Backstepping sliding mode control method for heavy-duty forklift pump-controlled lifting system and based on non-linear observer

Abstract

The present invention relates to the technical field of electro-hydraulic servo control. Provided is a backstepping sliding mode control method for a heavy-duty forklift pump-controlled lifting system and based on a non-linear observer. In the method, a non-linear robust sliding mode position servo controller with disturbance compensation is designed on the basis of the idea of a backstepping method. Aiming at the problem of the difficulty of controlling the precision of a heavy-duty forklift pump-controlled lifting position, the present invention realizes precise load observation, takes non-linearity and parameter uncertainty into consideration, and uses a sliding mode term to address non-linearity and uncertainty, thereby reducing the effects of abrupt load changes, external disturbance, and unmodeled dynamics on control precision, and achieving a high-precision tracking performance.

Description

Heavy forklift pump control lifting system backstepping sliding mode control method based on nonlinear observer TECHNICAL FIELD

[0001] The present application relates to the technical field of electro-hydraulic servo control, in particular to a heavy forklift pump control lifting system backstepping sliding mode control method based on a nonlinear observer. BACKGROUND

[0002] Precise forking is one of the most important functions for heavy forklifts to work efficiently. Under the background of double carbon, distributed pump control lifting systems will gradually replace centralized valve control lifting systems due to the elimination of energy loss. However, the position servo precision of pump control systems is difficult to guarantee due to the strong nonlinearities of hydraulic systems, severe load changes, parameter uncertainties, and uncertain nonlinearities.

[0003] Currently, domestic and foreign scholars mainly use classical model-free control algorithms, model-based control algorithms, and intelligent control algorithms for position servo of heavy forklift pump control lifting systems. PID control is a classical model-free control method, which is simple to design but cannot guarantee tracking precision when facing parameter changes and external disturbances. Model-based articulated steering path tracking control methods mainly include pure tracking algorithms, feedback linearization, LQR, MPC, etc. These algorithms can achieve certain tracking effects, but few of them consider the effects of hydraulic system nonlinearities, parameter uncertainties, and uncertain nonlinear disturbances. Intelligent control methods mainly include fuzzy logic control strategies, neural network control, reinforcement learning control, etc. Intelligent control methods have good adaptability and robustness. However, they require a large number of training data sets, are computationally complex, and have uncertainties, which cannot completely guarantee the absolute precision and safety of heavy forklift forking. Therefore, it is crucial to ensure the absolute tracking precision of heavy forklift pump control lifting systems under the background of energy saving, which have strong nonlinearities, large load inertia changes, and long-time varying disturbances during operation.

[0004] Therefore, the present application is proposed.

[0005] SUMMARY

[0006] The present application provides a heavy forklift pump control lifting system backstepping sliding mode control method based on a nonlinear observer, which can at least partially improve the above problems.

[0007] To achieve the above purpose, the present application adopts the following technical solutions:

[0008] A heavy forklift pump control lifting system backstepping sliding mode control method based on a nonlinear observer, comprising:

[0009] Obtain a shift control target signal and an oil cylinder signal collected by a nonlinear disturbance observer, wherein the oil cylinder signal includes an oil cylinder displacement signal, an oil cylinder speed signal, and an oil cylinder two-cavity pressure signal.

[0010] The output of the nonlinear disturbance observer is sent to a gain adjustment module to convert the observed disturbance into a control amount of the corresponding input channel;

[0011] A pre-trained backstepping sliding mode controller is called to preprocess the shift control target signal and the control amount of the input channel to obtain the actual control rotation angular velocity of the bidirectional fixed displacement pump, and the formula is:

[0012] Wherein, V t is the total volume of the two cavities of the hydraulic cylinder, and the unit is m 3 , beta e is the bulk modulus, and the unit is Pa, D p is the displacement of the bidirectional fixed displacement pump, and the unit is m 3 / rad, A p is the effective area of the hydraulic cylinder piston, and the unit is m 2 , C i is the leakage coefficient in the hydraulic cylinder, and the unit is (m 3 / s) / Pa, M is the total mass of the piston and the load converted to the piston, and the unit is kg, the state variable x0=[x1,x2,x3] T , T is a matrix transpose symbol, is the high-order derivative of the virtual control law alpha2, s2 and s3 are the sliding mode surfaces, and k3 is the sliding mode gain adjustment coefficient.

