A control method, device and medium of an electro-hydraulic servo system

Abstract

The embodiments of this specification disclose a control method, device and medium for an electro-hydraulic servo system, and relate to the technical field of electro-hydraulic servo control. The method comprises: constructing a mathematical model of a valve-controlled double-rod hydraulic cylinder to obtain a system state-space equation; designing an expanded sliding mode observer based on the system state-space equation; defining a tracking error vector of the electro-hydraulic servo system so as to design a position tracking error limiting controller according to the tracking error vector of the electro-hydraulic servo system and the expanded sliding mode observer; using the position tracking error limiting controller to control the electro-hydraulic servo system so that the electro-hydraulic servo system operates stably, using the expanded sliding mode observer to online estimate and compensate for external mismatch interference, and using the output limited controller of the expanded sliding mode observer to effectively improve the tracking accuracy of the system.

Description

Technical Field

[0001] The present invention relates to the field of electro-hydraulic servo control technology, and in particular to a control method, device and medium of an electro-hydraulic servo system. Background Art

[0002] The electro-hydraulic servo system refers to a hydraulic control system with servo elements (servo valves or servo pumps) as the core of the control. It is usually composed of a command device, a controller, an amplifier, a hydraulic source, a servo element, an actuator, a feedback sensor and a load. The electro-hydraulic servo system has been widely used in the field of industrial control because of its unique advantages such as fast response speed, high load stiffness and high control power.

[0003] The electro-hydraulic servo system is developing towards high precision. From the traditional linear system theory to the currently popular back-stepping controller based on nonlinear model, various controllers are being applied to the electro-hydraulic servo system to improve the control accuracy of the system. However, during its operation, the external interference of the electro-hydraulic servo system will affect the operation of the electro-hydraulic servo system. The existing controller cannot control the tracking error of the electro-hydraulic servo system within a certain range, and it is difficult to achieve high-precision control of the position closed loop of the electro-hydraulic servo system. Summary of the invention

[0004] One or more embodiments of the present specification provide a control method, device and medium for an electro-hydraulic servo system, which are used to solve the following technical problems: during its operation, external interference to the electro-hydraulic servo system will affect the operation of the electro-hydraulic servo system, and the existing controller cannot control the tracking error of the electro-hydraulic servo system within a certain range, making it difficult to achieve high-precision control of the position closed loop of the electro-hydraulic servo system.

[0005] One or more embodiments of this specification adopt the following technical solutions:

[0006] One or more embodiments of the present specification provide a control method for an electro-hydraulic servo system, the method comprising: constructing a mathematical model of a valve-controlled double-rod hydraulic cylinder; designing an expanded sliding mode observer based on the mathematical model of the valve-controlled double-rod hydraulic cylinder; defining a tracking error vector of the electro-hydraulic servo system so as to design a position tracking error limiting controller based on the tracking error vector of the electro-hydraulic servo system and the expanded sliding mode observer; and using the position tracking error limiting controller to control the electro-hydraulic servo system so that the electro-hydraulic servo system operates stably.

[0007] Furthermore, a mathematical model of a valve-controlled double-rod hydraulic cylinder is constructed, specifically including: determining a flow continuity equation and a load force balance equation of the hydraulic cylinder, and constructing a mathematical model of the valve-controlled double-rod hydraulic cylinder based on the hydraulic cylinder flow continuity equation and the load force balance equation; determining state variables of the electro-hydraulic servo system; and determining a state space equation of the electro-hydraulic servo system based on specified state variables of the electro-hydraulic servo system.

[0008] Furthermore, the expression of the hydraulic cylinder flow continuity equation is as follows:

[0009]

[0010] Among them, Q L The load flow of the hydraulic cylinder, Q1 is the flow of the hydraulic cylinder oil inlet, Q2 is the flow of the hydraulic cylinder oil return port, A p is the effective area of ​​the hydraulic cylinder piston, x p is the displacement of the hydraulic cylinder piston rod, C tl is the total leakage coefficient of the hydraulic cylinder, p L is the pressure difference between the two chambers of the hydraulic cylinder, V t is the total volume of the oil inlet chamber and the oil return chamber of the hydraulic cylinder, β e is the effective bulk elastic modulus of the hydraulic cylinder oil;

[0011] The load force balance equation is expressed as follows:

[0012]

[0013] in, m is the total mass, B p is the viscous damping coefficient of the hydraulic cylinder, F L is the external force of the hydraulic cylinder, F F is the friction between the piston rod and the cylinder barrel of the hydraulic cylinder;

[0014] The specified state variable is x is the specified state variable;

[0015] The state space equation of the electro-hydraulic servo system is expressed as follows:

[0016]

