阅读说明：本技术 考虑输出离散性的电液伺服系统非线性自抗扰控制方法 (Output-discreteness-considered non-linear active disturbance rejection control method for electro-hydraulic servo system ) 是由 赵丁选 杜苗苗 倪涛 杜松 王丽丽 陈浩 马丽哲 刘振华 于 2019-10-10 设计创作，主要内容包括：本发明公开了一种考虑输出离散性的电液伺服系统非线性自抗扰控制方法,属于电液位置伺服控制技术领域,包括以下步骤：步骤1,建立电液位置伺服系统的数学模型；步骤2,依据建立的数学模型设计考虑输出离散性的非线性扩张状态观测器；步骤3,基于观测器的估计值设计非线性自抗扰控制器的自抗扰控制率；步骤4,调节非线性自抗扰控制器的设计参数,直到达到预期的控制效果。本发明解决了电液位置伺服系统中的非线性、不确定扰动和输出信号离散性对控制品质的不良影响,实现高精度的位置跟踪控制。(The invention discloses an electro-hydraulic servo system nonlinear active disturbance rejection control method considering output discreteness, which belongs to the technical field of electro-hydraulic position servo control and comprises the following steps: step 1, establishing a mathematical model of an electro-hydraulic position servo system; step 2, designing and considering a nonlinear extended state observer outputting discreteness according to the established mathematical model; step 3, designing the active disturbance rejection control rate of the nonlinear active disturbance rejection controller based on the estimated value of the observer; and 4, adjusting the design parameters of the nonlinear active disturbance rejection controller until the expected control effect is achieved. The invention solves the problem of the adverse effects of nonlinearity, uncertain disturbance and output signal discreteness on the control quality in the electro-hydraulic position servo system, and realizes high-precision position tracking control.)

1. The nonlinear active disturbance rejection control method of the electro-hydraulic servo system considering the output discreteness is characterized by comprising the following steps of:

step 1, establishing a mathematical model of an electro-hydraulic position servo system;

step 2, designing and considering a nonlinear extended state observer outputting discreteness according to the established mathematical model;

step 3, designing the active disturbance rejection control rate of the nonlinear active disturbance rejection controller based on the estimated value of the observer;

and 4, adjusting the design parameters of the nonlinear active disturbance rejection controller until the expected control effect is achieved.

2. The method for controlling nonlinear active disturbance rejection of an electro-hydraulic servo system considering output discreteness according to claim 1, wherein the specific process of step 1 is as follows:

according to Newton's second law, a kinetic equation of the inertial load is established:

in the formula (1), m is the mass of the inertial load; y is the displacement of the inertial load; p₁And P₂The oil pressure of a rodless cavity and a rod cavity of the hydraulic cylinder respectively; a. the₁And A₂The equivalent areas of a rodless cavity and a rod cavity of the hydraulic cylinder are respectively; f_LIs an external load force applied to the electro-hydraulic position servo system; b_sIs the coefficient of viscous friction; (t) a model perturbation term representing coulomb friction and other unmodeled dynamic constituents;

neglecting the external leakage of the hydraulic cylinder, the pressure dynamic equation of the oil in the rodless cavity and the rod cavity of the hydraulic cylinder is as follows:

v in formula (2)₁＝V₁₀+A₁Y tableShowing the control volume of the rodless chamber; v₂＝V₂₀-A₂y represents the control volume of the rod chamber; v₁₀And V₂₀Respectively representing the initial control volumes of a rodless cavity and a rod cavity of the hydraulic cylinder; beta is a_eIs the effective elastic modulus of the oil; c_iThe internal leakage coefficient of the hydraulic cylinder; q₁The flow rate of the fluid flowing into the rodless cavity of the hydraulic cylinder; q₂The oil return flow of a rod cavity of the hydraulic cylinder is provided; q. q.s₁(t) and q₂(t) model disturbance terms consisting of internal leakage modeling errors and other unmodeled dynamics in the pressure dynamics of the rodless cavity and the rod cavity of the hydraulic cylinder respectively;

the flow equations of the rodless cavity and the rod cavity of the hydraulic cylinder are as follows:

in the formula (3)

because the dynamic response frequency of the servo valve is far higher than that of an electro-hydraulic position servo system, the displacement of the valve core and the control input can be approximately proportional, namely

x_v＝k_iu (5)

