CN112631133B - Hydraulic position servo system control method based on double energy accumulators - Google Patents

Hydraulic position servo system control method based on double energy accumulators Download PDF

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CN112631133B
CN112631133B CN202011579241.8A CN202011579241A CN112631133B CN 112631133 B CN112631133 B CN 112631133B CN 202011579241 A CN202011579241 A CN 202011579241A CN 112631133 B CN112631133 B CN 112631133B
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王伟平
杜文芳
李倩
高仕恒
胡建军
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Jiangsu Normal University
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    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
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    • F15—FLUID-PRESSURE ACTUATORS; HYDRAULICS OR PNEUMATICS IN GENERAL
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    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F15—FLUID-PRESSURE ACTUATORS; HYDRAULICS OR PNEUMATICS IN GENERAL
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Abstract

A hydraulic position servo system control method based on double accumulators comprises the following steps: firstly, establishing a mathematical model of an electro-hydraulic position servo system, and calculating ideal values of two-cavity pressure and oil supply pressure according to an expected track and a parameter nominal value so as to set an energy accumulator parameter; setting a robust controller based on ideal pressure and setting control rules of the switching valve and the unloading overflow valve; and finally, the stability and the energy conservation of the controller are proved and analyzed. The invention is different from the traditional hydraulic position servo control method, the system has the functions of energy saving and position control at the same time by switching the double hydraulic accumulators and controlling the proportional directional valve, and the multi-target problem of energy saving and position tracking is effectively solved on the premise of only using a position sensor.

Description

Hydraulic position servo system control method based on double energy accumulators
Technical Field
The invention relates to the technical field of electro-mechanical-hydraulic servo control, in particular to a hydraulic servo system energy-saving and position tracking multi-target control method based on double hydraulic accumulators.
Background
The electro-hydraulic servo system has the outstanding advantages of large power-weight ratio, quick dynamic response, good pressure and flow controllability, flexible power transmission and the like, and is widely applied to the fields of aviation, aerospace, automobiles, ships, engineering machinery and the like. With the development of these fields and the continuous progress of the technical level, a high-performance electro-hydraulic servo system is urgently needed as a support. The existing electro-hydraulic servo system only focuses on the tracking precision and ignores the energy consumption efficiency. Since the hydraulic servo system tends to move cyclically, considerable energy is wasted regardless of the energy consumption.
Aiming at the problem of low energy consumption of an electro-hydraulic servo system, some researches provide certain solutions. The adoption of the variable pump can improve the system efficiency to a great extent, but the response of the variable pump limits the further application of the variable pump in the field of electro-hydraulic servo control to a certain extent. The pressure loss can be reduced by using the variable pressure control, but it cannot solve a large amount of overflow energy loss.
Disclosure of Invention
The invention aims to provide a method for solving the problem of energy conservation and high-precision tracking of multiple targets of a hydraulic servo system, and the method is used for solving the problems in the prior art.
In order to achieve the above purpose, the technical scheme of the invention is as follows:
a hydraulic position servo system control method based on double energy accumulators, the system structure includes high pressure energy accumulator, low pressure energy accumulator, double energy accumulator switching valve and unloading overflow valve, the switching rule of the double energy accumulator switching valve is set to realize the oil supply of the energy accumulators with different pressure grades to the system, when the energy accumulator is used as the auxiliary power source to supply oil, the unloading overflow valve unloads the pump, when the pump supplies oil to the energy accumulator and the hydraulic cylinder, the unloading overflow valve is used as the safety valve, the control method includes:
step 1: establishing a hydraulic servo system mathematical model based on the double hydraulic accumulators;
and 2, step: calculating ideal two-cavity pressure of the hydraulic cylinder and ideal oil supply pressure according to the expected tracking track and the nominal value of the system parameter, thereby setting the parameters of the energy accumulator;
and 3, step 3: a robust controller based on the desired pressure is set and the control rules for the switching valve and the unloading spill valve are set.
Further, the step 1 comprises:
the supply pressure is expressed as
Figure BDA0002863976760000021
Wherein p is s For supply pressure, p h 、p l The pressures of the high-pressure accumulator and the low-pressure accumulator are respectively;
the model of the accumulator is derived from the ideal gas equation, i.e.
