Adaptive neural network fixed time control method of electro-hydraulic servo system with model uncertainty

Abstract

The invention discloses an adaptive neural network fixed time control method for an electro-hydraulic servo system with model uncertainty, and the method comprises the related steps: carrying out the modeling of an electro-hydraulic servo system, and obtaining a state equation; defining a consistency tracking error z1 of a valve response position of the electro-hydraulic servo system, and designing a first virtual control law alpha1; the method comprises the following steps: designing a first virtual law alpha 1 and a second virtual law alpha 2, defining a consistency tracking error z2 of the response speed of an electro-hydraulic servo system valve, designing a second virtual law alpha 2 and a self-adaptive law # imgabs0 #, defining a consistency tracking error z3 of the pressure borne by the electro-hydraulic servo system valve, designing a final actual control law u and a self-adaptive law # imgabs1 # based on a Matlab / Simulink simulation platform and an electro-hydraulic servo experiment platform, and carrying out an experiment on the algorithm. The invention provides self-adaptive neural network fixed time control of an electro-hydraulic servo system, and the rapid convergence performance and the steady-state precision of a hydraulic system under the condition that a hydraulic model is uncertain are improved. Strict theoretical derivation proves that the electro-hydraulic servo system has actual fixed time stability in different system initial states, so that all system state errors are converged to be close to zero within fixed time and are irrelevant to initial conditions of the electro-hydraulic servo system. Finally, simulation and experiment results verify the effectiveness of the control method.

Description

Technical Field

[0001] The invention relates to the technical field of intelligent control of electro-hydraulic servo systems, in particular to an adaptive neural network fixed-time control method for electro-hydraulic servo systems with model uncertainty. Background Art

[0002] The electro-hydraulic servo system is an important device widely used in the field of automation, such as hydraulic manipulators, exoskeletons, and load simulators. Due to the existence of unknown hydraulic parameters, such as spring stiffness coefficient, viscous damping coefficient, flow coefficient, etc., it is not easy to obtain an accurate model of the electro-hydraulic servo system. In addition, the unknown external load in the system also brings difficulties to the design of the controller. Therefore, it is not easy to obtain high-precision tracking performance of the electro-hydraulic servo system.

[0003] The model uncertainty of the electro-hydraulic servo system includes hydraulic parameter uncertainty, functional nonlinearity and unknown external disturbances. In order to obtain high-precision tracking performance, these uncertainties must be effectively resolved. For hydraulic parameter uncertainty, adaptive control is an effective way to deal with these uncertainties. At the same time, in order to weaken the adverse effects of parameter uncertainty, some model-based adaptive control methods have been proposed to improve the steady-state accuracy of the system output. However, since the functional uncertainty becomes the main uncertainty of the system, the model-based adaptive control must first ensure the stability of the system at the expense of performance. Fortunately, fuzzy logic systems and radial basis function neural network networks provide good solutions for approximating nonlinear functional uncertainty. Although general adaptive control methods have handled the uncertainty of hydraulic parameters and functions well, there has been no quantitative analysis of the convergence speed problem of the electro-hydraulic servo system to improve the dynamic characteristics during the transition process.

[0004] It should be noted that the general adaptive control of the electro-hydraulic servo system only guarantees the asymptotic stability or uniformly bounded stability of the system output. Theoretically, the convergence time of the system is infinite. In contrast, finite-time control allows the system to enter the final stable state in a finite time and has been shown to have faster convergence speed, better robustness and stronger anti-interference than non-finite-time control. In this paper, a fixed-time adaptive neural network control method for electro-hydraulic servo system is proposed to improve the fast convergence performance and steady-state accuracy of the hydraulic cylinder position.