Defining state variables

in the formula (6)

In the formula (6), the load parameters m and F_LWill vary with the operating conditions, hydraulic parameter b_s，β_eAnd C_iThe parameters alpha, beta and b can change along with the positions of the piston and the valve core, so that the parameters are uncertain; suppose gamma_n，g_n'，α_n，β_n，b_nNominal values of the parameters gamma, g', alpha, beta, b, respectively, model error terms and disturbance terms to be caused by variations of the parameters gamma and g

Considering that the output of the electro-hydraulic position servo system is discrete sampling points in the actual control process, the mathematical model of the whole electro-hydraulic position servo system can be expressed as follows:

in the formula (7), the mathematical model of the electro-hydraulic position servo system consists of continuous dynamics of a state vector and discrete sampling point output of the electro-hydraulic position servo system, and is a continuous-discrete mixed uncertain model.

3. The method for controlling nonlinear active disturbance rejection of the electro-hydraulic servo system considering the output discreteness as claimed in claim 2, wherein the specific process of step 2 comprises:

step 2.1, converting a mathematical model of the electro-hydraulic position servo system into an error dynamics model;

step 2.2, designing a nonlinear extended state observer considering output discreteness;

step 2.3, proving the convergence of the nonlinear extended state observer;

step 2.4, calculating the allowable maximum sampling period of the electro-hydraulic position servo system;

the specific process of the step 2.1 is as follows:

defining an error variable e₁Y-upsilon, where upsilon is an ideal displacement tracking signal,

in the formula (8)

To facilitate the nonlinear extended state observer design, the following assumptions are defined:

assume that 1: the ideal displacement tracking signal v is third order continuous and bounded; the electrohydraulic position servo system works under normal working condition, namely, P is satisfied_r＜P₁,P₂＜P_s(ii) a General mechanical disturbance d of electrohydraulic position servo system₁(t) and the total hydraulic disturbance d₂(t) are sufficiently smooth and bounded so that the total disturbance δ (t) of the error dynamics and its derivatives

Assume 2:

The specific process of the step 2.2 is as follows:

taking δ (t) as the expansion state e of the error kinetic system₄Then, a nonlinear extended state observer considering the output dispersion is designed according to equation (8), which is of the form:

in the formula (10), vectorIs given as vector e ═ e₁ e₂ e₃ e₄]^TXi (t) is the discrete output tracking error e₁(t_k) The continuous predicted value of (a) is,

assume that 3:

The specific process of the step 2.3 is as follows:

defining a weighted error variable eta [ etaeta eta ] according to an error dynamics system (8) and a nonlinear extended state observer (10) taking output dispersion into account₁ η₂ η₃ η₄]^TWherein

According to the theory of geometric homogeneity, if

according to a weighted error dynamics system, defining the following Lyapunov function

V₁(η,η_ξ)＝V_θ(η)+V_L(η_ξ) (14)

In the formula (14), V_θ(η) satisfies the above-mentioned geometric homogeneity theorem,k is a normal number and phi (t) satisfies

Wherein tau is_maxThe maximum sampling period allowed by the electro-hydraulic position servo system;

to V_θ(η) is derived

From assumptions 1-3 and equation (13)

To V_L(η_ξ) Derived by derivation

Selecting

Substituting equation (19) into equation (18) yields

From the formulae (14), (17) and (20)

Can be obtained by calculation when

In the same way, when

Then, the formula (21) can be converted into

For Lyapunov function V₁(η,η_ξ)＝V_θ(η)+V_L(η_ξ) Its initial value can be expressed as