Figure BDA0002863976760000022
Wherein p is i H, l is accumulator pressure, n is gas index, V i0 I ═ h, l is the accumulator volume, p i0 I h, l is accumulator pre-charge pressure, Q ia H, l is the flow of the accumulator;
the working volume of the accumulator is
Figure BDA0002863976760000023
In the formula, p i1 ,p i2 I is h, l is the maximum and minimum working pressure of the accumulator, V iw H, l is the working volume of the accumulator;
a simplified model of the relief valve is as follows
Figure BDA0002863976760000024
Wherein Q r Is the flow of the safety valve, Q p For pump flow, Re mode is energy recovery mode, Id mode is idle mode;
in Re mode, the excess flow is completely absorbed by the accumulator, so the overflow flow is zero;
in idle mode, the overflow flow is equal to the flow provided by the pump when the system is unloaded;
the flow rate of the two chambers is related to the input signal as follows
Figure BDA0002863976760000025
Wherein Q 1 And Q 2 Flow rate of inlet and outlet chambers, k q Is the flow gain factor of the servo valve, A v Is the valve port area, k x For the gain of the valve, u is the PDV input signal, g 1 、g 2 The expression is as follows
Figure BDA0002863976760000026
Figure BDA0002863976760000027
Wherein p is 1 And p 2 Inlet and outlet chamber pressures, p, respectively t The pressure of the oil tank is used, and rho is the density of the oil liquid;
the pressure dynamics of the two chambers can be written as
Figure BDA0002863976760000031
Wherein A is 1 And A 2 Is the effective area of two chambers of the cylinder, C t ＝C i +C e As a total leakage coefficient, C e And C i Respectively an outer leakage coefficient and an inner leakage coefficient, beta e Is the effective bulk modulus, x, of the system p Is the piston position; h 2 beta e /V t In which V is t Is the total variable volume;
the force balance equation of the system is expressed as
Figure BDA0002863976760000032
Where m is the load mass, B c Is the viscous damping coefficient, k is the ambient stiffness, F L Periodic external loading forces induced periodically for the desired trajectory; f L A Fourier series fit with finite terms may be used;
Figure BDA0002863976760000033
the state variable vector of the system is defined as formula (10)
Figure BDA0002863976760000034
The state variables are reconstructed to equation (11),to convert the system into a strict feedback form, wherein a c ＝A 2 /A 1 ；
Figure BDA0002863976760000035
The overall system can be represented in the state space form of equation (12):
Figure BDA0002863976760000036
Figure BDA0002863976760000037
wherein d is 1 ,d 2 Representing the uncertainty and uncertainty nonlinearity of the parameter.
Further, step 2 comprises: to be provided with
Figure BDA0002863976760000038
Represents p i I is an ideal value of 1,2, s; in forward motion, i.e.