[0017] Where θ1 = A p / m,θ2=B p / m,θ3=4A p β e / V t ,θ4=4C tl β e / V t ,θ5=4βe / V t , Δ1=Δθ1x3-Δθ2x2-F L / mF F / m+μ, Δ1 is used to represent the interference term caused by external load force, friction force, parameter change and structural vibration, Δθ1 and Δθ2 are used to represent the parameter changes of θ1 and θ2 respectively, Δ2=-Δθ3x2-Δθ4x3, Δ2 is used to represent the interference caused by the parameter changes of θ3 and θ4, Υ1 and Υ2 are the change rates of the two external interferences Δ1 and Δ2, y=x1 is the displacement output of the system, f1(x2,x3)=θ1x3-θ2x2, f2(x2,x3)=-θ3x2-θ4x3.

[0018] Furthermore, it is characterized in that f1(x2, x3) and f2(x2, x3) satisfy the Lipschitz condition with respect to x2 and x3, and there are four Lipschitz constants γ1, γ2, γ3 and γ4 satisfying the following conditions:

[0019]

[0020]

[0021] Furthermore, based on the mathematical model of the valve-controlled double-rod hydraulic cylinder, an expansion sliding mode observer is designed, which specifically includes:

[0022] According to the state space equation of the electro-hydraulic servo system, a 5th-order extended sliding mode observer is used, wherein the expression of the 5th-order extended sliding mode observer is as follows:

[0023]

[0024]

[0025] in, i=1,2,3. is the system state variable x i , the estimated value of i=1,2,3. i=1,2.Yes The estimated value of i=1,2. i ,i=1,2,3,4,5. is the control gain of the extended sliding mode observer;

[0026] based on The expression for the observation error dynamics is determined as:

[0027]

[0028]

[0029] The extended sliding mode observer is determined by the equal value injection principle of the sliding mode observer and the specified saturation function. The expression of the extended sliding mode observer is as follows:

[0030]

[0031]

[0032]

[0033] Among them, δ i ,i=1,2,3.are three small positive real numbers.

[0034] Furthermore, the tracking error vector of the electro-hydraulic servo system is:

[0035] z=[z1,z2,z3] T =[y d -x1,x2-α1,x3-α2] T ,

[0036] Where z1 is the system output displacement tracking error, and |z1| <k b , k b The tracking error of the system is limited, and the output of the system satisfies k cl <x1<k cu , k cu =y d +k b , k cl =y d -k b , α1 and α2 are two virtual control quantities designed by the controller. Further, according to the error vector of the electro-hydraulic servo system and the extended sliding mode observer, a position tracking error limit controller is designed, which specifically includes: based on the error vector of the electro-hydraulic servo system, combining the state space equation of the electro-hydraulic servo system and the two estimated values ​​of the extended sliding mode observer and Determine a control law that meets the requirements, and the control law that meets the requirements makes the tracking error of the electro-hydraulic servo system satisfy |z1| <k b and And the expression of the control law that meets the requirements is as follows:

[0037]

[0038] Among them, k i , i=1,2,3 are control gains. If the control gain L i+3 , i=1,2 is appropriately selected as L i+3 >1 / 4k i+1,i=1,2, then |z1| <k b ; and z will fall into a bounded hypersphere H r , and keep at H r Inside,

[0039]

[0040] Among them, ξ i =L i+3 -1 / 4k i+1 ,i=1,2.

[0041] Furthermore, after using the position tracking error limit controller to control the electro-hydraulic servo system so that the electro-hydraulic servo system operates stably, the method also includes: defining a Lyapunov function and calculating the derivative of the Lyapunov function with respect to time; determining the positive or negative value of the derivative of the Lyapunov function with respect to time; and determining that the electro-hydraulic servo system is in a stable operating state when the value of the derivative of the Lyapunov function with respect to time is less than 0.

[0042] One or more embodiments of the present specification provide a control device for an electro-hydraulic servo system, including:

[0043] at least one processor; and a memory in communication with the at least one processor; wherein,

[0044] The memory stores instructions executable by the at least one processor, the instructions being executed by the at least one processor to enable the at least one processor to:

[0045] Construct a mathematical model of a valve-controlled double-rod hydraulic cylinder; design an expanded sliding mode observer based on the mathematical model of the valve-controlled double-rod hydraulic cylinder; define a tracking error vector of the electro-hydraulic servo system so as to design a position tracking error limiting controller according to the tracking error vector of the electro-hydraulic servo system and the expanded sliding mode observer; use the position tracking error limiting controller to control the electro-hydraulic servo system so that the electro-hydraulic servo system operates stably.

