CN117742151A - Sliding mode variable structure control method of electrohydraulic servo valve - Google Patents
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Abstract
The invention discloses a sliding mode variable structure control method of an electrohydraulic servo valve, which comprises the steps of deducing a system state equation through a bonding diagram, selecting a sliding mode surface, constructing a system error state model, designing a sliding mode controller, writing a sliding mode equation, designing a system control variable, realizing sliding mode variable structure control of the electrohydraulic servo valve, simulating by using simulation software MATLAB/Simulink, and constructing a test platform to optimize and verify the designed sliding mode variable structure controller of the electrohydraulic servo valve. The invention solves the problems of slower tracking speed, lower tracking position precision, nonlinearity of the system, time-varying uncertainty factors and the like of the electrohydraulic servo control valve, further improves the control precision of the system, eliminates buffeting of the system and improves the robustness of the system control.
Description
Technical Field
The invention relates to a sliding mode variable structure control method of an electrohydraulic servo valve, in particular to a control method of the electrohydraulic servo valve, and belongs to the field of automatic control.
Background
With the high-speed development of science and technology, the electromechanical liquid control technology is widely applied in various industries. In high-risk operation, an electrohydraulic automatic control robot is used for replacing a person to finish submarine operation and construction of a toxic site; in the manufacturing industry, an electrohydraulic control manipulator is used for replacing a person to finish welding, paint spraying, assembly and the like on an automatic production line; the control device is used for controlling the position, speed and time of an automatic production line; the processing center is used for processing mechanical parts so as to realize high-precision automatic processing of hexahedrons. In automobiles and engineering vehicles, a machine liquid servo steering system is used; the automatic gear shifting device is used for unmanned automobile and automatic gear shifting. Steering systems for aircraft in the military industry; a steering engine device for radar tracking and ships; position control of missiles, automatic control of a launching frame and the like.
And (3) sliding mode variable structure control: also known as sliding mode control or variable structure control, is essentially a special type of nonlinear control, the nonlinearities of which appear as discontinuities in the control. This control strategy differs from other controls in that the "architecture" of the system is not fixed, but rather can be purposefully constantly changed in a dynamic process, depending on the current state of the system, forcing the system to move in accordance with a predetermined "sliding mode" of state trajectory. The sliding mode can be designed and is irrelevant to object parameters and disturbance, so that the sliding mode variable structure control has the advantages of quick response, insensitivity to parameter changes and disturbance, no need of on-line identification of a system, simple physical realization and the like. The sliding mode variable structure control appears in the 50 s of the 20 th century, and has developed over 70 years, so that the sliding mode variable structure control becomes a design method of a control system, and is suitable for linear and nonlinear, deterministic and uncertainty systems, centralized control, decentralized control and the like. The control method enables the system state to slide along the sliding mode surface through the switching of the control quantity, so that the system has invariance when being subjected to parameter variation and external interference.
Electro-hydraulic servo systems are typically nonlinear systems and there are many uncertainty factors (including but not limited to parameter variations, external disturbances, etc.). These non-linearities and uncertainties complicate the dynamic behavior of electrohydraulic servo systems and therefore make it difficult to build accurate mathematical models of the system. The robustness of the sliding mode variable structure control is strong, and the controlled object with parameter change and external disturbance can be effectively controlled through the adjustment and change of the controller structure, so that the sliding mode variable structure control is widely applied to the design of an electrohydraulic servo system. However, when the parameters of the system model are unknown in advance, it is difficult to obtain a proper equivalent control law, and the switching control for processing the uncertainty item in the conventional sliding mode variable structure control causes the system to generate a high-frequency jitter phenomenon. As the electrohydraulic servo control valve is used as a key element of electrohydraulic servo control, the problems of low tracking speed, low tracking position precision, poor robustness and the like exist due to the factors of nonlinearity, time-varying uncertainty and the like of the electrohydraulic servo system, so that the control precision of the intermediate system needs to be further improved, and the control robustness is improved.
In the prior art, the invention patent with the application number of CN202111219878.0 discloses an asynchronous sliding mode control method oriented to a random nonlinear system, and the invention adopts a hidden Markov model to solve the asynchronous problem in the design of a sliding mode controller; the invention is constructed by combining modal dependence with output feedback in the form ofMeanwhile, the asynchronous relation between the system and the sliding mode surface is characterized on the basis of a hidden Markov model. The invention patent with the application number of CN201910250486.7 discloses a chaotic track tracking method based on an active integral sliding mode, which comprises the following steps of: s1, for an n-dimensional chaotic system with uncertain modeling and external interference signals, establishing a track tracking error system according to a state equation and an expected track of the chaotic system; s2, combining an active control method with an integral sliding mode control method, establishing an active integral sliding mode controller equation, and carrying out balance control on a track tracking error system by adopting the active integral sliding mode controller equation; the tracking method provided by the invention can carry out balance control on the track tracking error system to form a closed loop system, the track tracking error gradually converges to zero, and the purpose of track tracking control of the chaotic system is achieved.
In view of the above, the prior art has not provided a solution to the above and related problems.