[0013] In summary, the backstepping sliding mode control method for the pump-controlled lifting system of the heavy forklift based on the nonlinear observer aims to establish a closed pump-controlled steering nonlinear system mathematical model, consider the existence of large parameter uncertainty, uncertain nonlinearity and unknown disturbance in the steering system, design a backstepping sliding mode controller based on the nonlinear observer, so that the system obtains asymptotic tracking steady-state performance and realizes high-energy-efficiency and high-precision lifting of the heavy forklift. Compared with the prior art, the present application has the following advantages: (1) precise observation of the load of the lifting system is realized; (2) the disturbance compensation design backstepping sliding mode controller greatly reduces the influence of large load mutation on the lifting system, realizes high-precision control tracking performance, and the simulation results verify its effectiveness. BRIEF DESCRIPTION OF DRAWINGS

[0014] Fig. 1 is a flowchart of the backstepping sliding mode control method for the pump-controlled lifting system of the heavy forklift based on the nonlinear observer provided by the embodiment of the present application;

[0015] Fig. 2 is a backstepping sliding mode control principle diagram of the pump-controlled lifting system based on the nonlinear observer provided by the embodiment of the present application;

[0016] Fig. 3 is a principle diagram of the pump-controlled lifting system of the heavy forklift provided by the embodiment of the present application;

[0017] FIG. 4 is a control input curve of the system under the action of the backstepping sliding mode control provided by the embodiment of the application;

[0018] FIG. 5 is a tracking error curve of the system under the action of the backstepping sliding mode control based on the nonlinear observer, the backstepping sliding mode control without the observer, and the PID control provided by the embodiment of the application;

[0019] FIG. 6 is a load observation curve provided by the embodiment of the application. DETAILED DESCRIPTION

[0020] In order to make the objectives, technical solutions and advantages of the application clearer, further detailed description will be made to the application in combination with embodiments. It should be understood that the specific embodiments described herein are only used to explain the application and not used to limit the application.

[0021] Referring to FIGS. 1 to 6, the first embodiment of the application discloses a backstepping sliding mode control method for a pump-controlled lifting system of a heavy forklift based on a nonlinear observer, which can be executed by a backstepping sliding mode control device for a pump-controlled lifting system of a heavy forklift based on a nonlinear observer (hereinafter referred to as a control device), in particular, by one or more processors in the control device to implement the following method:

[0022] S101, a shift control target signal and a cylinder signal collected by a nonlinear disturbance observer are obtained, wherein the cylinder signal includes a cylinder displacement signal, a cylinder speed signal, and a cylinder two-cavity pressure signal;

[0023] S102, the output of the nonlinear disturbance observer is sent to a gain adjustment module to convert the observed disturbance into a control amount of a corresponding input channel;

[0024] S103, a pre-trained backstepping sliding mode controller is called to pre-process the shift control target signal and the control amount of the input channel to obtain the actual control rotation angular velocity of the bidirectional quantitative pump, and the formula is:

[0025] V = V1+ V2, wherein V is the total volume of the two cavities of the hydraulic cylinder, the unit is m t , β is the volume elastic modulus, the unit is Pa, D 3 is the displacement of the bidirectional quantitative pump, the unit is m e / rad, A p is the effective area of the hydraulic cylinder piston, the unit is m 3 , C p is the leakage coefficient in the hydraulic cylinder, the unit is (m 2 V = V1+ V2, wherein V is the total volume of the two cavities of the hydraulic cylinder, the unit is m i , β is the volume elastic modulus, the unit is Pa, D 3 / s) / Pa, M is the total mass of the piston and the load converted to the piston, in kg, the state variable x0 = [x1, x2, x3] T , T is a matrix transpose symbol, is the high-order derivative of the virtual control law a2, s2 and s3 are the sliding mode surfaces, and k3 is a sliding mode gain adjustment coefficient.