Figure BDA0002863976760000039
The ideal valve port equation is expressed as:
Figure BDA00028639767600000310
wherein
Figure BDA0002863976760000041
Is composed of
Figure BDA0002863976760000042
Ideal value of, Δ p 1 And Δ p 2 The valve port pressure difference of the proportional direction valve;
the desired pressure differential at the valve inlet is:
Figure BDA0002863976760000043
wherein u is max Is the maximum input signal absolute value of the proportional directional valve, and alpha is an adjusting parameter;
the desired valve outlet pressure differential is:
Figure BDA0002863976760000044
combining formula (8), if the oil tank pressure is zero, then the minimum oil supply pressure of the hydraulic cylinder in the extending stage is:
Figure BDA0002863976760000045
wherein p is emin Is the minimum supply pressure during the extension phase of the hydraulic cylinder;
the minimum oil supply pressure in the retraction stage of the hydraulic cylinder is as follows:
Figure BDA0002863976760000046
wherein p is emin Is the minimum supply pressure during the retraction phase of the hydraulic cylinder;
the minimum working pressure of the low-pressure accumulator and the high-pressure accumulator is defined as:
p l2 ＝p emin ,p h2 ＝p rmin (19)
defining the maximum working pressure of the high-pressure accumulator and the low-pressure accumulator as
p i1 ＝δp i2 ,i＝h,l (20)
Wherein δ >1 is a constant adjustment coefficient;
the working volume of the accumulator is as follows:
V iw ＝(A 1 +A 2 )L,i＝h,l (21)
wherein L is the stroke of the hydraulic cylinder;
volume V of accumulator i0 I ═ h, l can be derived from formula (3);
the desired oil supply pressure is expressed by the following expressions (1) and (2):
Figure BDA0002863976760000047
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0002863976760000051
Figure BDA0002863976760000052
ideal hydraulic cylinder two-chamber pressure
Figure BDA0002863976760000053
Can be derived from equations (15) and (8):
Figure BDA0002863976760000054
further, a robust controller based on ideal pressure is as follows:
defining the sliding mode is as follows:
Figure BDA0002863976760000055
wherein z is 1 ＝x 1 -x d Indicates the tracking error, k 1 Is the feedback gain;
differentiating equation (24) yields:
Figure BDA0002863976760000056
let x 3 Is a virtual control input, then x 3 Calculated value of (a) 2 Has the following forms:
Figure BDA0002863976760000057
which is alpha 2a Is a model compensation term, α 2s Is the model stabilizing term, k 2 Is the feedback gain, x 2 Obtained by differentiation of the displacement.
Let z 3 ＝x 3 -α 2 An error is expressed by substituting equation (26) for equation (25):
Figure BDA0002863976760000058
according to formula (12), z 3 Can be expressed as
Figure BDA0002863976760000061
The actual control signal may be expressed as
Figure BDA0002863976760000062
Wherein k is 3 Is the gain of the feedback that is,
Figure BDA0002863976760000063
further, the switching rule of the switching valve is as follows: when the hydraulic cylinder extends out, the oil is supplied to the low-pressure accumulator; the high pressure accumulator is supplied with oil when the hydraulic cylinder is retracted.
Further, the control rule of the unloading overflow valve is as follows: when the accumulator is used as auxiliary power source to supply oil, the unloading overflow valve can unload the pump, and when the pump is used to supply oil to accumulator and hydraulic cylinder, the unloading overflow valve can be used as safety valve.
Further, the method also comprises the step 4: the stability of the controller and the system energy conservation are verified.
Further, the step 4 comprises:
defining the Lyapunov equation as:
Figure BDA0002863976760000064
the derivative of the derivative V may prove to be less than or equal to 0, i.e. the controller is stable;
the system energy saving is demonstrated as follows:
for a conventional hydraulic servo system, the efficiency can be expressed as:
Figure BDA0002863976760000065
wherein p is L And Q L Respectively load pressure and load flow.
For a fixed displacement pump, the pump should provide a flow equal to or greater than the maximum no-load flow
Figure BDA0002863976760000066
By substituting formula (32) for formula (31)
Figure BDA0002863976760000067
Wherein
Figure BDA0002863976760000068
The maximum efficiency of the traditional hydraulic servo system is about 0.38 obtained by the formula.
The efficiency of the system in Re mode can be expressed as:
Figure BDA0002863976760000071
from the above equation, the maximum efficiency in Re mode can reach 1, while the Id mode system does not provide energy. The overall efficiency of the system is therefore higher than that of a conventional hydraulic servo system.
Compared with the prior art, the invention has the following beneficial technical effects:
compared with the traditional electro-hydraulic servo control system, the method can obviously improve the system efficiency on the premise of ensuring the tracking precision; compared with the energy-saving method of the existing electro-hydraulic servo system, the method can reduce throttling loss and cancel overflow loss on the premise of ensuring quick response, and theoretically has higher efficiency.
Drawings
Fig. 1 shows a hydraulic servo system based on dual hydraulic accumulators.
FIG. 2 is a schematic diagram of a hydraulic servo system energy-saving and position tracking multi-target control method based on double hydraulic accumulators.
Fig. 3 is a comparison of the proposed controller and PI controller tracking error for a sinusoidal desired signal.
Fig. 4 is a comparison of the proposed controller and PI controller tracking error for a square wave desired signal.