Disclosure of Invention
The invention relates to a sliding mode control method for an electrohydraulic servo valve, which mainly aims to realize the control of output displacement by controlling input current. In order to overcome the defects and shortcomings in the prior art, the tracking control of the position and the speed is realized through the sliding mode variable structure and the self-adaptive control, so that the problems of uncertainty and complex nonlinearity of parameters of the electrohydraulic servo control valve are effectively solved, a sliding mode control method with better effect is provided for eliminating buffeting phenomenon generated by a conventional sliding mode variable structure control system, and the tracking dynamic performance of the system is further improved.
The invention is realized by the following technical scheme:
a sliding mode variable structure control method of an electrohydraulic servo valve comprises the following steps:
s1, constructing a system bonding diagram, and deducing and establishing a system state equation according to causal relations among elements in the system bonding diagram;
s2, designing a sliding mode surface according to a system state equation to obtain an error element matrix, and establishing a system error state model;
s3, selecting a sliding mode surface to design a sliding mode controller according to a system error state model, establishing a sliding mode equation by utilizing a sliding mode condition and an equivalent control method, and calculating to obtain a system control variable u j The sliding mode variable structure control of the system is realized.
Preferably, the bonding diagram comprises four subsystem bonding diagrams which are respectively built up of an electronic amplifier, a permanent magnet moving iron type torque motor, a front nozzle valve and a slide valve, and then the keys with the same number are connected to form a total bonding diagram.
Preferably, the system state equation is:
wherein,the system state variable derivative is the system state variable derivative, X is the system state variable, U is the input control variable, A is the coefficient matrix of the system state variable, and B is the coefficient matrix of the input control variable.
Preferably, the system error state model is:
wherein,is the derivative of the error variable, E is the error variable, F is the outside worldThe disturbance variable U is an input control variable, A is a coefficient matrix of the system state variable, and B is a coefficient matrix of the input control variable.
Preferably, the sliding mode equation is:
wherein:the system state variable derivative is that x is a system state variable element, I is an identity matrix, S is a switching function, A is a coefficient matrix of the system state variable, B is a coefficient matrix of an input control variable, and C is a triangular matrix.
Preferably, the system control variable u j Is calculated according to the exponential approach law and the generalized sliding mode condition.
Preferably, the method further comprises:
s4, researching the capability of a servo valve output signal to track an input signal of the servo valve through a simulation analysis model, wherein the input signal is voltage, and the output signal is spool displacement of a spool valve.
Preferably, the simulation model is a system dynamic characteristic Simulink simulation model built by combining a Simulink module library according to a controlled object state space equation and a sliding mode equation relation between an input variable and an output variable of a designed sliding mode controller.
Preferably, the method further comprises:
s5, performing test verification on the basis of simulation data, and observing the influence of input signal change on the dynamic performance of the electrohydraulic servo valve;
and S6, optimally designing the sliding mode variable structure control method according to the test data obtained in the S4.
Preferably, a sliding mode controller designed by the sliding mode variable structure control method of the electrohydraulic servo valve as claimed in any one of claims 1 to 9, wherein the sliding mode controller is used for controlling variable u in a system j In the case of stabilization, the tracking delay time does not exceed 1s.
Compared with the prior art, the invention has the following advantages:
(1) The invention is to deduce and establish a system state equation by constructing a system bonding diagram, design a sliding mode surface, and design a sliding mode controller by selecting the sliding mode surface, thereby realizing the purpose of controlling the sliding mode variable structure of the system, having the functions of simple controller design, high system response speed and more stable control effect, solving the problems of uncertainty of parameters of the electrohydraulic servo control valve and buffeting phenomenon of a complex nonlinear system, improving the tracking dynamic performance parameters of the system and improving the robustness of control.
(2) The invention obtains the purpose of deducing the state space equation and then solving the output equation by respectively establishing four subsystem bonding graphs of the electronic amplifier, the permanent magnet moving iron type moment motor, the front nozzle valve and the slide valve and connecting the keys with the same number to form a total bonding graph.
(3) The invention is realized by establishingThe system state equation of (2) plays roles in describing the relation among the system state variables and solving an output equation.
(4) The invention is realized by establishingThe system error state model not only describes the relation between the error variable E and the input control variable U as well as the external disturbance variable F, but also can know the influence of the input control variable U on the error variable E through the system error state model, so that a sliding mode variable structure control method with smaller error is designed, and the aim of more accurately controlling the system is fulfilled.
(5) The invention is realized by establishingThe sliding modal equation of the model is used for describing the relation between the switching surface and the state variable, and then the purpose of solving the motion equation is achieved.
(6) The invention is calculated by the exponential approach law and generalized sliding mode conditionTo the system control variable u j The sliding mode variable structure control device has the function of enabling the sliding mode variable structure control to be more accurate.
(7) The invention researches the capability of the servo valve output signal to track the input signal through the simulation analysis model, achieves the aim of further improving the control precision of the system, and plays a role in optimizing the design parameters of the system.