Defining an tight set

the inequality (24) is obviously satisfied, selected

Integration of both sides of equation (27) can be obtained

Is obvious (eta )_ξ) Stay in the setWithin Ω, and as can be seen from equation (27), the Lyapunov function V₁(η,η_ξ) Is strictly decreasing, so (η, η)_ξ) Converging asymptotically with increasing time t to within a sufficiently small bounded range;

further, the formula (13) can also be used to obtain

This means that when t > t_rWhen ρ is large enough, the estimation error of the non-linear extended state observer designed in step 2.2 considering the output dispersion will converge to zero, where t_rIs a time constant dependent on the parameter p; therefore, the convergence of the designed observer is ensured;

the specific process of step 2.4 is as follows:

for that shown in equation (19)

4. The method for controlling nonlinear active disturbance rejection of the electro-hydraulic servo system considering output discreteness according to claim 3, wherein the specific process of the step 3 comprises:

step 3.1, designing the active disturbance rejection control rate based on the estimated value of the observer;

step 3.2, proving the closed loop stability of the electro-hydraulic position servo system;

the specific process of step 3.1 is as follows:

designing the active disturbance rejection control rate of the electro-hydraulic position servo system according to the estimated value of the nonlinear extended state observer considering output discreteness obtained in the step 2

Parameter α in formula (31)_jJ-1, 2,3 is chosen such that the matrix a is Hurwitz,

the specific process of the step 3.2 is as follows:

substituting the active disturbance rejection control rate (31) into the formula (8) can obtain

Wherein

A^TP+PA＝-Q (33)

Wherein Q is a positive definite matrix; defining Lyapunov function V₂＝e^TPe, derived therefrom

From equation (29), when ρ > ρ ″, there is a normal constant Γ_i，t_eSo that

Substituting equation (35) into equation (34) results in

Wherein

Wherein

As can be seen from equation (38), when t → ∞ is reached, the equation

5. The method for controlling nonlinear active disturbance rejection of an electro-hydraulic servo system considering output discreteness according to claim 4, wherein the specific process of step 4 is as follows:

selecting design parameter k of nonlinear extended state observer considering output dispersion₁，k₂，k₃，k₄Let xi_eFor the Hurwitz matrix, the design parameter α is selected₁，α₂，α₃And A is a Hurwitz matrix, the control parameter rho of the active disturbance rejection controller is adjusted to meet rho > rho, the convergence of the nonlinear extended state observer and the stability of the whole closed-loop system are ensured, and the design parameter of the nonlinear active disturbance rejection controller is adjusted on the basis of meeting the conditions until the expected displacement tracking effect is achieved.

6. The method for controlling nonlinear active disturbance rejection of an electro-hydraulic servo system considering output discreteness as claimed in claim 1, wherein when the system parameters which can be obtained by the electro-hydraulic position servo system are very small, the method comprises the following steps:

step I: establishing a second-order simplified mathematical model of the electro-hydraulic position servo system:

in the formula (39), the compound represented by the formula (I),

step II: establishing an error dynamics model of a second-order electro-hydraulic position servo system

Regarding f (x) in the formula (40) as the total disturbance variable of the second order error dynamics systemAnd the following assumptions are given: assuming overall interference for a second order systemSufficiently smooth and bounded, its derivative

Nonlinear extended state observer considering output error dispersion according to formula (40)

In the formula (41), vectorIs a vector

proving the convergence of a second-order nonlinear extended state observer considering output dispersion;

calculating the allowable maximum sampling period of the electro-hydraulic position servo system;

step III: active disturbance rejection control rate designed for second-order model of electro-hydraulic position servo system

Selecting parametersAnd alpha₂Make it

the closed loop stability of the whole electro-hydraulic position servo system under the designed second-order nonlinear active disturbance rejection controller considering output discreteness is proved;

step IV: selecting design parameters of second-order nonlinear active disturbance rejection controller

Technical Field

The invention relates to the technical field of electro-hydraulic position servo control, in particular to a nonlinear active disturbance rejection control method of an electro-hydraulic servo system with output discreteness taken into consideration.