[0046] One or more embodiments of this specification provide a non-volatile computer storage medium storing computer executable instructions, wherein the computer executable instructions are configured to:

[0047] Construct a mathematical model of a valve-controlled double-rod hydraulic cylinder; design an expanded sliding mode observer based on the mathematical model of the valve-controlled double-rod hydraulic cylinder; define a tracking error vector of the electro-hydraulic servo system so as to design a position tracking error limiting controller according to the tracking error vector of the electro-hydraulic servo system and the expanded sliding mode observer; use the position tracking error limiting controller to control the electro-hydraulic servo system so that the electro-hydraulic servo system operates stably.

[0048] At least one of the above-mentioned technical solutions adopted in the embodiments of this specification can achieve the following beneficial effects: the tracking error of the controller based on the extended sliding mode observer can be guaranteed to be within a small range, and the extended sliding mode observer is used to online estimate and compensate for external mismatch interference. Due to the compensation of the external interference by the extended sliding mode observer, the system tracking accuracy is further improved; therefore, the output limited controller using the extended sliding mode observer effectively improves the tracking accuracy of the system. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] In order to more clearly illustrate the technical solutions in the embodiments of this specification or the prior art, the following briefly introduces the drawings required for use in the embodiments or the prior art description. Obviously, the drawings described below are only some embodiments recorded in this specification. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative labor. In the drawings:

[0050] Figure 1 A flow chart of a control method of an electro-hydraulic servo system provided in an embodiment of this specification;

[0051] Figure 2 A schematic diagram of the structure of a valve-controlled double-rod hydraulic cylinder provided in an embodiment of this specification;

[0052] Figure 3 A schematic diagram of a control result based on a backstepping controller provided in an embodiment of this specification;

[0053] Figure 4 A schematic diagram of a control result based on an output limited controller provided in an embodiment of this specification;

[0054] Figure 5 A schematic diagram of control results of an output limited controller based on an extended sliding mode observer provided in an embodiment of this specification;

[0055] Figure 6 A schematic diagram of the structure of a control device of an electro-hydraulic servo system provided in an embodiment of this specification. DETAILED DESCRIPTION

[0056] In order to enable those skilled in the art to better understand the technical solutions in this specification, the technical solutions in the embodiments of this specification will be clearly and completely described below in conjunction with the drawings in the embodiments of this specification. Obviously, the described embodiments are only part of the embodiments of this specification, not all of the embodiments. Based on the embodiments of this specification, all other embodiments obtained by ordinary technicians in this field without creative work should fall within the scope of protection of this specification.

[0057] The electro-hydraulic servo system refers to a hydraulic control system with servo elements (servo valves or servo pumps) as the core of the control. It is usually composed of a command device, a controller, an amplifier, a hydraulic source, a servo element, an actuator, a feedback sensor and a load. The electro-hydraulic servo system has been widely used in the field of industrial control because of its unique advantages such as fast response speed, high load stiffness and high control power.

[0058] The electro-hydraulic servo system is developing towards high precision. From the traditional linear system theory to the currently popular back-stepping controller based on nonlinear model, various controllers are being applied to the electro-hydraulic servo system to improve the control accuracy of the system. However, during its operation, the external interference of the electro-hydraulic servo system will affect the operation of the electro-hydraulic servo system. The existing controller cannot control the tracking error of the electro-hydraulic servo system within a certain range, and it is difficult to achieve high-precision control of the position closed loop of the electro-hydraulic servo system.

[0059] The embodiments of this specification provide a control method for an electro-hydraulic servo system. It should be noted that the execution subject in the embodiments of this specification can be a server or any device with data processing capabilities. Figure 1 A flow chart of a control method of an electro-hydraulic servo system provided in an embodiment of this specification is shown as follows: Figure 1 As shown, it mainly includes the following steps:

[0060] Step S101, constructing a mathematical model of a valve-controlled double-rod hydraulic cylinder.

[0061] Constructing a mathematical model of a valve-controlled double-rod hydraulic cylinder specifically includes: determining a flow continuity equation and a load force balance equation of the hydraulic cylinder, and constructing a mathematical model of the valve-controlled double-rod hydraulic cylinder based on the flow continuity equation and the load force balance equation of the hydraulic cylinder; determining the state variables of the electro-hydraulic servo system; and determining the state space equation of the electro-hydraulic servo system based on the specified state variables of the electro-hydraulic servo system.

[0062] In one embodiment of the present specification, a mathematical model of a valve-controlled double-rod hydraulic cylinder is constructed in combination with a structural schematic diagram of the valve-controlled double-rod hydraulic cylinder. Figure 2 A schematic diagram of the structure of a valve-controlled double-rod hydraulic cylinder provided in the embodiment of this specification is shown in FIG. Figure 2 As shown, Ap is the effective area of ​​the hydraulic cylinder piston, x p is the displacement of the hydraulic cylinder piston rod, p1 is the pressure at the hydraulic cylinder oil inlet, Q1 is the flow rate at the hydraulic cylinder oil inlet, p2 is the pressure at the hydraulic cylinder oil return port, Q2 is the flow rate at the hydraulic cylinder oil return port, p s is the oil source pressure.