(8) According to the invention, through the relation between the state space equation of the controlled object and the designed sliding mode controller variables and the combination of the system dynamic characteristic Simulink simulation model built by the Simulink module library, the system dynamic simulation research is realized, and the functions of optimizing design parameters and improving the system precision are achieved.
(9) According to the invention, through test verification performed on the basis of simulation data, the influence of input signal change on the dynamic performance of the electrohydraulic servo valve is observed, so that the design parameters are further optimized, and the aim of optimizing a sliding mode variable structure control method is fulfilled.
In summary, the invention realizes the tracking control of position and speed through the sliding mode variable structure and the self-adaptive control, effectively solves the problems of uncertainty and complex nonlinearity of parameters of the electrohydraulic servo control valve in the prior art, and the problems of slower tracking speed, lower tracking position precision and the like of the electrohydraulic servo control valve caused by the problems, reduces or eliminates the buffeting phenomenon in the system control process, improves the tracking dynamic performance of the system, further improves the system control precision, and improves the robustness of the system control. When the electrohydraulic servo valve adopting the sliding mode variable structure control method disclosed by the invention is used for tracking the track, the effect of tracking the ideal displacement vector by the actual displacement vector is good, when the initial value is 0.1mm, the tracking of the ideal track curve can be realized in about 1s, and the actual track curve is very close to the ideal track curve, the convergence is fast, the tracking error is smaller, and the engineering application value is higher.
Drawings
FIG. 1 is a system bond diagram of the present invention;
FIG. 2 is a simulation model of the system of the present invention;
FIG. 3 is a position tracking of the present invention;
FIG. 4 is a control input of the present invention;
FIG. 5 is a phase trajectory of the present invention;
FIG. 6 is a proportional valve test platform of the electro-hydraulic servo valve of the present invention;
FIG. 7 is a position tracking of the present invention;
fig. 8 is a control input of the present invention.
Detailed Description
The present invention will be described in further detail with reference to examples, but embodiments of the present invention are not limited thereto.
Example 1:
the embodiment discloses a sliding mode variable structure control method of an electrohydraulic servo valve, which comprises the following steps:
s1, constructing a system bonding diagram, and deducing and establishing a system state equation according to causal relations among elements in the system bonding diagram;
s2, designing a sliding mode surface according to a system state equation to obtain an error element matrix, and establishing a system error state model;
s3, designing a sliding mode controller, deducing and establishing a sliding mode equation according to sliding mode conditions and an equivalent control method, and calculating to obtain a system control variable u j The sliding mode variable structure control of the system is realized.
As shown in FIG. 1, S1, a system bonding diagram and a state space equation are established:
the embodiment is based on a nozzle type electrohydraulic servo valve structure (from Wang Chunhang master code, hydraulic control system [ M ]) in the prior art, beijing: mechanical industry Press, 2007:88-89.) to respectively establish four subsystem bonding diagrams of an electronic amplifier, a permanent magnet moving iron type moment motor, a front nozzle valve and a slide valve, and then the bonding diagrams of the same number keys are connected to form a total bonding diagram, wherein the bonding diagram is shown in figure 1. The generalized bond map symbols have the meanings given in Table 1; the physical quantities in the bond map are shown in Table 2.
TABLE 1 generalized bond map symbol meanings
| Parameter name | Parameter value | Parameter name | Parameter value |
| e | Potential variable | S f | Flow source |
| f | Flow variable | TF | Inverter |
| R | Resistive element | GY | Gyrator |
| C | Capacitive element | 0 | 0 section |
| I | Inertial element | 1 | 1-section |
| S e | Potential source |
TABLE 2 meaning of physical quantity in bond map of system
| Parameter name | Parameter value | Parameter name | Parameter value |
| S e1 | Input voltage | R 72 | Oil inlet gap liquid resistance |
| m a | Amplifier coefficient | R 81 | Oil return gap liquid resistance |
| I 11 ＝I 18 | Left and right coil inductor | C 73 | Liquid container of oil inlet cavity |
| R 12 ＝R 19 | ThrottlingLiquid resistance of up-down oil inlet of thin film of device | S e79 | Oil pressure is supplied |
| I 15 | Moment of inertia | S e84 | Load(s) |
| R 17 | Bearing damping | I 64 | Inertial force on slide core |
| C 16 | Spring tube elasticity | R 63 | Friction damping |
| R 38 ，R 47 | Liquid resistance on left and right sides of baffle | C 66 | Spring force of spring rod |
| C 36 ，C 45 | Sliding core two-end cavity liquid container | I 83 | Inertial force of load |
| R 34 ，R 43 | Liquid resistance of left and right fixed throttle mouth | R 82 | Friction damping |
| S e33 ，S e42 | Oil pump oil supply pressure |
Selecting as state variables the energy variables of the energy storage elements with integral causality, which are p 11 ，p 15 ，q 16 ，p 18 ，q 36 ，q 45 ，p 64 ，q 66 ，p 83 Nine. And q 73 Satisfying the differential causal relationship, algebraic deduction is performed when the system state equation is established.
Setting system state variables:
X＝[p 11 p 15 q 16 p 18 q 36 q 45 p 64 p 66 p 83 ] T (1)
wherein: x is a system state variable and T is a transposed matrix symbol.