[0005] Firstly, the parameter uncertainties are separated from the actual model of the electro-hydraulic servo system, and the matching and mismatching model uncertainties are constructed. Then, the radial basis function neural network is used to compensate for these model uncertainties. At the same time, an adaptive estimation law with power terms is designed to ensure that the weight norm estimation error of the radial basis function neural network converges to near zero within a fixed time. At present, most advanced controllers for electro-hydraulic servo systems only obtain uniformly bounded stability or asymptotic stability, which only ensures that the expected tracking error converges within infinite time. The adaptive neural network fixed-time control method we proposed makes the electro-hydraulic servo system uniformly stable within an actual fixed time, that is, all state errors and estimation errors converge within a fixed time, which is independent of the initial state of the system. Summary of the invention

[0006] The object of the present invention is to provide an adaptive neural network fixed time control method for an electro-hydraulic servo system with model uncertainty to solve the problems raised in the above background technology.

[0007] To achieve the above object, the present invention provides the following technical solution: an adaptive neural network fixed time control method for an electro-hydraulic servo system with model uncertainty, comprising the following steps:

[0008] S1: Model the electro-hydraulic servo and obtain the state equation;

[0009] S2: Define the consistency tracking error z1 of the valve position response of the electro-hydraulic servo system and design the first virtual control law α1;

[0010] S3: Define the consistency tracking error z2 of the valve speed response of the electro-hydraulic servo system, design the second virtual law α2 and the adaptive law

[0011] S4: Define the consistency tracking error z3 of the pressure on the electro-hydraulic servo system valve, and design the final actual control law u and adaptive law

[0012] S5: Experiment on the algorithm based on Matlab / Simulink simulation platform and electro-hydraulic servo experimental platform.

[0013] Compared with the prior art, the present invention has the following beneficial effects:

[0014] 1. This control method separates the parameter uncertainty from the actual model of the electro-hydraulic servo system and constructs the matching model uncertainty and the mismatch model uncertainty. Then, the radial basis function neural network is used to compensate for these model uncertainties. At the same time, an adaptive estimation law with power terms is designed to effectively ensure that the weight norm estimation error of the radial basis function neural network converges to near zero within a fixed time.

[0015] 2. Most of the current advanced controllers for electro-hydraulic servo systems only achieve uniformly bounded stability or asymptotic stability, which ensures that the demand tracking error converges in infinite time. The proposed fixed-time adaptive neural network control method obtains a practical fixed-time stability of the electro-hydraulic servo system, that is, all state errors and estimation errors converge in a fixed time, which is independent of the initial system conditions, and can achieve higher convergence speed and better tracking accuracy by selecting appropriate parameters. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 It is a schematic diagram of the electro-hydraulic servo system of the present invention;

[0017] Figure 2 It is a schematic diagram of the controller flow of the present invention;

[0018] Figure 3 It is a schematic diagram of position tracking simulation of the present invention;

[0019] Figure 4 It is a schematic diagram of the simulation of the cylinder speed and load pressure response of the present invention;

[0020] Figure 5 A schematic diagram of a control voltage simulation of a servo valve of the present invention;

[0021] Figure 6 It is a schematic diagram of the weight norm estimation simulation of the present invention;

[0022] Figure 7 It is a schematic diagram of the electro-hydraulic servo system experimental platform of the present invention;

[0023] Explanation of the reference numerals: 1: oil pump, 2: pressure switch, 3: servo valve, 4: external load, 5: hydraulic cylinder, 6: displacement sensor, 7: accumulator, 8: pressure sensor, 9: target computer, 10: data monitoring, 11: control algorithm, 12: host computer, 13: inverter power supply.