FIG. 5 is a graph of cylinder chamber pressure and supply pressure for a sinusoidal desired signal.
FIG. 6 is a graph of cylinder chamber pressure and supply pressure for a square wave desired signal.
Fig. 7 shows the power of the system under a sinusoidal, square wave desired signal, and the power of a conventional system.
Fig. 8 shows the power consumption of the system for a sinusoidal, square wave desired signal, and the power consumption of a conventional system.
1-a high pressure accumulator; 2-a low pressure accumulator; 3-a switching valve; 4-a proportional directional valve; 5-proportional relief valve/unloading relief valve; 6-a displacement sensor; 7-a mass block; 8-loading the system; 9-driving the system.
The specific implementation mode is as follows:
the technical solution of the present invention will be clearly and completely described below with reference to the accompanying drawings and specific embodiments. It is to be understood that the described embodiments are merely exemplary of the invention, and not restrictive of the full scope of the invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Examples
As shown in fig. 1, the system structure related to the method of the present invention includes a high-pressure accumulator 1, a low-pressure accumulator 2, a switching valve 3, a proportional directional valve 4, a proportional relief valve/unloading relief valve 5, a displacement sensor 6, a mass block 7, a loading system 8 and a driving system 9, the switching rules of the switching valves of the double accumulators are set to realize that the accumulators with different pressure levels supply oil to the system, when the accumulator is used as an auxiliary power source to supply oil, the unloading relief valve unloads a pump, and when the pump supplies oil to the accumulator and a hydraulic cylinder, the unloading relief valve is used as a relief valve.
As shown in FIG. 2, the method for controlling the hydraulic position servo system based on the double accumulators comprises the following steps:
step 1: establishing a hydraulic servo system mathematical model based on the double hydraulic accumulators;
step 2: calculating ideal two-cavity pressure of the hydraulic cylinder and ideal oil supply pressure according to the expected tracking track and the nominal value of the system parameter, thereby setting the parameters of the energy accumulator;
and 3, step 3: a robust controller based on the ideal pressure is set and the control rules of the switching valve and the unloading overflow valve are set.
Further, the step 1 comprises:
the oil supply pressure is expressed as
Figure BDA0002863976760000081
Wherein p is s For supply pressure, p h 、p l The pressures of the high-pressure accumulator and the low-pressure accumulator are respectively;
the model of the accumulator is derived from the ideal gas equation, i.e.
Figure BDA0002863976760000082
Wherein p is i H, l is accumulator pressure, n is gas index, V i0 I ═ h, l is the accumulator volume, p i0 I h, l is accumulator pre-charge pressure, Q ia H, l is the flow of the accumulator;
the working volume of the accumulator being
Figure BDA0002863976760000083
In the formula, p i1 ,p i2 I is h, l is the maximum and minimum working pressure of the accumulator, V iw H and l is the working volume of the accumulator;
a simplified model of the relief valve is as follows
Figure BDA0002863976760000084
Wherein Q r Is the flow of the safety valve, Q p For pump flow, Re mode is energy recovery mode, Id mode is idle mode;
in Re mode, the excess flow is completely absorbed by the accumulator, so the overflow flow is zero;
in idle mode, the overflow flow is equal to the flow provided by the pump when the system is unloaded;
in the present invention, the natural frequency of the servo valve is much higher than that of the hydraulic servo system, so the valve dynamics are often neglected without significant degradation of control performance. Therefore, the relationship between the valve port area and the valve input signal can be expressed by a simple proportional expression. According to the above analysis, the flow rate of the two chambers is related to the input signal as follows:
the flow rate of the two chambers is related to the input signal as follows
Figure BDA0002863976760000091
Wherein Q 1 And Q 2 Flow rate of inlet and outlet chambers, k q Is the flow gain factor of the servo valve, A v Is the valve port area, k x For the gain of the valve, u is the PDV input signal, g 1 、g 2 The expression is as follows
Figure BDA0002863976760000092
Figure BDA0002863976760000093
Wherein p is 1 And p 2 Inlet and outlet chamber pressures, p, respectively t The pressure of the oil tank is used, and rho is the density of the oil liquid;
the pressure dynamics of the two chambers can be written as
Figure BDA0002863976760000094
Wherein A is 1 And A 2 Is the effective area of two chambers of the cylinder, C t ＝C i +C e As a total leakage coefficient, C e And C i Respectively, the outer leakage coefficient and the inner leakage coefficient, beta e Is the effective bulk modulus, x, of the system p Is the piston position. In practice, h is related to the speed of the actuator. However, to utilize the proposed method, h is expressed as h ═ 2 β e /V t In which V is t Is the total variable volume, the difference between this value and the true value is concentrated in the uncertainty introduced later.