The pressure provided by the oil pump is input, and the back pressure flowing back to the oil tank is set to zero, so the input control variable is:
U＝[s e1 s e33 s e42 s e79 s e84 ] T (2)
wherein: s is S e1 S is the input voltage e33 Oil supply pressure for oil pump S e42 Oil supply pressure for oil pump S e79 To supply oil pressure S e84 For the load, T is the transpose matrix symbol.
The energy storage element characteristic equation with integral causal relation can be written by a bonding diagram:
wherein: c 16 C is the elasticity of the spring tube 36 C, liquid volume of cavities at two ends of slide core 45 C, liquid volume of cavities at two ends of slide core 66 E is the elasticity of the spring rod 16 Is a 16-key potential variable, e 36 Is a 36-key potential variable, e 45 Is a 45-key potential variable, e 66 Is 66 key potential variable, f 11 Is 11 key stream variable, f 15 15 key flow variable, f 18 Is 18 key stream variable, f 64 Is a 64 key stream variable, f 83 For the 83 key stream variable, I 83 The inertial force of the load is i is the number.
The energy storage element characterization equation with differential causal relationship can also be derived:
q 73 ＝c 73 e 73 (4)
and:
e 73 ＝s e79 (5)
wherein: q 73 C is an energy variable 73 E is the elasticity of the spring tube 73 Is 73 key potential variable s e79 For supplying a voltage.
Resistive element characterization equations can be written by bond patterns:
in formula (6): e, e 12 Is a 12-bond potential variable, f 12 Is a 12-key flow variable, R 12 For supplying voltage e 17 Is 17 key potential variable, f 17 Is 17 key flow variable, R 17 E is bearing damping 19 Is 19 key potential variable, f 19 Is 19 key flow variable, R 19 E, oil liquid resistance is fed up and down for the throttle film 34 Is 34 key potential variable, f 34 For 34 key flow variable, R 34 Is the liquid resistance of the left fixed throttle, e 38 Is 38 key potential variable, f 38 As 38 key flow variable, R 38 Is the liquid resistance at the left side of the baffle, e 43 Is a 43-key potential variable, f 43 For the 43 key stream variable, R 43 Is right fixed choke liquidResistance e 47 Is 47 key potential variable, f 47 For the 47 key stream variable, R 47 E is the liquid resistance at the right side of the baffle plate 63 Is 63 key potential variable, f 63 Is 63 key flow variable, R 63 E is friction damping 72 Is a 72-key potential variable, f 72 For 72 key flow variable, R 72 For oil inlet gap liquid resistance, e 72 Is a 72-key potential variable, f 82 For 82 key flow variables, R 82 Is friction damping.
Potential and flow equations for energy storage elements with integral causal relationships can be written by bond graphs:
in the formula (7):is generalized momentum P 11 Derivative of>Is generalized momentum P 15 Derivative of>Is generalized momentum q 16 Derivative of>Is generalized momentum P 18 Derivative of>Is generalized momentum q 36 Derivative of>Is generalized momentum q 45 Is used for the purpose of determining the derivative of (c),is generalized momentum P 64 Derivative of>Is generalized momentum q 66 Derivative of>Is generalized momentum P 83 Derivative of c 16 C for spring tube elasticity 36 C, liquid volume of the left end cavity of the slide core 45 C, liquid volume of the right end cavity of the slide core 66 Is the elasticity of spring rod, I 11 Is the inductance of the left coil, I 15 For moment of inertia, I 18 For the right coil inductance, I 64 I is the inertial force on the slide core 83 Is the inertial force of the load, m a For the FT amplifier coefficient numbered a converter, m b For the FT amplifier coefficient numbered b converter, m c For the FT amplifier coefficient numbered c converter, m d For the FT amplifier coefficient numbered d converter, m e For the FT amplifier coefficient numbered e converter, m f For the FT amplifier coefficient numbered f converter, P 11 Is generalized momentum P 11 ，P 15 Is generalized momentum P 15 ，q 16 Is generalized momentum q 16 ，P 18 Is generalized momentum P 18 ，q 36 Is generalized momentum q 36 ，q 45 Is generalized momentum q 45 ，P 64 Is generalized momentum P 64 ，q 66 Is generalized momentum q 66 ，P 83 Is generalized momentum P 83 ，R 12 For oil inlet liquid resistance on the throttle film, R 17 For bearing damping, R 19 For oil inlet liquid resistance under the restrictor film, R 34 Is the liquid resistance of the left fixed throttle, R 38 Is the liquid resistance at the left side of the baffle, R 43 Is the liquid resistance of the right fixed throttle, R 47 R is the liquid resistance on the right side of the baffle plate 63 R is friction damping of slide core 82 R is friction damping of load a Is the coefficient of GY amplifier of a gyrator with the number a, r b Is the coefficient of GY amplifier of the number b gyrator, s is the integrating ring, s e1 For input voltage s e33 Left pressure of oil pump supply s e42 Right pressure of oil supply for oil pump s e79 In order to supply the oil pressure,s e84 is a load.