[0024] Figure 8 It is a schematic diagram of the position tracking experiment of the present invention;

[0025] Fig. 9 It is a schematic diagram of the cylinder speed and load pressure response experiment of the present invention;

[0026] Fig.10 This is a schematic diagram of a control voltage experiment of the servo valve of the present invention;

[0027] Fig.11 It is a schematic diagram of the weight norm estimation experiment of the present invention; DETAILED DESCRIPTION

[0028] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0029] See also Figure 2 The present invention provides a technical solution: an adaptive neural network fixed time control method for an electro-hydraulic servo system with model uncertainty. The research ideas of the present invention are as follows:

[0030] Firstly, the uncertainty of electro-hydraulic servo is modeled, and the electro-hydraulic servo system model with uncertainty is established. Then, based on the backstepping technology, radial basis neural network adaptive control technology and fixed time stable control theory, a fixed time stable neural network adaptive controller is designed. Finally, the proposed method is simulated and experimented. The results show that the electro-hydraulic servo system can track the given reference signal well, has good control accuracy, and effectively reduces the convergence time.

[0031] An adaptive neural network fixed time control method for an electro-hydraulic servo system with model uncertainty comprises the following steps:

[0032] S1: Based on Newton's second law, the dynamic model of the electro-hydraulic servo system can be given as follows:

[0033]

[0034] Where m represents the additional load mass, K represents the load stiffness coefficient, b represents the viscosity coefficient, and y represents the position of the hydraulic valve. Indicates the speed of the hydraulic valve, Indicates the acceleration of the hydraulic valve, A p is the annular area of ​​the hydraulic cylinder chamber, p L is the pressure exerted by the load.

[0035] Therefore, the model of the electro-hydraulic servo system can be described by the following differential equation:

[0036]

[0037] in, K sv is the control hydraulic valve gain, u is the control servo valve voltage, β e is the effective volume modulus, C tl is the total leakage coefficient of the hydraulic cylinder, ω is the slope of the hydraulic valve area, ρ is the density of the hydraulic oil, C dis the flow coefficient, sgn(·) represents the sign function: when ·>0, sgn(·)=1; when ·<0, sgn(·)=-1; when ·=0, sgn(·)=0; y o Represents system output.

[0038] Taking into account the uncertainty of hydraulic parameters, we establish an electro-hydraulic system model:

[0039]

[0040] Among them, the nominal parameters are given as follows:

[0041]

[0042] The model uncertainty of the mismatch is given by:

[0043]

[0044]

[0045] Among them, the above and is the uncertainty due to the uncertainty of the water pressure parameters and is indicated by The value of the given value is represented by the symbol represents the uncertain value caused by uncertainty.

[0046] S2: Tracking error is defined as z1 = x1-y d , where y d is the demand trajectory. We get z i The derivative of is as follows;

[0047]

[0048] Here, we regard x2 as the control variable. Then, the error variable z2 and the virtual controller α1 are defined as follows:

[0049] z2=x2-α1

[0050]

[0051] in, l>1, b1>0, c1>0.

[0052] S3: Taking the derivative of z2, we get

[0053]

[0054] Treat x3 as a new control variable and define a new error variable as follows:

[0055] z3=x3-α2

[0056]

[0057] Among them, b2>0, c2>0, is the estimated value of θ2, and the error is defined as Basis Functions Usually defined as:

[0058]

[0059] in, is a real number.

[0060] In order to Converge in a fixed time and design an adaptive estimation law as follows:

[0061]

[0062] Among them, r2>0, ξ2>0, σ2>0.

[0063] S4: Taking the derivative of z3, we get

[0064]

[0065] The actual control law u is designed as follows:

[0066]

[0067] Among them, b3>0, c3>0, is the estimated value of θ3, and the error is defined as Basis Functions Defined as:

[0068]

[0069] in, is a real number.

[0070] In order to Converge in a fixed time and design an adaptive estimation law as follows:

[0071]

[0072] Among them, r3>0, ξ3>0, σ3>0.

[0073] S5: In order to verify the effectiveness of the proposed method, the algorithm was simulated and experimented based on the Matlab / Simulink platform and the electro-hydraulic servo experimental platform.

[0074] Further, the step S05 includes:

[0075] S51: The hydraulic parameters of the electro-hydraulic servo system are shown in Table 1. At the same time, the external load F L =50sin(πt)N, expected output y d =sin(πt)mm.