[0063] Determine the hydraulic cylinder flow continuity equation and load force balance equation. According to the hydraulic cylinder flow continuity equation and load force balance equation, construct the mathematical model of the valve-controlled double-rod hydraulic cylinder. The expression of the hydraulic cylinder flow continuity equation is as follows:

[0064]

[0065] Among them, C tl is the total leakage coefficient of the hydraulic cylinder, p L is the pressure difference between the two chambers of the hydraulic cylinder, V t is the total volume of the oil inlet chamber and the oil return chamber of the hydraulic cylinder, β e is the effective bulk elastic modulus of the hydraulic cylinder oil.

[0066] The load force balance equation is expressed as follows:

[0067]

[0068] in, m is the total mass, B p is the viscous damping coefficient of the hydraulic cylinder, F L is the external force of the hydraulic cylinder, F F It is the friction between the hydraulic cylinder piston rod and the cylinder barrel.

[0069] The load flow of the hydraulic cylinder is controlled by the valve core displacement of the electro-hydraulic servo valve

[0070]

[0071] Among them, x v is the displacement of the electro-hydraulic servo valve, C d is the discharge coefficient of the electro-hydraulic servo valve, w is the throttling window area gradient of the electro-hydraulic servo valve, ρ is the density of the hydraulic oil, p s is the pressure of the hydraulic oil source, then the control voltage of the electro-hydraulic servo valve is:

[0072]

[0073] Among them, u L is the control voltage of the electro-hydraulic servo valve, Q r is the rated flow of the electro-hydraulic servo valve at the rated pressure drop, Δp r is the rated pressure drop of the electro-hydraulic servo valve, u maxIt is the maximum voltage of the electro-hydraulic servo valve.

[0074] Select the system state variable as the specified state variable is x is the specified state variable, then the state space equation of the system can be obtained as follows:

[0075]

[0076] Where θ1 = A p / m,θ2=B p / m,θ3=4A p β e / V t ,θ4=4C tl β e / V t ,θ5=4β e / V t , Δ1=Δθ1x3-Δθ2x2-F L / mF F / m+μ, Δ1 is used to represent the interference term caused by external load force, friction force, parameter change and structural vibration, Δθ1 and Δθ2 are used to represent the parameter changes of θ1 and θ2 respectively, Δ2=-Δθ3x2-Δθ4x3, Δ2 is used to represent the interference caused by the parameter changes of θ3 and θ4, γ1 and γ2 are the change rates of the two external interferences Δ1 and Δ2, y=x1 is the displacement output of the system, f1(x2,x3)=θ1x3-θ2x2, f2(x2,x3)=-θ3x2-θ4x3.

[0077] In one embodiment of this specification, two situations are assumed. First, assumption 1: the desired displacement y of the electro-hydraulic servo system is d and its first, second, and third time derivatives and are all bounded, Δ1 and Δ2 and their rates of change γ1 and γ2 are all bounded, that is, Δ i ≤Δ imax , γ i ≤γ imax ,i=1,2., and the changes of Δ1 and Δ2 are slow. The second assumption is: f1(x2,x3) and f2(x2,x3) satisfy the Lipschitz conditions with respect to x2 and x3, and there are four Lipschitz constants γ1, γ2, γ3 and γ4 that satisfy the following conditions:

[0078]

[0079]

[0080] in, and i=1,2,3. It will be defined in the following step 102.

[0081] Step S102, designing an expansion sliding mode observer based on the mathematical model of the valve-controlled double-rod hydraulic cylinder.

[0082] In one embodiment of the present specification, according to the state space equation of the electro-hydraulic servo system, that is, formula (5), the following 5th-order extended sliding mode observer is considered, wherein the expression of the 5th-order extended sliding mode observer is as follows:

[0083]

[0084]

[0085] in, i=1,2,3. is the system state variable x i , the estimated value of i=1,2,3. i=1,2.Yes The estimated value of i=1,2. i ,i=1,2,3,4,5. is the control gain of the extended sliding mode observer;

[0086] based on The expression for the observation error dynamics is determined as:

[0087]

[0088]

[0089] In this case, it is considered that there is a sufficiently large control gain L i+3 >0,i=1,2., and σ i , i = 1, 2, 3. is a small positive parameter, which can ensure that the observation error vector It approaches 0 within a finite time T>0.