The coefficient matrix a of the system state variables is:
the elements in the coefficient matrix A are:
a 11 ＝-R 12 /I 11 ，a 12 ＝-r a /I 15 ，a 21 ＝r a /I 11 ，a 22 ＝-R 17 /I 15 ，a 23 ＝-1/c 16 ，a 24 ＝r b /I 18 ，a 25 ＝-1/m b c 36 ，a 26 ＝-1/m b c 45 ，a 27 ＝r a /sI 64 ，a 32 ＝1/I 15 ，a 42 ＝-r a /I 15 ，a 44 ＝-R 19 /I 18 ，a 52 ＝1/m b I 15 ，a 55 ＝-(1/R 34 c 36 +1/R 34 c 38 )，a 57 ＝-m c /I 64 ，a 62 ＝1/m b I 15 ，a 66 ＝-(1/R 43 c 46 +1/R 47 c 47 )，a 67 ＝-m c /I 64 ，a 75 ＝m 36 /c 36 ，a 76 ＝m d /c 45 ，a 77 ＝-(R 63 /I 64 +1/I 64 )，a 78 ＝-1/c 66 ，a 87 ＝1/I 64 ，a 99 ＝-R 82 /I 83 。
the coefficient matrix B of the input control variable is:
the elements in the coefficient matrix B are:
b 11 ＝m a ，b 41 ＝m a ，b 52 ＝1/R 34 ，b 63 ＝1/R 43 ，b 74 ＝-1/m e ，b 94 ＝m f ，b 95 ＝1。
and (3) making:
the state equation is expressed as:
wherein:the system state variable derivative is the system state variable derivative, X is the system state variable, U is the input control variable, A is the coefficient matrix of the system state variable, and B is the coefficient matrix of the input control variable.
With motor output torque T (e 30 ) And angular velocity ω (f) 30 ) For example, the output equation of the system is obtained:
wherein: e, e 30 For outputting torque T, c to the motor 16 For the elasticity of the spring tube, I 11 Is the inductance of the left coil, I 15 For the moment of inertia of the armature assembly, I 18 For the right coil inductance, I 64 R is the inertial force on the slide core a Is the coefficient of GY amplifier of a gyrator with the number of a and p 15 Is generalized momentum P 15 ，q 16 Is generalized momentum q 16 ，p 18 To be generalized momentum P 18 ，p 64 Is generalized momentum P 64 ，R 15 For damping of left bearing, R 17 And the damping is right bearing damping, and s is an integral ring.
Wherein: f (f) 30 For angular velocity ω, I 15 For armature assembly moment of inertia, p 15 Is generalized momentum P 15 。
And (3) making:
Y＝[y 1 y 2 ] T (14)
wherein: y is the observed output variable, Y 1 For outputting the first variable element, y 2 For the observed output second variable, T is the matrix rotor sign.
Then:
wherein: c is a state variable coefficient matrix, C 16 For the elasticity of the spring tube, I 11 Is the inductance of the left coil, I 15 For the moment of inertia of the armature assembly, I 18 For the right coil inductance, I 64 R is the inertial force on the slide core a Is the coefficient of GY amplifier system of gyrator, r b Is the coefficient of the gyrator GY amplifier, R 15 For damping of left bearing, R 17 And the damping is right bearing damping, and s is an integral ring.
D＝0 (16)
Y＝Cx+Du (17)
Wherein: c is a state variable coefficient matrix, D is a state variable coefficient matrix, u is a system control variable, x is a system state variable element, Y is an observed output variable, and Y is an observed output variable element.
Because the system belongs to a multi-input-multi-output control system, the purpose of solving an output equation is to reflect the influence of an input variable on an output variable, so that more accurate control of the system for selecting a proper input variable is found out.
S2, designing a sliding mode surface according to a system state equation to obtain an error element matrix, and establishing a system error state model;
for a single input system:
X∈R n ，U∈R m
X＝[x 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 ] T
wherein:the system state variable derivative is the system state variable derivative, X is the system state variable, U is the input control variable, A is the coefficient matrix of the system state variable, and B is the coefficient matrix of the input control variable.
The design sliding die surface is as follows:
wherein:
C＝[c 1 c 2 …c n-1 1] T
parameter c 1 ，c 2 ，...c n-1 The method meets the following conditions:
p n-1 +c n-1 p n-2 +…+c 2 p+c 1
for Hurwitz, p is the operator. Then:
s(x)＝c 1 x 1 +c 2 x 2 +c 3 x 3 +…+c 8 x 8 +x 9 (20)
polynomial:
p 8 +c 7 p 6 +…+c 2 p+c 1
for Hurwitz, then:
p 8 +c 7 p 6 +…+c 2 p+c 1 ＝0 (21)
the real part of the eigenvalue is a negative number.
For a tracking control system, a sliding mode surface function is set as follows:
wherein: e (t) is the error of the error,the coefficient c > 0, which is the error derivative.
For a mimo system, let the error be:
e ij ＝u ij -x ij (23)
wherein: e, e ij For the error of the ith output at the jth input, u ij For system input, x ij I=1, 2,3.. 9,j =1, 2, 3..5 for the system output. Then:
wherein:for error derivative>Input derivative for system>For the system output derivative +.>For the system output derivative, u ij Input second derivative for system, +.>The second derivative is output for the system.