[0076] Table 1 Hydraulic parameters

[0077] Considering the limited computing resources, the radial basis neural network uses 5 neural network elements and the input vector is selected as and The Gaussian function uses and The width of the Gaussian function is uniformly chosen to be The controller's parameters are defined as b i =c i =30,r j =1,τ j =0.5,ξ j =0.2,σ j =0.2, i = 1, 2, 3 and j = 2, 3. The initial conditions of the closed-loop system are x1(0) = 15 mm, x2(0) = 0 mm / s, x3(0) = 0 N, θ2(0) = θ3(0) = 0.

[0078] In order to emphasize the advantages of fixed-time neural network adaptive control, two classical control methods are used for comparison: 1) Proportional-integral control: e1(t) = x1-y d , k1=300, k2=1; tracking error is defined as z1(t)=x1-y d . 2) Standard backstepping control: z1 = x1-y d , z2=x1-α1, z3=x1-α2, b1=80, b2=80, b3=450.

[0079] The simulation results are as follows Figures 3 to 6 The tracking performance of the electro-hydraulic servo system with three different methods is shown in Figure 3 As shown in Figure 2, it can be easily concluded that the proposed fixed-time neural network adaptive control method has a faster convergence speed, which illustrates the advantage of fixed-time control. In addition, the use of neural network to solve the uncertainty of the model also shows higher steady-state accuracy. The system state responses x2 and x3 are as follows: Figure 4As shown in , they all converge quickly to bounded values ​​in a finite time. The rapid convergence of the electro-hydraulic servo system causes x2 and x3 to overshoot in the initial stage, but then quickly transition to a steady state. The control voltage is Figure 5 As shown, it is obviously a bounded sinusoidal signal. Using radial basis neural network and The weight norm of is estimated as Figure 6 As shown, they also converge quickly to their respective stable values.

[0080] S52: In order to further verify the feasibility of the proposed control scheme, the following Figure 7 The electro-hydraulic servo system experimental platform shown in the figure. The piston position and chamber pressure are measured by displacement sensors and pressure sensors respectively. The NI data acquisition card collects system status information such as position and pressure and sends it to the host computer. After the host computer completes the calculation, the control voltage is input to the servo valve through the digital-to-analog converter. The servo valve then adjusts the hydraulic servo valve position by controlling the forward channel flow. The entire closed-loop system runs with a step time of 1 millisecond.

[0081] The range of motion of the hydraulic cylinder is ±50 mm, so for safety reasons, the desired trajectory is selected as y d =30sin(πt)mm. The initial conditions of the closed-loop system are x1(0)=30mm, x2(0)=0mm / s, x3(0)=156N, θ2(0)=θ3(0)=0. The controller parameters of the three control methods are selected as follows. 1) Fixed-time neural network adaptive control method: b1=30, c1=40, b2=40, c2=50, b3=40, c3=50, r j =1,τ j =0.5,ξ j =0.15,σ j =0.2, j=2,3, and the other parameters are the same as the simulation experiment. 2) Proportional integral control: k1=900, k2=500; 3) Standard backstepping control: b1=150, b2=150, b3=150.

[0082] The experimental results of the three controllers are shown in Figures 8 to 11 As shown in the figure, all controllers ensure the stability of the electro-hydraulic servo system. Figure 8 As shown in the figure, the steady-state accuracy of proportional-integral control and standard backstepping controller is very poor due to the lack of model uncertainty. The proposed fixed-time neural network adaptive control takes into account the fixed-time convergence and model uncertainty of the electro-hydraulic servo system, and its convergence speed and steady-state accuracy are better than those of the other two controllers. Hydraulic cylinder velocity x2, load pressure x3, control voltage u and weight norm estimation and like Figures 9 to 11 As shown in Figure 2, these closed-loop system signals are bounded and approach steady state quickly, which proves the effectiveness of the proposed fixed-time neural network adaptation. The results show that both fixed-time neural network adaptive control and standard backstepping control have better stabilization performance than proportional-integral control for the expected tracking error.