[0090] The proof process is as follows: First, consider the following three sliding surfaces: i=1,2,3., and its time derivative is

[0091]

[0092] The following inequality can be obtained

[0093]

[0094] Therefore, if but And the sliding surface S1 will reach the sliding state within T1>0. Further, formula (12) can be obtained:

[0095]

[0096] Secondly, according to the second assumption proposed in step S101, formula (13) can be obtained:

[0097]

[0098] make but and will approach 0 within T2>0; further, get and The kinetic expression of is as follows:

[0099]

[0100] Similarly, according to assumption 2, we get formula (15):

[0101]

[0102] choose but will approach 0 within T3>0, and We get formula (16):

[0103]

[0104] visible is a first-order differential equation, and its solution is

[0105]

[0106] It can be seen that as long as L5>0, It will converge to 0 within T4>0, so it can be seen The convergence and is irrelevant; therefore, formula (14) can be rewritten as

[0107]

[0108] Similar to formula (17), they are all first-order differential equations. Therefore, as long as L4>0, It will converge to 0 within T5>0. Define a new variable T as

[0109] T=sup{T1, T2, T3, T4, T5}. (19)

[0110] In summary, the following conclusions are drawn: It will converge to 0 within a finite time T>0.

[0111] Through the equal value injection principle of the sliding mode observer and the appropriate saturation function, the final form of the extended sliding mode observer is determined, where the final expression of the extended sliding mode observer is as follows:

[0112]

[0113]

[0114]

[0115] Among them, δ i ,i=1,2,3.are three small positive real numbers.

[0116] Through the above technical solution, the expansion sliding mode observer is used to online estimate and compensate for external mismatch interference, thereby further improving the tracking accuracy of the electro-hydraulic servo system.

[0117] Step S103, defining the error vector of the electro-hydraulic servo system, so as to design a position tracking error limiting controller according to the error vector of the electro-hydraulic servo system and the extended sliding mode observer.

[0118] In one embodiment of the present specification, a tracking error vector of an electro-hydraulic servo system is defined as:

[0119] z=[z1,z2,z3] T =[y d -x1,x2-α1,x3-α2] T ,

[0120] Where z1 is the system output displacement tracking error, and |z1| <k b , k b The tracking error of the system is limited, and the output of the system satisfies k cl <x1<k cu , k cu =y d +k b , k cl =y d -k b , α1 and α2 are two virtual control quantities designed by the controller. In one embodiment of the present specification, based on the error vector of the electro-hydraulic servo system, the state space equation of the electro-hydraulic servo system, that is, formula (5), and the two estimated values ​​of the extended sliding mode observer are combined. and There exists the following control law that meets the requirements, so that the tracking error of the electro-hydraulic servo system satisfies |z1| <k b and

[0121]

[0122] Among them, k i , i=1,2,3 are control gains. If the control gain L i+3 , i=1,2 is appropriately selected as L i+3 >1 / 4k i+1 ,i=1,2, then |z1| <k b ; and z will fall into a bounded hypersphere H r , and keep at H r Inside,

[0123]

[0124] Among them, ξ i =L i+3 -1 / 4k i+1 ,i=1,2. Prove it by following the steps below:

[0125] First, consider the following obstacle Lyapunov function: based on Its derivative with respect to time is:

[0126]

[0127] Based on the virtual control amount α1, we can get

[0128]

[0129] Secondly, based on Consider the Lyapunov function Its derivative with respect to time is:

[0130]

[0131] Based on the virtual control amount α2 and Available

[0132]

[0133] Finally, consider Consider the Lyapunov function Its derivative with respect to time is:

[0134]

[0135] Based on Q L and Available

[0136]

[0137] Therefore, if L i+3 >1 / 4k i+1 ,i=1,2., z will fall into H within a finite time t1>0 r , and keep the inner section at H r Inside, Furthermore, the output tracking error of the system satisfies |z1| <k b and

[0138] Step S104: Use a position tracking error limiting controller to control the electro-hydraulic servo system so that the electro-hydraulic servo system operates stably.

[0139] In one embodiment of the present specification, a position tracking error limit controller is used to control the electro-hydraulic servo system, and the stability of the formed closed-loop system is verified, a Lyapunov function is defined, and the derivative of the Lyapunov function with respect to time is calculated; the positivity of the value of the derivative of the Lyapunov function with respect to time is determined; when the value of the derivative of the Lyapunov function with respect to time is less than 0, the electro-hydraulic servo system is determined to be in a stable operating state, that is, the closed-loop system is stable.