Therefore:
formula (26), and formula (28): n is the output number and m is the input number.
Then the error element matrix is:
establishing a system error state model:
wherein:the system is characterized in that the system is composed of an error variable derivative, an error variable, an input control variable, an external disturbance variable, a coefficient matrix of a system state variable and a coefficient matrix of the input control variable.
E＝[e 1 e 2 e 3 e 4 e 5 e 6 e 7 e 8 e 9 ] T
Wherein: e, e 1 For the first output error under the action of five inputs e 2 The same applies for the error of the second output under the effect of five inputs.
F＝[f 1 f 2 f 3 f 4 f 5 f 6 f 7 f 8 f 9 ] T
Wherein: f (f) 1 As disturbance variable element, f 2 The rest is the same as disturbance variable element.
A. B is still a coefficient matrix, and general expressions of formula (8) and formula (9) are:
the design principle of the sliding mode surface is as follows: a sliding mode refers to a state of the system being constrained to move on a sub-manifold. Typically, the initial state of the system is not necessarily on the sub-manifold, and the function of the variable structure controller is to trend and maintain the state trace of the system on the sub-manifold for a limited time, a process called reachability. The state trajectory of the system moves in a sliding mode and eventually tends to the origin, a process called sliding mode motion.
S3, selecting a sliding mode surface for sliding mode controller design, deducing and establishing a sliding mode equation according to sliding mode conditions and an equivalent control method, and calculating to obtain a system control variable u j The sliding mode variable structure control of the system is realized.
The sliding mode surface is selected first when designing the sliding mode controller. Since m=5, five switching planes are selected.
Setting:
S＝Cx (32)
wherein: s epsilon R m C is an m n coefficient matrix, where m is the row of the matrix and n is the column of the matrix.
s j ＝c j x，j＝1，2，3…m
j＝1，2，3...m
The sliding mode condition is as follows:obtaining:
j＝1，2，3...m
the equivalent control method comprises the following steps:
then:
u eq ＝-(CB) -1 CA x (36)
wherein: u (U) eq Is the equivalent control quantity.
The charging condition CB for existence of the sliding mode is not odd, so the sliding mode equation is as follows:
typically C is a triangular matrix, CB is not odd. Then C is:
c is a 5 row 9 column triangular matrix.
The system switching function is:
wherein: s is [ S ] 1 ，s 2 ，s 3 ，s 4 ，s 5 ] T X is [ X ] 1 ，x 2 ，x 3 …x 9 ] T 。
When sliding the mode s 1 When=0, the system motion equation is:
column vector derivative, x 1 : n-1 dimensional column vector, U 1 : m-1 dimensional column vectors; a is that 1 : (n-1) the (n-1) dimensional matrix, B 1 : (m-1) the (m-1) dimensional matrix, the elements of which can be found.
When sliding the mode s 1 =0 and s 2 When=0, the system motion equation is:
when sliding the mode s 1 ＝0、s 2 ＝0...s k When=0, the system motion equation is:
wherein: k=1, 2,3,4,5.
According to the corresponding elements of the matrix, a sliding mode equation can be written. And the design of system control variables, wherein the system sliding mode movement consists of approaching movement and sliding mode movement. Several typical approach laws are common as follows.
Isokinetic approach law:
exponential approach law:
power approach law:
general approach laws:
with an exponential approach law, m=5, then the system control variable:
u＝[u 1 u 2 u 3 u 4 u 5 ] T
the vector of the exponential approach law is expressed as:
wherein:
ε＝diag[ε 1 ε 2 ε 3 ε 4 ε 5 ]，ε i ＞0(48)
k＝diag[k 1 k 2 k 3 k 4 k 5 ]，k i ＞0(49)
sgns＝diag[sgn(s 1 )…sgn(s 5 )] T (50)
the switching function is:
the method is obtained by generalized sliding mode conditions:
c j (Ax+Bu)＝-ε j sgn(s j )-k j s j (52)
where j=1, 2,3,4,5. Solving for system control variable u j 。
The logic deducing sequence of each step in the sliding mode variable structure control method is as follows:
bonding diagram, system state equation, system error state model, sliding mode device design and system control variable design
Furthermore, in order to optimize design parameters, the capability of the output signal of the servo valve to track the input signal of the servo valve is researched, and the capability of the output signal of the servo valve to track the input signal of the servo valve is increased by S4, wherein the input signal is voltage, and the output signal is spool displacement of the spool valve.