[0026] Preferably, before acquiring the cylinder signal collected by the nonlinear disturbance observer, the method further comprises:

[0027] Based on a preset condition, a mathematical model of a pump-controlled lifting system of a heavy fork truck is established, wherein the preset condition is that the hydraulic cylinder only has internal leakage, has no external leakage, the load of the hydraulic cylinder is an inertial load, and has no elastic load, and specifically:

[0028] The flow equation of the bidirectional quantitative pump of the mathematical model is: L = D p w

[0029] wherein w is the rotational angular velocity of the bidirectional quantitative pump, in rad / s;

[0030] The flow continuity equation of the hydraulic cylinder is:

[0031] wherein Q1 and Q2 are the flows of the two cavities of the hydraulic cylinder, in m 3 / s, x p is the piston displacement, in m, p1 and p2 are the pressures of the two cavities of the hydraulic cylinder, in Pa, and V1 and V2 are the volumes of the two cavities of the hydraulic cylinder, in m 3 , is the first-order derivative of the piston displacement, and are the first-order derivatives of the pressures of the two cavities of the hydraulic cylinder;

[0032] The load pressure is defined as p L =p1-p2, the load flow is defined as Q L =(Q1+Q2) / 2, and two formulas of the flow continuity equation of the hydraulic cylinder are combined to obtain:

[0033] wherein is the first-order derivative of the load pressure;

[0034] According to Newton's second law, the balance equation of the output force of the hydraulic cylinder and the load is:

[0035] wherein is the second-order derivative of the piston displacement, B cviscous damping coefficient of the piston and the load, unit: N / (m / s), f d which are difficult to model accurately, including external disturbance force, un-modeled friction;

[0036] Define state variables The state space equation of the steering system can be obtained from the above formula as:

[0037] Based on the mathematical model, the nonlinear disturbance observer is designed for estimating and compensating the disturbance of the system, specifically:

[0038] The specific formula of the nonlinear disturbance observer is:

[0039] wherein, is the load observation value, z is the state of the nonlinear disturbance observer, p(x1, x2) is a nonlinear function to be designed, is the first-order derivative of the nonlinear disturbance observer state, L(x1, x2) is the gain of the nonlinear observer, B C viscous damping coefficient of the piston and the load;

[0040] The gain L(x1, x2) of the nonlinear observer needs to satisfy: wherein, is the lifting cylinder speed signal;

[0041] Define the observation error of the nonlinear disturbance observer as: wherein, is the first-order derivative of the disturbance value, d is the disturbance value;

[0042] Generally, there is no prior knowledge of the differential of the disturbance d, and it is assumed that the change of the disturbance relative to the dynamic characteristics of the observer is slow,

[0043] The dynamic equation of the observer error system is:

[0044] wherein, is the first-order derivative of the disturbance observation error value, is the disturbance observation value error value, is the first-order derivative of the load observation value;

[0045] From the above formula, by appropriately selecting L(x1, x2)>0, the observation error of the observer can be made to converge exponentially.

[0046] Select L(x1, x2) = b, b>0 constant, and design p(x1, x2) = -Mbx2, M is the observation gain.

[0047] Preferably, the output of the nonlinear disturbance observer is sent to a gain adjustment module to convert the observed disturbance into the control quantity of the corresponding input channel, specifically:

[0048] wherein the gain is 1 / M, and u d = d / M, u d .

[0049] Preferably, before the pre-trained backstepping sliding mode controller is called to preprocess the shift control target signal and the control quantity of the input channel, the mathematical model and the nonlinear disturbance observer are further included to design a backstepping sliding mode observer, specifically:

[0050] A first sliding surface s1 = x1-y d , a second sliding surface s2 = x2-a1, and a third sliding surface s3 = x3-a2 are designed, wherein y d is a target signal, a1 is a first virtual control rate, and a2 is a second virtual control rate.