[0140] In one embodiment of the present specification, the Lyapunov function is defined as:

[0141]

[0142] Its derivative with respect to time is as follows:

[0143]

[0144] Based on the results of formula (11), formula (13), formula (14), formula (15), formula (18) and formula (22), formula (31) can be rewritten as follows:

[0145]

[0146] if and The following conclusions can be drawn:

[0147]

[0148] Due to L i+3 >1 / 4k i+1 ,i=1,2. So that ξ i >0,i=1,2., and k i >0,i=1,2,3., it can be seen that only is a positive term, and the other terms are negative terms. These negative terms can ensure that Under the action of , the convergence of the closed-loop system is guaranteed.

[0149] Due to Δ i , i = 1, 2. Usually changes slowly, and its change rate is γ i ,i=1,2. It may be a very small value, so it can be considered as γ i ≈0,i=1,2. Therefore,

[0150]

[0151] It can be seen that the closed-loop system is stable.

[0152] The present specification also provides an application example of a control method for an electro-hydraulic servo system, wherein the hydraulic system oil source pressure P is set. s =8×10 6 Pa, effective area A of double-rod hydraulic cylinder p =1.88×10 -3 m 2 , hydraulic system load mass m = 500kg, hydraulic system viscous damping coefficient B p =7500N / (m / s), the total volume of the hydraulic cylinder oil inlet chamber and oil return chamber V t =0.38×10 -3 m 3 , the total leakage coefficient of the hydraulic system C tl =6.9×10 -13 m 3 / (s / Pa), hydraulic oil bulk elastic modulus β e =1×10 9 Pa; Set the system tracking error to k b =1mm. Consider Δ1=2sin(2πωt), Δ2=2×10 9 sin(2πωt).

[0153] According to the above settings, three controllers are used respectively to compare the system tracking errors obtained by using the three controllers. First, the backstepping controller is used. According to the state space equation, the control law of the backstepping controller is set as The control gains are selected as k1=319, k2=300, k3=300, and the corresponding results of the backstepping controller are obtained, such as Figure 3 As shown, Figure 3 A schematic diagram of control results based on a backstepping controller provided in an embodiment of this specification.

[0154] Next is the output limited controller, which makes and The output limited controller is obtained, and the control gains are selected as k1=200, k2=1900, k3=200, and the corresponding result of the output limited controller is obtained, such as Figure 4 As shown, Figure 4 A schematic diagram of a control result based on an output limited controller provided in an embodiment of this specification.

[0155] The third is an output-constrained controller based on an extended sliding mode observer. and The proposed controller acts on the electro-hydraulic servo system, and selects L1 = 70, L2 = 5 × 10 3 , L3=9×10 9 , L4=400, L5=200, δ1=δ2=0.01, δ3=0.05, k1=200, k2=1900 and k3=200, and the corresponding results of the output limited controller based on the extended sliding mode observer are obtained, such as Figure 5 As shown, Figure 5 A schematic diagram of control results of an output limited controller based on an extended sliding mode observer provided in an embodiment of this specification, Figure 5 (a) is the tracking effect, Figure 5 (b) shows the variation curve of z1, Figure 5 (c) represents x1 and The change curve of Figure 5 (d) represents x2 and The change curve of Figure 5 (e) represents x3 and The change curve of Figure 5 (f) represents Δ1 and The change curve of Figure 5 (g) indicates The change curve of Figure 5 (h) represents Δ2 and The change curve of Figure 5 (i) Representation The change curve.

[0156] The least mean square root (RMSE) is used to illustrate the tracking performance of the three controllers, where the least mean square root formula is as follows:

[0157]

[0158] Among them, R in,i is the reference signal, R out,i is the information fed back from the sensor, and n represents the signal length.

[0159] The three controllers are applied to the electro-hydraulic servo system respectively, and the error peaks and minimum root mean square (RMSE) corresponding to the three controllers are obtained. The results are shown in the following table:

[0160] Table 1 Error peak and minimum root mean square RMSE corresponding to the three controllers

[0161] Controller Type <![CDATA[Peak error |z1| / m]]> RMSE / m Backstepping controller 0.0018 <![CDATA[9.5559×10 -4 ]]> Output Limited Controller <![CDATA[5.9814×10 -4 ]]> <![CDATA[3.5638×10 -5 ]]> Controller Based on Extended Sliding Mode Observer <![CDATA[5.9814×10 -4 ]]> <![CDATA[2.5242×10 -5 ]]>

[0162] As shown in Table 1, the tracking error of the backstepping controller exceeds 0.001m, and both the output limited controller and the controller based on the extended sliding mode observer proposed in the embodiment of this specification can ensure that the tracking error meets the requirements. In addition, among the minimum root mean squares of the three, the minimum root mean square of the controller based on the extended sliding mode observer proposed in the embodiment of this specification is the smallest, indicating that the tracking performance of the controller based on the extended sliding mode observer is the best.