Simulation is carried out by using MATLAB/Simulink software, and main parameters of the electro-hydraulic servo valve are shown in the following table 3:
TABLE 3 principal parameters of electrohydraulic servo valves
| Name of the name | Parameter value |
| Rated oil supply pressure/Pa | 200*10 5 |
| Rated flow/(L/min) | 15 |
| Rated current/mA | 10 |
| Spool diameter/mm | 5 |
| Diameter/mm of slide valve rod | 3 |
| Nozzle valve aperture/mm | 0.4 |
| Fixed throttle aperture/mm | 0.2 |
| Motor feedback rod stiffness/(N.m/rad) | 3.8 |
| Spring tube stiffness/(N.m/rad) | 10 |
| Magnetic spring rate/(N.m/rad) | 7.5 |
The main study is the ability of the servo valve output signal to track its input signal. Voltage(s) e1 ) For input, spool displacement x of spool valve 66 (q 66 ) Is output. According to the state space equation of the controlled object and the relation between designed sliding mode controller variables, a system dynamic characteristic Simulink simulation model built by combining a Simulink module library is shown in fig. 2:
the system dynamic characteristic Simulink simulation model comprises: the system comprises a Sine wave module (Sine wave module), a Clock module (Clock module) for displaying simulation time, a Mux module (signal mixing input module) for combining vectors or scalars into large vectors, an S-function module (S-function module) for inputting simulation control functions, a Chap4-4ctr1 module (control design program module) for designing a control program and a Toworkspace module (variable module for outputting information and data of a plurality of parameters to ensure that the input signals and the output signals can obtain corresponding data according to the design requirements of the Simulink simulation model, so that the capability of the output signals of the servo valves to track the input signals of the servo valves can be accurately researched.
Working principle of system dynamic characteristic Simulink simulation model: simulink is one of the toolkits of MATLAB, providing a graphical environment for interactive dynamic system modeling, simulation, and analysis. The system can perform modeling, simulation, analysis and other works of the system aiming at a control system, a signal processing system, a communication system and the like. The system which can be processed comprises a linear system and a nonlinear system; discrete, continuous and hybrid systems; single-task, multi-task discrete event systems.
The system model parameters and the simulation parameters of the system are set as follows: let sine function input be sint, initial condition of controlled object be [0.10,0.10 ]]The elements of coefficient matrices A and B of the error state equation (29) are calculated according to physical and structural parameters, and corresponding numerical values are set in a program according to simulation requirements. The numbers of each element of the vector epsilon and the vector k are set by a controller (47) of exponential approach. Setting a simulation step length of 0.10ms and a simulation time of 8s. The simulation results are shown in fig. 3,4 and 5. Simulation results show that: the electrohydraulic servo valve control system meets the requirements of stability and rapidness, the valve core displacement tracking input voltage is very stable, the precision is high, and the design requirements are met. From the simulation curve of FIG. 3, it can be seen that the electro-hydraulic servo valve has good effect of tracking the actual displacement vector of the valve core to an ideal displacement vector when tracking the track, and the ideal track curve is tracked after about 1s when the initial value is 0.1 mm. It can be seen from the simulation curve of fig. 4 that the control input u is stationary when the trajectory tracking control is performed. The change condition of the tracking error e and the error change rate de two track vectors at the phase plane can be seen from the simulation curve of fig. 5. Black solid line k i =0, black solid line k i Phase trajectory curve=10 … converges to node (0, 0).
Furthermore, in order to optimize the sliding mode variable structure control method, the influence of input signal change on the dynamic performance of the electrohydraulic servo valve is observed, and the rationality of design parameters is verified, so that the following steps are added:
s5, performing test verification on the basis of simulation data, and observing the influence of input signal change on the dynamic performance of the electrohydraulic servo valve;
and S6, optimally designing the sliding mode variable structure control method according to the test data obtained in the S4.
And performing test verification on the basis of the simulation data. The influence of the input change on the dynamic performance of the nozzle type electrohydraulic servo valve is observed, and a test platform is shown in fig. 6.
The experiment table consists of four parts, namely a hydraulic station, an electric control part, a vertical instrument cabinet and a data acquisition industrial personal computer. The industrial personal computer is a control core of the whole system, is internally provided with a high-precision data acquisition card and a standard analog output unit, and can realize CAT for the whole system. Chinese test software based on Window2k and XP operating system. The hydraulic system provides hydraulic oil and pressure for the tested product, and part of the hydraulic system applies load to the electrohydraulic servo valve; in addition, the hydraulic transmission system for supplying oil is provided, and the test bed is provided. The test control system mainly provides control signals, is connected with the control computer and the test bed, and provides input and output signals and the like.
The electrohydraulic servo valve was mounted on a test verification platform for experiments, and the test results are shown in fig. 7 and 8. Shown by fig. 7: the nozzle electrohydraulic servo valve is stabilized step by oscillating for 0.4s under the input excitation. Fig. 8 shows: when track tracking control is performed, the control input u is stable, and a short buffeting phenomenon occurs.
Although the embodiment uses the nozzle electrohydraulic servo valve as an example to carry out test verification and obtain a test result, the method for controlling the sliding mode of the servo valve by using the same working principle, namely adopting the sliding mode variable structure control method of the invention or adopting the sliding mode variable structure control method of the invention to carry out conversion setting, is applicable to the invention and belongs to the protection range of the sliding mode variable structure control method of the invention.