[0051] For the first sliding surface, the derivative is taken:

[0052] To make the first subsystem reach the sliding surface and move on the sliding surface, a virtual control law a1 is designed, s2 = x2-a1, wherein, is the first-order derivative of the first sliding surface, is the first-order derivative of the target signal, and k1 is the gain coefficient of the first sliding surface.

[0053] A Lyapunov function V1 is selected The derivative of V1 is taken, and wherein s is a sliding surface.

[0054] The derivative of the second sliding surface is taken:

[0055] wherein d1(x1, t) is a disturbance value function.

[0056] To make the second subsystem reach the sliding surface and move on the sliding surface, a virtual control law a2 is designed: Since the high-order derivative of the virtual control a1 is used in the subsequent design, a2 can be obtained wherein k2 is the gain coefficient of the second sliding surface, is the error of the load observation value with respect to the actual load value, sign() is a sliding term, μ2 and ε2 are constants, μ2 > 1, and 1 > ε2 > 0.

[0057] Take the alternative Lyapunov function Derivation of V2:

[0058] Condition The s3s2 term of V will be eliminated in the next step design, when the condition is satisfied, the second subsystem is stable, then the second subsystem will be ultimately bounded, the error of the system is in the range of , and it can be obtained that

[0059] Derivation of the third sliding mode surface:

[0060] Wherein, e is the error, e1 is the first error, e2 is the second error, e3 is the third error, Vt is the sum of the volume of the oil tank;

[0061] The actual control law is obtained as:

[0062] Preferably, it further comprises:

[0063] The Lyapunov stability theory is used to prove the stability of the backstepping sliding mode controller based on nonlinear observation, and the result that the system tracking error is asymptotically stable is obtained, which is specifically:

[0064] Select Lyapunov function Derivation of V, under the premise of satisfying , it can be obtained that: is the difference between the true value and the predicted value.

[0065] In this embodiment, for the system, under the condition that the assumption condition is satisfied, the nonlinear disturbance observer and the control law are used, all signals in the closed-loop system are bounded, then the system is bounded stable. From the above formula, it can be seen that the signals in the closed-loop system are uniformly ultimately bounded, and The closed-loop system is stable.

[0066] In this embodiment, by adjusting the gain L(x1, x2), k 1、 k 2、 μ2, ε2, the nonlinear backstepping sliding mode controller designed for the pump-controlled lifting system of the heavy forklift can make the system innovative to obtain the result that the tracking error converges to 0. The principle of the nonlinear observation-based backstepping sliding mode position controller is shown in FIG. 2.

[0067] In order to examine the performance of the designed controller, the physical parameters of the pump-controlled lifting servo system of the heavy forklift in the simulation are shown in Table 1:

[0068] Table 1 system physical parameter table

[0069] The expected instruction of the given system is x d = 0.05sin (π)m

[0070] The following controller is taken in the simulation:

[0071] The backstepping sliding mode controller takes k1=k2=k3=5, μ2=1.5, ε2=0.2; the observer parameter takes L=15.

[0072] The PID controller parameter is set to P=15000, I=100, D=0.

[0073] The tracking error, the nonlinear observer is as shown in Figures 4 and 5, and it can be seen from Figure 5 that the maximum error of the heavy-duty forklift backstepping sliding mode position servo control based on the nonlinear observer is 5.21x10-3m, which is higher in control precision than the PID and the backstepping sliding mode control without the observer, and the tracking performance is more superior.

[0074] The above is the preferred embodiment of the present application, it should be noted that for those skilled in the art, without departing from the principles of the present application, can make a number of improvements and refinements, these improvements and refinements are also considered to be within the scope of the present application.

