Output Speed ​​Estimation ,forward n The sum of disturbance estimates for layer -1 ; as well as Real-time acquired input voltage u After control gain estimation b 0 Processed value u*b 0 .

4. A linear active disturbance rejection control system for an electro-hydraulic servo system based on CESO, characterized in that, It uses the CESO-based linear active disturbance rejection control method for electro-hydraulic servo systems as described in any one of claims 1-3; The CESO-based electro-hydraulic servo system linear active disturbance rejection control system includes: Cascaded extended state observer, used for monitoring the input voltage of the EHSS acquired in real time. u and output displacement x The data were processed to obtain several different sets of displacement estimates, velocity estimates, and disturbance estimates. The state selector is used in conjunction with the cascaded extended state observer to select the final displacement estimate, velocity estimate, and total disturbance estimate. The state feedback controller is used to calculate the corrected voltage based on the selected displacement estimate, velocity estimate, and total disturbance estimate, and use this corrected voltage as the new input voltage for the EHSS. .

5. The linear active disturbance rejection control system for the CESO-based electro-hydraulic servo system according to claim 4, characterized in that, The state feedback controller inputs a reference signal, which is used to calculate the displacement error with the displacement estimate.

6. A readable storage medium, characterized in that, The readable storage medium stores computer program instructions, which are read and executed by a processor to perform the linear active disturbance rejection control method for an electro-hydraulic servo system based on CESO as described in any one of claims 1-3.

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