The force balance equation of the system is expressed as
Figure BDA0002863976760000095
Where m is the load mass, B c Is viscousDamping coefficient, k is the ambient stiffness, F L Periodic external loading forces induced periodically for the desired trajectory; f L A Fourier series fit with finite terms may be used;
Figure BDA0002863976760000096
the state variable vector of the system is defined as formula (10)
Figure BDA0002863976760000097
In order to convert the system into a strict feedback form, facilitating the extension of the setup process of the state observer, the state variables are reconstructed as equation (11), where a c ＝A 2 /A 1 ，
Figure BDA0002863976760000098
The overall system can be represented in state space form as equation (12):
Figure BDA0002863976760000101
Figure BDA0002863976760000102
wherein d is 1 ,d 2 Representing uncertainty and uncertainty nonlinearities of the parameters, such as external load fitting errors and unmodeled friction.
The step 2 comprises the following steps: in order to select a suitable accumulator to reduce the throttling losses as much as possible, it is necessary to calculate a minimum supply pressure. For offline analysis, the setup process uses expected values rather than actual values. For the sake of simplicity, it is preferred that,
Figure BDA0002863976760000103
is used to represent p i I is an ideal value of 1,2, s.
In a forward motion, i.e.
Figure BDA0002863976760000104
When, neglecting uncertainties such as leakage, the ideal valve port equation can be expressed as:
Figure BDA0002863976760000105
wherein
Figure BDA0002863976760000106
Is composed of
Figure BDA0002863976760000107
Ideal value of (d), Δ p 1 And Δ p 2 The valve port pressure difference of the proportional direction valve;
for a given trajectory, the pressure drop across the control valve with the valve fully open is minimal. But now the tracking error cannot be adjusted by means of the proportional directional valve. Therefore, if the opening degree of the control valve can be maintained at a high value, the contradiction can be resolved.
Thus, the desired pressure differential at the valve inlet is:
Figure BDA0002863976760000108
wherein u max Is the maximum input signal absolute value of the proportional directional valve, and alpha is an adjusting parameter;
the desired valve outlet pressure differential is:
Figure BDA0002863976760000109
according to the above analysis and in combination with equation (8), assuming that the tank pressure is zero, the minimum supply pressure during the extension phase of the hydraulic cylinder is:
Figure BDA0002863976760000111
wherein p is emin Is the minimum supply pressure at the extension stage of the hydraulic cylinder;
similar to the extension phase, the minimum supply pressure for the retraction phase of the hydraulic cylinder is:
Figure BDA0002863976760000112
wherein p is emin Is the minimum supply pressure of the hydraulic cylinder in the retraction phase;
the minimum working pressure of the low and high pressure accumulators is defined as:
p l2 ＝p emin ,p h2 ＝p rmin (19)
in order to minimize throttling losses, the difference between the maximum operating pressure and the minimum operating pressure should be relatively small. Thus, the maximum working pressure of the high and low pressure accumulators is defined as:
p i1 ＝δp i2 ,i＝h,l (20)
wherein δ >1 is a constant adjustment coefficient;
to reduce the accumulator volume and at the same time avoid frequent charging and discharging, the working volume of the accumulator is given by:
V iw ＝(A 1 +A 2 )L,i＝h,l (21)
wherein L is the stroke of the hydraulic cylinder;
volume V of accumulator i0 I ═ h, l can be derived from formula (3);
accumulator pre-charge pressure p i0 I-h, l is given by an empirical formula. The volume V of the energy accumulator i0 I ═ h, l can be derived from formula (3).