The sliding mode variable structure control method of the electrohydraulic servo valve in the embodiment is different from the conventional sliding mode variable structure control method in that: sliding mode variable structure control is essentially a special type of nonlinear control, the nonlinearity of which manifests as control discontinuities, and this control strategy differs from other controls in that the "structure" of the system is not fixed, but rather can be purposefully varied in a dynamic process according to the current state of the system (such as deviations and their derivatives, etc.), forcing the system to move along a state trajectory of a predetermined "sliding mode".
Furthermore, in order to design and obtain a sliding mode controller with more accurate system dynamic performance control, no system buffeting phenomenon and more robustness, the sliding mode variable structure control method of the electrohydraulic servo valve is adopted for design and optimization, the designed sliding mode controller has good effect of tracking an ideal displacement vector by an actual displacement vector when tracking a track, and an ideal track curve is tracked after about 1s when an initial value is 0.1mm, and the actual track curve is very close to the ideal track curve, converges fast, tracking error is smaller, and the sliding mode controller has higher engineering application value.
It should be noted again that: in the present embodiment of the present invention,for the system state variable derivative, A is the coefficient matrix of the system state variable, B is the coefficient matrix of the input control variable, C is the triangular matrix,>the method is characterized in that the method comprises the steps of taking an error variable derivative, taking an error variable as an E, taking an external disturbance variable as an F, taking an identity matrix as an I, taking a diagonal matrix as a K, taking a switching function as a S, taking U as an input control variable, taking X as a system state variable, taking X as a system state variable element and taking Y as an output variable. In the sliding mode variable structure control method of the electrohydraulic servo valve, various introduced parameters need to be clarified so as to avoid unnecessary repeated work caused by significant errors between dynamic performance and simulation and experimental verification data of the electrohydraulic servo valve in the using process of the control method due to substitution errors.
The foregoing description is only a preferred embodiment of the present invention, and is not intended to limit the present invention in any way, and any simple modification, equivalent variation, etc. of the above embodiments according to the technical principles of the present invention fall within the scope of the present invention.
Claims (10)
1. The sliding mode variable structure control method of the electrohydraulic servo valve is characterized by comprising the following steps of:
s1, constructing a system bonding diagram, and deducing and establishing a system state equation according to causal relations among elements in the system bonding diagram;
s2, designing a sliding mode surface according to a system state equation to obtain an error element matrix, and establishing a system error state model;
s3, selecting a sliding mode surface to design a sliding mode controller according to a system error state model, establishing a sliding mode equation by utilizing a sliding mode condition and an equivalent control method, and calculating to obtain a system control variable u j The sliding mode variable structure control of the system is realized.
2. The sliding mode variable structure control method of the electrohydraulic servo valve according to claim 1, wherein the system bonding diagram comprises four subsystem bonding diagrams of an electronic amplifier, a permanent magnet moving iron type torque motor, a front nozzle valve and a slide valve which are respectively established, and then the same number keys are connected to form a total bonding diagram.
3. The sliding mode variable structure control method of an electrohydraulic servo valve of claim 2 wherein said system state equation is:wherein (1)>The system state variable derivative is the system state variable derivative, X is the system state variable, U is the input control variable, A is the coefficient matrix of the system state variable, and B is the coefficient matrix of the input control variable.
4. The sliding mode variable structure control method of the electro-hydraulic servo valve according to claim 3, wherein the system error state model is:wherein (1)>The system is characterized in that the system is composed of an error variable derivative, an error variable, an external disturbance variable, an input control variable, a coefficient matrix of a system state variable and a coefficient matrix of the input control variable.
5. The sliding mode variable structure control method of an electrohydraulic servo valve of claim 4 wherein said sliding mode equation is:wherein: />The system state variable derivative is that x is a system state variable element, I is an identity matrix, S is a switching function, A is a coefficient matrix of the system state variable, B is a coefficient matrix of an input control variable, and C is a triangular matrix.
6. The method for controlling a sliding mode variable structure of an electrohydraulic servo valve of claim 5 wherein a system control variable u j Is calculated according to the exponential approach law and the generalized sliding mode condition.
7. The sliding mode variable structure control method of an electro-hydraulic servo valve according to claim 1, further comprising:
s4, researching the capability of a servo valve output signal to track an input signal of the servo valve through a simulation analysis model, wherein the input signal is voltage, and the output signal is spool displacement of a spool valve.
8. The sliding mode variable structure control method of the electrohydraulic servo valve according to claim 7, wherein the simulation model is a system dynamic characteristic Simulink simulation model built by combining a Simulink module library according to a controlled object state space equation and a sliding mode equation relation between an input variable and an output variable of a designed sliding mode controller.
9. The sliding mode variable structure control method of an electro-hydraulic servo valve according to claim 7, further comprising:
s5, performing test verification on the basis of simulation data, and observing the influence of input signal change on the dynamic performance of the electrohydraulic servo valve;
and S6, optimally designing the sliding mode variable structure control method according to the test data obtained in the S4.
10. A sliding mode controller designed by the sliding mode variable structure control method of the electrohydraulic servo valve as claimed in any one of claims 1 to 9, characterized in that the sliding mode controller is used for controlling variable u in a system j In the case of stabilization, the tracking delay time does not exceed 1s.
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