[0163] According to the results of the three controllers, combined with Figure 3 , Figure 4 , Figure 5 As shown in Table 1, the three controllers can stabilize the electro-hydraulic servo system and keep the tracking error of the system within a certain range. Among them, the tracking error of the traditional backstepping controller cannot be guaranteed to be within 0.001m, the tracking error of the output limited controller can be guaranteed to be within 0.001m, and the tracking error set by the controller is limited to 0.001m, which meets the requirements. The tracking error of the output limited controller based on the extended sliding mode observer can be guaranteed to be within 0.001m, and the tracking error set by the controller is limited to 0.001m, which also meets the requirements. In addition, the extended sliding mode observer can compensate for external interference. Due to the compensation of the extended sliding mode observer for external interference, the tracking accuracy of the system is further improved; in summary, the output limited controller based on the extended sliding mode observer effectively improves the tracking accuracy of the system.

[0164] The present specification also provides a control device for an electro-hydraulic servo system, such as Figure 6 As shown, the device includes: at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, and the instructions are executed by the at least one processor so that the at least one processor can: construct a mathematical model of a valve-controlled double-rod hydraulic cylinder; design an expanded sliding mode observer based on the mathematical model of the valve-controlled double-rod hydraulic cylinder; define a tracking error vector of the electro-hydraulic servo system so as to design a position tracking error limiting controller based on the tracking error vector of the electro-hydraulic servo system and the expanded sliding mode observer; and use the position tracking error limiting controller to control the electro-hydraulic servo system so that the electro-hydraulic servo system operates stably.

[0165] The embodiments of this specification also provide a non-volatile computer storage medium storing computer executable instructions, wherein the computer executable instructions are configured to: construct a mathematical model of a valve-controlled double-rod hydraulic cylinder; design an expanded sliding mode observer based on the mathematical model of the valve-controlled double-rod hydraulic cylinder; define a tracking error vector of an electro-hydraulic servo system so as to design a position tracking error limiting controller based on the tracking error vector of the electro-hydraulic servo system and the expanded sliding mode observer; and use the position tracking error limiting controller to control the electro-hydraulic servo system so that the electro-hydraulic servo system operates stably.

[0166] Each embodiment in this specification is described in a progressive manner, and the same or similar parts between the embodiments can be referred to each other, and each embodiment focuses on the differences from other embodiments. In particular, for the device, equipment, and non-volatile computer storage medium embodiments, since they are basically similar to the method embodiments, the description is relatively simple, and the relevant parts can be referred to the partial description of the method embodiment.

[0167] The above is a description of a specific embodiment of the specification. Other embodiments are within the scope of the appended claims. In some cases, the actions or steps recorded in the claims can be performed in an order different from that in the embodiments and still achieve the desired results. In addition, the processes depicted in the drawings do not necessarily require the specific order or continuous order shown to achieve the desired results. In some embodiments, multitasking and parallel processing are also possible or may be advantageous.

[0168] The above description is only one or more embodiments of this specification and is not intended to limit this specification. For those skilled in the art, one or more embodiments of this specification may have various changes and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of one or more embodiments of this specification shall be included in the scope of the claims of this specification.

Claims

1. A control method for an electro-hydraulic servo system, characterized in that: The method comprises: Construct a mathematical model of a valve-controlled double-rod hydraulic cylinder; Based on the mathematical model of the valve-controlled double-rod hydraulic cylinder, an expansion sliding mode observer is designed; Defining a tracking error vector of the electro-hydraulic servo system so as to design a position tracking error limiting controller according to the tracking error vector of the electro-hydraulic servo system and the extended sliding mode observer; Controlling the electro-hydraulic servo system using the position tracking error limiting controller so that the electro-hydraulic servo system operates stably; Construct a mathematical model of a valve-controlled double-rod hydraulic cylinder, including: Determine a hydraulic cylinder flow continuity equation and a load force balance equation, and construct a mathematical model of the valve-controlled double-rod hydraulic cylinder based on the hydraulic cylinder flow continuity equation and the load force balance equation; Determining a state variable of the electro-hydraulic servo system; Determining a state space equation of the electro-hydraulic servo system according to a specified state variable of the electro-hydraulic servo system; Based on the mathematical model of the valve-controlled double-rod hydraulic cylinder, an expansion sliding mode observer is designed, which specifically includes: According to the state space equation of the electro-hydraulic servo system, a 5th-order extended sliding mode observer is used, wherein the expression of the 5th-order extended sliding mode observer is as follows: in, is the system state variable x i , the estimated value of i=1,2,3. yes The estimated value of L i ,i=1,2,3,4,5. is the control gain of the extended sliding mode observer; based on The expression for the observation error dynamics is determined as: The extended sliding mode observer is determined by the equal value injection principle of the sliding mode observer and the specified saturation function. The expression of the extended sliding mode observer is as follows: Among them, δ i ,i=1,2,3.are three small positive real numbers.