According to the above analysis in combination with equations (1) and (2), the oil supply pressure is desirably expressed as:
Figure BDA0002863976760000113
wherein the content of the first and second substances,
Figure BDA0002863976760000114
Figure BDA0002863976760000115
ideal two-chamber pressure of hydraulic cylinder
Figure BDA0002863976760000121
Can be derived from equations (15) and (8):
Figure BDA0002863976760000122
further, a robust controller based on ideal pressure is as follows:
defining the sliding mode is as follows:
Figure BDA0002863976760000123
wherein z is 1 ＝x 1 -x d Indicates the tracking error, k 1 Is the feedback gain;
differentiating equation (24) yields:
Figure BDA0002863976760000124
let x 3 Is a virtual control input, then x 3 Calculated value of (a) 2 Has the following forms:
Figure BDA0002863976760000125
wherein alpha is 2a Is a model compensation term, α 2s Is the model stabilizing term, k 2 Is the feedback gain, x 2 Obtained by differentiating the displacement.
Let z 3 ＝x 3 -α 2 An error is expressed by substituting equation (26) for equation (25):
Figure BDA0002863976760000126
according to formula (12), z 3 Can be expressed as
Figure BDA0002863976760000127
The actual control signal can be expressed as:
Figure BDA0002863976760000128
wherein k is 3 Is the gain of the feedback that is,
Figure BDA0002863976760000129
the switching rule of the switching valve is as follows: when the hydraulic cylinder extends out, oil is supplied to the low-pressure energy accumulator; the high pressure accumulator is supplied with oil when the hydraulic cylinder is retracted.
The control rule of the unloading overflow valve is as follows: when the accumulator is used as auxiliary power source to supply oil, the unloading overflow valve can unload the pump, and when the pump is used to supply oil to accumulator and hydraulic cylinder, the unloading overflow valve can be used as safety valve.
Further comprising the step 4: analyzing and verifying the stability of the controller and the energy conservation of the system:
defining the Lyapunov equation as:
Figure BDA0002863976760000131
the derivative of the derivative V may prove to be less than or equal to 0, i.e. the controller is stable;
the system energy savings are demonstrated as follows:
for a conventional hydraulic servo system, the efficiency can be expressed as:
Figure BDA0002863976760000132
wherein p is L And Q L Respectively load pressure and load flow.
For fixed displacement pumps, the pump should provide a flow equal to or greater than the maximum no-load flow
Figure BDA0002863976760000133
By substituting formula (32) for formula (31)
Figure BDA0002863976760000134
Wherein
Figure BDA0002863976760000135
The maximum efficiency of the traditional hydraulic servo system is about 0.38, which can be obtained by the formula.
The efficiency of the system in Re mode can be expressed as:
Figure BDA0002863976760000136
from the above equation, the maximum efficiency in Re mode can reach 1, while the Id mode system does not provide energy. The overall efficiency of the system is therefore higher than that of a conventional hydraulic servo system.
In the aspect of position tracking, the controller of the invention utilizes the ideal pressure setting robust controller obtained in the step 2 to control a proportional directional valve, so that the hydraulic cylinder tracks a given track. And the controller only needs to input a displacement signal; in terms of energy saving, the switching valve is switched according to the switching rule set in the step 3, so that the high-pressure accumulator and the low-pressure accumulator supply oil to the hydraulic cylinder according to the motion stage of the hydraulic cylinder, and pressure loss is reduced. The unloading overflow valve is respectively used as an unloading valve and a safety valve according to working conditions, so that overflow loss is eliminated. 3-8 are graphs comparing different tracking errors, pressure curves, power curves, and energy consumption curves when the desired trajectory is a sinusoidal signal and when the desired trajectory is a square wave signal. Compared with the traditional electro-hydraulic servo control system, the method can obviously improve the system efficiency on the premise of ensuring the tracking precision; compared with the energy-saving method of the existing electro-hydraulic servo system, the method can reduce throttling loss and cancel overflow loss on the premise of ensuring quick response, and theoretically has higher efficiency.