Background

The electro-hydraulic servo system has the advantages of high power density, large output force/torque and quick dynamic response, and is widely applied to industry. However, the electro-hydraulic servo system is a typical non-linear system, such as flow, pressure non-linearity, and positive and negative stroke open loop gain and dynamic non-linearity caused by structural asymmetry of the cylinder. In addition, the electro-hydraulic servo system also comprises a large number of uncertain disturbance factors, such as system parameters of load mass, hydraulic cylinder viscous damping coefficient, leakage coefficient, hydraulic oil elastic modulus and the like which are easy to change along with temperature, and uncertain nonlinearity of unmodeled friction force, unmodeled dynamics, external interference and the like in the system. The characteristics bring great challenges to high-performance electro-hydraulic position servo control, and especially, the existence of uncertain disturbance can cause the reduction of control quality and even cause the instability of a system. The exploration of the nonlinear and uncertain data in the system can be processed simultaneously, and the realization of the high-precision control of the electro-hydraulic position servo system is always the target pursued in the field of engineering control.

With the development of control theory, many advanced control algorithms are used for an electro-hydraulic position servo system, such as feedback linearization, adaptive control, inversion control, sliding mode variable structure control, robust control and the like, but the control methods have great limitations in application. On one hand, a controller designed based on the control algorithm usually depends on an accurate mathematical model, and the model is easily unmatched due to parameter uncertainty and uncertain nonlinearity existing in an electro-hydraulic servo system, so that the designed controller is weak in anti-interference capability and difficult to meet the high-precision control requirement. On the other hand, the control algorithm mostly needs all state information of the system when designing the controller, and in many engineering practices, only displacement information can be directly measured due to constraints of factors such as mechanical structure, volume, cost and the like, so that the designed controller is difficult to be applied to practice. Even if other signals (such as speed, pressure, etc.) can be measured, they can cause severe measurement noise, which can seriously degrade the performance of the full-state feedback controller.

The active disturbance rejection technology does not depend on an accurate mathematical model, only utilizes output information of a system to estimate and compensate an undetectable state and uncertain disturbance in real time, and has the advantages of strong disturbance rejection capability, high control precision and high response speed, so that the active disturbance rejection technology has incomparable advantages of other control algorithms in the aspect of electro-hydraulic position servo control. The patent "a self-adaptive control method of auto-disturbance rejection of hydraulic motor position servo system", publication number is CN 104345638B; the patent "a linear active disturbance rejection control method and device of electro-hydraulic position servo control system", publication number CN108873702A, all adopt the active disturbance rejection technology to design the controller, but all are based on a linear extended state observer. Experts such as hangoh and the like, who propose an auto-disturbance rejection technology, consider that a nonlinear extended state observer has better performance than a linear extended observer, but at present, the application of the observer in the field of electro-hydraulic position servo control is very limited, and one important reason is that the stability of the observer is difficult to prove.

In addition, the active disturbance rejection controllers designed based on the extended state observer exist at present and are designed in a continuous time domain. It is known that when the controller is applied in practice, the computer control system relied on is a digital discrete system, and the output signal obtained by the sensor is also a discrete sampling point, and the observation performance and convergence of the observer based on continuous time domain design will be affected by the discrete sampling process, and the original performance is difficult to guarantee. Therefore, it is urgently needed to design a non-linear active disturbance rejection control method considering output discreteness, so as to further improve the control effect of the active disturbance rejection controller in actual application.

Disclosure of Invention

The invention provides a nonlinear active disturbance rejection control method of an electro-hydraulic servo system considering output discreteness, which aims to solve the problem that nonlinearity, uncertain disturbance and output signal discreteness in the electro-hydraulic position servo system have adverse effects on control quality and realize high-precision position tracking control.