[0083] It should be noted that, in this article, relational terms such as first and second, etc. are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of further restrictions, the elements defined by the statement "comprise a ..." do not exclude the presence of other identical elements in the process, method, article or device including the elements.

Claims

1. An adaptive neural network fixed-time control method for an electro-hydraulic servo system with model uncertainty, characterized in that: The following steps are involved: S1: Model the electro-hydraulic servo and obtain the state equation; S2: Define the consistency tracking error z1 of the valve position response of the electro-hydraulic servo system and design the first virtual control law α1; S3: Define the consistency tracking error z2 of the valve speed response of the electro-hydraulic servo system, design the second virtual law α2 and the adaptive law S4: Define the consistency tracking error z3 of the pressure on the electro-hydraulic servo system valve, and design the final actual control law u and adaptive law S5: Experiment on the algorithm based on Matlab / Simulink simulation platform and electro-hydraulic servo experimental platform.

2. The adaptive neural network fixed time control method for an electro-hydraulic servo system with model uncertainty according to claim 1, characterized in that: The step S1 is specifically as follows: Based on Newton's second law, the dynamic model of the electro-hydraulic servo system can be given as follows: Where m represents the additional load mass, K represents the load stiffness coefficient, b represents the viscosity coefficient, and y represents the position of the hydraulic valve. Indicates the speed of the hydraulic valve, Indicates the acceleration of the hydraulic valve, A p is the annular area of ​​the hydraulic cylinder chamber, p L is the pressure exerted by the load. Therefore, the model of the electro-hydraulic servo system can be described by the following differential equation: in, K sv is the control hydraulic valve gain, u is the control servo valve voltage, β e is the effective volume modulus, C tl is the total leakage coefficient of the hydraulic cylinder, ω is the slope of the hydraulic valve area, ρ is the density of the hydraulic oil, C d is the flow coefficient, sgn(·) represents the sign function: when ·>0, sgn(·)=1; when ·<0, sgn(·)=-1; when ·=0, sgn(·)=0; y o Represents system output. Taking into account the uncertainty of hydraulic parameters, we establish an electro-hydraulic system model: Among them, the nominal parameters are given as follows: The model uncertainty of the mismatch is given by: Among them, the above expression and is the uncertainty due to the uncertainty of the water pressure parameters and is indicated by The value of the given value is represented by the symbol represents the uncertain value caused by uncertainty.

3. The adaptive neural network fixed time control method for an electro-hydraulic servo system with model uncertainty according to claim 1, characterized in that: The step S2 is as follows: Tracking error is defined as z1 = x1-y d , where y d is the demand trajectory. We get z i The derivative of is as follows; Here, we regard x2 as the control variable. Then, the error variable z2 and the virtual controller α1 are defined as follows: z2=x2-α1 in, l>1, b1>0, c1>0.

4. The adaptive neural network fixed time control method for an electro-hydraulic servo system with model uncertainty according to claim 1, characterized in that: The step S3 is as follows: Taking the derivative of z2, we get Treat x3 as a new control variable and define a new error variable as follows: z3=x3-α2 Among them, b2>0, c2>0, is the estimated value of θ2, and the error is defined as Basis Functions Defined as: in, is a real number. In order to Converge in a fixed time and design an adaptive estimation law as follows: Among them, r2>0, ξ2>0, σ2>0.

5. The adaptive neural network fixed time control method for an electro-hydraulic servo system with model uncertainty according to claim 1, characterized in that: The step S4 is as follows: Taking the derivative of z3, we get The actual control law u is designed as follows: Among them, b3>0, c3>0, is the estimated value of θ3, and the error is defined as Basis Functions Defined as: in, is a real number. In order to Converge in a fixed time and design an adaptive estimation law as follows: Among them, r3>0, ξ3>0, σ3>0.

Images