Claims (6)

1. A hydraulic position servo system control method based on double energy accumulators, the system structure includes high pressure energy accumulator, low pressure energy accumulator, double energy accumulator diverter valve and unloading overflow valve, the switching rule of the double energy accumulator diverter valve is set to realize the oil supply of the energy accumulators with different pressure grades to the system, when the energy accumulator is used as the auxiliary power source to supply oil, the unloading overflow valve unloads the pump, when the pump supplies oil to the energy accumulator and the hydraulic cylinder, the unloading overflow valve is used as the safety valve, the method is characterized in that, it includes:
step 1: establishing a hydraulic servo system mathematical model based on the double hydraulic accumulators;
and 2, step: calculating ideal two-cavity pressure of the hydraulic cylinder and ideal oil supply pressure according to the expected tracking track and the nominal value of the system parameter, thereby setting the parameters of the energy accumulator;
and step 3: setting a robust controller based on ideal pressure and setting control rules of a switching valve and an unloading overflow valve;
the step 1 comprises the following steps:
the oil supply pressure is expressed as
Figure FDA0003797939460000011
Wherein p is s For supply pressure, p h 、p l The pressures of the high-pressure accumulator and the low-pressure accumulator are respectively;
the model of the accumulator is derived from the ideal gas equation, i.e.
Figure FDA0003797939460000012
Wherein p is i H, l is accumulator pressure, n is gas index, V i0 I ═ h, l is the accumulator volume, p i0 H, l is accumulator pre-charge pressure, Q ia H, l is the flow of the accumulator;
the working volume of the accumulator being
Figure FDA0003797939460000013
In the formula, p i1 ,p i2 I is h, l is the maximum and minimum working pressure of the accumulator, V iw H, l is the working volume of the accumulator;
a simplified model of the unloading overflow valve is as follows
Figure FDA0003797939460000014
Wherein Q r Is the flow of the safety valve, Q p For pump flow, Re mode is energy recovery mode, Id mode is idle mode; in the energy recovery mode, the redundant flow is completely absorbed by the energy accumulator, so that the overflow flow is zero; in idle mode, the overflow flow is equal to the flow provided by the pump when the system is unloaded;
the flow rate of the two chambers is related to the input signal as follows
Figure FDA0003797939460000015
Wherein Q 1 And Q 2 Flow rate of inlet and outlet chambers, k q Is the flow gain factor of the servo valve, A v Is the valve port area, k x U is the PDV input signal, g is the gain of the valve 1 、g 2 The expression is as follows
Figure FDA0003797939460000021
Figure FDA0003797939460000022
Wherein p is 1 And p 2 Inlet and outlet chamber pressures, p, respectively t The pressure of the oil tank is used, and rho is the density of the oil liquid;
dynamic pressure writing of two chambers
Figure FDA0003797939460000023
Wherein A is 1 And A 2 Is the effective area of two chambers of the cylinder, C t ＝C i +C e As a total leakage coefficient, C e And C i Respectively an outer leakage coefficient and an inner leakage coefficient, beta e Is the effective bulk modulus, x, of the system p Is the piston position; h 2 beta e /V t In which V is t Is the total variable volume;
the force balance equation of the system is expressed as
Figure FDA0003797939460000024
Where m is the mass of the load, B c To be viscous dampingCoefficient, k is the environmental stiffness, F L Periodic external loading forces induced periodically for the desired trajectory; f L Fitting with a finite Fourier series;
Figure FDA0003797939460000025
the state variable vector of the system is defined as formula (10)
Figure FDA0003797939460000026
The state variables are reconstructed into equation (11) to transform the system into a strict feedback form, where a c ＝A 2 /A 1 ；
Figure FDA0003797939460000027
The overall system is represented in the state space form of equation (12):
Figure FDA0003797939460000028
Figure FDA0003797939460000031
wherein d is 1 ,d 2 Representing the uncertainty and uncertainty nonlinearity of the parameter.
2. The method of claim 1, wherein step 2 comprises: to be provided with
Figure FDA0003797939460000032
Represents p i I is an ideal value of 1,2, s; in a forward motion, i.e.