Claims

1. A backstepping sliding mode control method for pump-controlled lifting system of heavy-duty forklift based on nonlinear observer, characterized in that, The method comprises the following steps: Obtaining a shift control target signal and a cylinder signal collected by a nonlinear disturbance observer, wherein the cylinder signal comprises a cylinder displacement signal, a cylinder speed signal and a cylinder two-cavity pressure signal; The output of the nonlinear disturbance observer is sent to a gain adjustment module to convert the observed disturbance into a control amount of a corresponding input channel; A pre-trained backstepping sliding mode controller is called to preprocess the shift control target signal and the control quantity of the input channel to obtain the actual control rotation angular velocity of the bi-directional quantitative pump, and the formula is as follows: where V t is the total volume of the two chambers of the hydraulic cylinder, in m 3 , β e is the bulk modulus, in Pa, D p is the displacement of the bidirectional metering pump, in m 3 / rad, A p is the effective area of the hydraulic cylinder piston, in m 2 , C i is the leakage coefficient in the hydraulic cylinder, in (m 3 / s) / Pa, M is the total mass of the piston and the load reduced to the piston, in kg, and the state variable x0 = [x1, x2, x3] T , T is the matrix transpose symbol, s2 and s3 are the high-order derivatives of the virtual control law a2, and k3 is a sliding mode gain adjustment coefficient.

2. The nonlinear observer-based heavy fork lift pump-controlled hoist system backstepping sliding mode control method according to claim 1, wherein, Before obtaining the cylinder signal collected by the nonlinear disturbance observer, the method further comprises the following steps: Based on a preset condition, a mathematical model of a pump-controlled lifting system of a heavy forklift is established, wherein the preset condition is that the hydraulic cylinder only has internal leakage, has no external leakage, and the hydraulic cylinder load is an inertial load without an elastic load; Based on the mathematical model, the nonlinear disturbance observer is designed to estimate and compensate the disturbance of the system.

3. The nonlinear observer-based heavy fork lift pump-controlled hoist system backstepping sliding mode control method according to claim 2, wherein, Based on a preset condition, a mathematical model of a pump-controlled lifting system of a heavy forklift is established, and specifically: The flow equation of the bidirectional quantitative pump of the mathematical model is: Q L = D p w Wherein w is the rotational angular velocity of the bidirectional quantitative pump, and the unit is rad / s; The flow continuity equation for the hydraulic cylinder is: Where Q1 and Q2 are the flow rate of the two chambers of the hydraulic cylinder, unit m 3 / s, x p is the displacement of the piston, unit m, p1 and p2 are the pressure of the two chambers of the hydraulic cylinder, unit Pa, V1 and V2 are the volume of the two chambers of the hydraulic cylinder, unit m 3 , for the first derivative of the piston displacement, and are the first-order derivatives of the pressures of the two cavities of the hydraulic cylinder, respectively; Load pressure is defined as p L Load flow is defined as Q L = (Q1+Q2) / 2, combining the two equations for flow continuity of the hydraulic cylinders, we get: wherein, is the first-order derivative of the load pressure; According to Newton's second law, the balance equation of the output force of the hydraulic cylinder and the load is obtained as: wherein B is the second derivative of the piston displacement, B c f is the viscous damping coefficient of the piston and load, in N / (m / s), f d B is the second derivative of the piston displacement, B c f is the viscous damping coefficient of the piston and load, in N / (m / s), f d B is the second derivative of the piston displacement, B c f is the viscous damping coefficient of the piston and load, in N / (m / s), f d B is the second derivative of the piston displacement, B <000001 Defining state variables From the above equations, the state space equations of the steering system are:

4. The nonlinear observer-based heavy fork lift pump-controlled hoist system backstepping sliding mode control method according to claim 3, wherein, Based on the mathematical model, the nonlinear disturbance observer is designed, and specifically: The specific formula of the nonlinear disturbance observer is: wherein is the load observation value, z is the state of the nonlinear disturbance observer, p(x1, x2) is a to-be-set a non-linear function of the count, L(x1, x2) is the gain of the nonlinear observer for the first derivative of the state of the nonlinear disturbance observer, B C Cp is the viscous damping coefficient of the piston and the load; The gain L(x1, x2) of the nonlinear observer needs to satisfy: wherein is the lifting cylinder speed signal; The observation error of the nonlinear disturbance observer is defined as: wherein is the first-order derivative of the disturbance value, d is the disturbance value; It is assumed that the variation of the disturbance with respect to the dynamic properties of the observer is slow, The observer error system dynamic equation is: wherein, to the first order derivative of the interference observation error value, for the interference observation value error value, is the first-order derivative of the load observation value; A constant L(x1, x2) = b, b > 0 is selected, and p(x1, x2) = -Mbx2 is designed, wherein M is an observation gain.

5. The nonlinear observer-based heavy fork lift pump-controlled hoist system backstepping sliding mode control method according to claim 4, wherein, The output of the nonlinear disturbance observer is sent to a gain adjustment module to convert the observed disturbance into a control quantity of the corresponding input channel, specifically: where the gain is 1 / M, and u d = d / M, u d is the compensation term.

6. The nonlinear observer-based heavy fork lift pump-controlled hoist system backstepping sliding mode control method according to claim 2, wherein, Before the pre-trained backstepping sliding mode controller is called to preprocess the shift control target signal and the control amount of the input channel, the mathematical model and the nonlinear disturbance observer are designed, and specifically: The first sliding surface s1 = x1 - y is designed d The second sliding surface s2 = x2 - a1 and the third sliding surface s3 = x3 - a2 are designed, wherein y d is a target signal, a1 is a first virtual control rate, and a2 is a second virtual control rate. For the first slip surface, the derivative is taken: The virtual control law a1,s2 = x2 - a1 is designed, wherein for the first sliding surface first derivative, is the first-order derivative of the target signal, k1 is the gain coefficient of the first sliding surface; Selecting a Lyapunov function Taking the derivative of V1 gives Wherein s is the sliding surface.

7. The nonlinear observer-based heavy fork lift pump-controlled hoist system backstepping sliding mode control method according to claim 6, wherein, Before the pre-trained backstepping sliding mode controller is called to preprocess the shift control target signal and the control amount of the input channel, the following steps are further included: Differentiate the second sliding surface: Wherein d1(x1, t) is a disturbance value function; Design virtual control law: where k2 is a gain coefficient of the second sliding mode surface, error of load actual value for load observation value, sign() is a sliding mode term, μ2 and ε2 are constants, μ2 > 1, and 1 > ε2 > 0; Taking an alternative Lyapunov function Differentiate V2 with respect to t: When the condition is met At this time, the second subsystem is stable, and the error of the system is within within the scope of the present invention, obtainable 8. The nonlinear-observer-based heavy fork lift pump-controlled hoist system backstepping sliding mode control method according to claim 7, wherein, Before the pre-trained backstepping sliding mode controller is called to preprocess the shift control target signal and the control amount of the input channel, the following steps are further included: Differentiate the third sliding surface: Wherein e is the error, e1 is the first error, e2 is the second error, e3 is the third error, and Vt is the sum of the volumes of the oil tanks; The actual control law is obtained as 9. The nonlinear-observer-based heavy fork lift pump-controlled hoist system backstepping sliding mode control method according to claim 8, wherein, Further comprising: The Lyapunov stability theory is used to prove the stability of the backstepping sliding mode controller based on nonlinear observation, and the result that the system tracking error is asymptotically stable is obtained.

10. The nonlinear-observer-based heavy fork lift pump-controlled hoist system backstepping sliding mode control method of claim 9, wherein, The Lyapunov stability theory is used to prove the stability of the backstepping sliding mode controller based on nonlinear observation, and specifically: Selecting a Lyapunov function Taking the derivative of V, we have Under the premise of the above, we have: is the difference between the true value and the predicted value.

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