2. The control method of an electro-hydraulic servo system according to claim 1, characterized in that: The expression of the hydraulic cylinder flow continuity equation is as follows: Among them, Q L The load flow of the hydraulic cylinder, Q1 is the flow of the hydraulic cylinder oil inlet, Q2 is the flow of the hydraulic cylinder oil return port, A p is the effective area of ​​the hydraulic cylinder piston, x p is the displacement of the hydraulic cylinder piston rod, C tl is the total leakage coefficient of the hydraulic cylinder, p L is the pressure difference between the two chambers of the hydraulic cylinder, V t is the total volume of the oil inlet chamber and the oil return chamber of the hydraulic cylinder, β e is the effective bulk elastic modulus of the hydraulic cylinder oil; The load force balance equation is expressed as follows: Where m is the total mass, B p is the viscous damping coefficient of the hydraulic cylinder, F L is the external force of the hydraulic cylinder, F F is the friction between the piston rod and the cylinder barrel of the hydraulic cylinder; The specified state variable is x is the specified state variable; The state space equation of the electro-hydraulic servo system is expressed as follows: Where θ1 = A p / m,θ2=B p / m,θ3=4A p β e / V t ,θ4=4C tl β e / V t ,θ5=4β e / V t , Δ1=Δθ1x3-Δθ2x2-F L / mF F / m+μ, Δ1 is used to represent the interference term caused by external load force, friction force, parameter change and structural vibration, Δθ1 and Δθ2 are used to represent the parameter changes of θ1 and θ2 respectively, Δ2=-Δθ3x2-Δθ4x3, Δ2 is used to represent the interference caused by the parameter changes of θ3 and θ4, Υ1 and Υ2 are the change rates of the two external interferences Δ1 and Δ2, y=x1 is the displacement output of the system, f1(x2,x3)=θ1x3-θ2x2, f2(x2,x3)=-θ3x2-θ4x3.

3. The control method of an electro-hydraulic servo system according to claim 2, characterized in that: The f1(x2, x3) and f2(x2, x3) satisfy the Lipschitz conditions with respect to x2 and x3, and there are four Lipschitz constants γ1, γ2, γ3 and γ4 that satisfy the following conditions:

4. The control method of an electro-hydraulic servo system according to claim 1, characterized in that: The tracking error vector of the electro-hydraulic servo system is: z=[z1,z2,z3] T =[y d -x1,x2-α1,x3-α2] T , Where z1 is the system output displacement tracking error, and |z1| <k b , k b The tracking error of the system is limited, and the output of the system satisfies k cl <x1<k cu , k cu =y d +k b , k cl =y d -k b , α1 and α2 are two virtual control quantities designed for the controller.

5. The control method of an electro-hydraulic servo system according to claim 1, characterized in that: According to the error vector of the electro-hydraulic servo system and the extended sliding mode observer, a position tracking error limiting controller is designed, which specifically includes: Based on the error vector of the electro-hydraulic servo system, the state space equation of the electro-hydraulic servo system and two estimated values ​​of the extended sliding mode observer are combined. and Determine a control law that meets the requirements, and the control law that meets the requirements makes the tracking error of the electro-hydraulic servo system satisfy |z1| <k b and And the expression of the control law that meets the requirements is as follows: Among them, k i , i=1,2,3 are control gains. If the control gain L i+3 , i=1,2 is appropriately selected as L i+3 >1 / 4k i+1 ,i=1,2, then |z1| <k b ; and z will fall into a bounded hypersphere H r , and keep at H r Inside, Among them, ξ i =L i+3 -1 / 4k i+1 ,i=1,2.

6. The control method of an electro-hydraulic servo system according to claim 1, characterized in that: After controlling the electro-hydraulic servo system using the position tracking error limiting controller so that the electro-hydraulic servo system operates stably, the method further includes: defining a Lyapunov function and calculating the derivative of the Lyapunov function with respect to time; Determining the positivity of the value of the derivative of the Lyapunov function with respect to time; When the value of the derivative of the Lyapunov function with respect to time is less than 0, it is determined that the electro-hydraulic servo system is in a stable operating state.

7. A control device for an electro-hydraulic servo system, characterized in that: The device comprises: at least one processor; and a memory in communication with the at least one processor; wherein, The memory stores instructions executable by the at least one processor, and the instructions are executed by the at least one processor to enable the at least one processor to perform the method according to any one of claims 1 to 6.

8. A non-volatile computer storage medium storing computer executable instructions, wherein the computer executable instructions are configured to: execute the method according to any one of claims 1 to 6.

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