Figure FDA0003797939460000033
The ideal valve port equation is expressed as:
Figure FDA0003797939460000034
wherein
Figure FDA0003797939460000035
Is composed of
Figure FDA0003797939460000036
Ideal value of (a) p 1 And Δ p 2 The valve port pressure difference of the proportional direction valve;
the desired pressure differential at the valve inlet is:
Figure FDA0003797939460000037
wherein u max Is the maximum input signal absolute value of the proportional directional valve, and alpha is an adjusting parameter;
the desired valve outlet pressure differential is:
Figure FDA0003797939460000038
combination formula (8), if oil tank pressure is zero, then the minimum oil supply pressure of pneumatic cylinder stretching stage is:
Figure FDA0003797939460000039
wherein p is emin Is the minimum supply pressure during the extension phase of the hydraulic cylinder;
the minimum oil supply pressure of the hydraulic cylinder in the retraction stage is as follows:
Figure FDA00037979394600000310
wherein p is rmin Is the minimum supply pressure during the retraction phase of the hydraulic cylinder;
the minimum working pressure of the low-pressure accumulator and the high-pressure accumulator is defined as:
p l2 ＝p emin ,p h2 ＝p rmin (19)
defining the maximum working pressure of the high-pressure accumulator and the low-pressure accumulator as
p i1 ＝δp i2 ,i＝h,l (20)
Wherein δ >1 is a constant adjustment coefficient;
the working volume of the accumulator is as follows:
V iw ＝(A 1 +A 2 )L,i＝h,l (21)
wherein L is the stroke of the hydraulic cylinder;
accumulator volume V i0 I ═ h, l is derived from formula (3);
the desired oil supply pressure is expressed by the following expressions (1) and (2):
Figure FDA0003797939460000041
wherein the content of the first and second substances,
Figure FDA0003797939460000042
Figure FDA0003797939460000043
ideal two-chamber pressure of hydraulic cylinder
Figure FDA0003797939460000044
According to the formulas (15) and (8)Leading out:
Figure FDA0003797939460000045
3. the method of claim 2, wherein the robust controller based on ideal pressure is as follows:
defining the sliding mode is as follows:
Figure FDA0003797939460000046
wherein z is 1 ＝x 1 -x d Indicates the tracking error, k 1 Is the feedback gain;
differentiating equation (24) yields:
Figure FDA0003797939460000047
let x 3 Is a virtual control input, then x 3 Calculated value of (a) 2 Has the following forms:
Figure FDA0003797939460000051
wherein alpha is 2a Is a model compensation term, α 2s Is a model stabilizing term, k 2 Is the feedback gain, x 2 Differential of displacement is adopted to obtain;
let z 3 ＝x 3 -α 2 An error is expressed by substituting equation (26) for equation (25):
Figure FDA0003797939460000052
according to formula (12), z 3 Is expressed as
Figure FDA0003797939460000053
The PDV input signal is represented as:
Figure FDA0003797939460000054
wherein k is 3 Is the gain of the feedback that is,
Figure FDA0003797939460000055
4. a method according to claim 3, characterized in that the switching rule of the switching valve is: when the hydraulic cylinder extends out, the oil is supplied to the low-pressure accumulator; the high pressure accumulator is supplied with oil when the hydraulic cylinder is retracted.
5. A method according to claim 3, wherein the control rules for the unloader overflow valve are: when the accumulator is used as auxiliary power source to supply oil, the unloading overflow valve can unload the pump, and when the pump is used to supply oil to accumulator and hydraulic cylinder, the unloading overflow valve can be used as safety valve.
6. The method of claim 2, further comprising step 4:
the Lyapunov equation is defined as:
Figure FDA0003797939460000056
the derivative of the derivative V proves to be less than or equal to 0, i.e. the controller is stable;
the system energy conservation performance is verified as follows:
the efficiency of the system in Re mode is expressed as:
Figure FDA0003797939460000057
wherein
Figure FDA0003797939460000058
p L And Q L Load pressure and load flow rate respectively;
from the above formula, the maximum efficiency in Re mode reaches 1, while the Id mode system provides no energy; where the Re mode is an energy recovery mode and the Id mode is an idle mode.
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