In order to solve the technical problems, the technical scheme adopted by the invention is as follows:

a nonlinear active disturbance rejection control method of an electro-hydraulic servo system considering output discreteness comprises the following steps:

step 1, establishing a mathematical model of an electro-hydraulic position servo system;

step 2, designing and considering a nonlinear extended state observer outputting discreteness according to the established mathematical model;

step 3, designing the active disturbance rejection control rate of the nonlinear active disturbance rejection controller based on the estimated value of the observer;

and 4, adjusting the design parameters of the nonlinear active disturbance rejection controller until the expected control effect is achieved.

Due to the adoption of the technical scheme, the invention has the technical progress that:

(1) the nonlinear active disturbance rejection control method of the electro-hydraulic servo system, which is designed by considering the output discreteness, does not depend on an accurate electro-hydraulic position servo system mathematical model, can effectively estimate the undetectable state and uncertain disturbance of the system and timely carry out disturbance compensation, and has stronger robustness;

(2) the nonlinear extended state observer of the electro-hydraulic servo system, which is designed by the invention and takes output discreteness into consideration, can obtain better performance than the traditional linear extended state observer, and solves the problem that the convergence of the nonlinear extended state observer is difficult to prove.

(3) According to the non-linear active disturbance rejection control method of the electro-hydraulic servo system considering the output discreteness, the output signal is considered as a discrete sampling point in practical application, and the discrete sampling process can affect the performance of the extended state observer designed in a continuous time domain, so that the discrete output signal is continuously estimated and used for designing the non-linear extended state observer, and a controller based on the design can obtain a better control effect than a non-linear active disturbance rejection controller not considering the discreteness of the output signal and a traditional linear active disturbance rejection controller.

(4) Aiming at the condition that the electro-hydraulic position servo system can obtain little model parameter information, the invention also designs a second-order simplified model-based non-linear active disturbance rejection controller considering output discreteness, and although the observation load of the non-linear extended state observer is increased to a certain extent, the invention can still obtain better control performance than the traditional linear active disturbance rejection controller.

Drawings

FIG. 1 is a flow chart of a nonlinear active disturbance rejection control method of an electro-hydraulic servo system considering output discreteness;

FIG. 2 is a schematic diagram of the electro-hydraulic position servo system;

FIG. 3 is a displacement tracking error comparison curve under a nonlinear active disturbance rejection controller (CD-NLADRC-3Order) which is designed based on a third-Order electro-hydraulic position servo system mathematical model and considers output discreteness and a nonlinear active disturbance rejection controller (NLADRC-3Order) which does not consider output discreteness;

FIG. 4 is a displacement tracking error contrast curve of a nonlinear active disturbance rejection controller (CD-NLADRC-3Order) designed based on a third-Order electro-hydraulic position servo system mathematical model and considering output discreteness, and under an existing linear active disturbance rejection controller (LADRC-3 Order);

FIG. 5 is a displacement tracking error contrast curve of a nonlinear active disturbance rejection controller (CD-NLADRC-2Order) designed based on a second-Order electro-hydraulic position servo system mathematical model and considering output discreteness and an existing linear active disturbance rejection controller (LADRC-2 Order).

Detailed Description

The present invention will be described in further detail with reference to the following examples:

with reference to fig. 1, the method for controlling nonlinear active disturbance rejection of an electro-hydraulic servo system considering output discreteness provided by the invention includes the following steps:

step 1, establishing a mathematical model of an electro-hydraulic position servo system;

step 2, designing and considering a nonlinear extended state observer outputting discreteness according to the established mathematical model;

step 3, designing the active disturbance rejection control rate of the nonlinear active disturbance rejection controller based on the estimated value of the observer;

and 4, adjusting the design parameters of the nonlinear active disturbance rejection controller until the expected control effect is achieved.