What is a servo valve and what it eats
Good day. I spent some time studying the so-called "servo valves." And to my regret, there was practically no information about them in runet. Therefore, I decided to be the first and publish some of my knowledge and observations that may be needed by fellow students, and not only by them.
Management of an object using technical means without human intervention is called automatic control. The main task of automatic control is to maintain a certain law of changing one or more physical quantities in the control object.
The objects of control of technical systems are kinematic mechanisms, electrical systems, thermal, chemical and other technological processes. The state of an object is characterized by state variables, which include angular and linear coordinates, velocities, and other mechanical variables describing the movements of kinematic mechanisms; currents or voltages of electrical circuit elements; temperature and density of substances in thermal and chemical processes, and any other physical quantities. To smoothly go to the mat. Servo valve models I will introduce the concept of dynamic link.
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At once I will make a reservation that the article will deal with dynamic links of the second order.
The dynamic link is a mathematical model of the simplest node, the functioning of which is described by differential equations.
In simple terms, a dynamic link is a device that receives an input signal and receives a response to an output signal.
The functioning of many real dynamic links is described by second-order linear differential equations with constant coefficients:
In 1955, Bill Moog designed the servovalve. This is an electro-hydraulic mechanical device that allows you to control the powerful hydraulic flow of the working fluid weak electrical signals. The design was very successful. Since then, servo valves have been used in various automatic control systems. They are used in rockets, airplanes, machine tools and many other technical objects.
The following figure shows in simplified form a servo valve together with an actuator.
The servo valve includes an electromagnet and a spool. In the channel P under high pressure flows the working fluid. Depending on the position of the spool, the working fluid flows through the channel P1 or through the channel P2. The control electrical voltage u (t) is applied to the electromagnet. The field of the electromagnet causes the spool to move in one direction or another from the neutral position, which in turn opens or closes the corresponding holes through which the working fluid flows. In the neutral position of the spool, both channels are closed. If the spool moves in a positive direction from the neutral position, the channel P1 opens and the flow of working fluid flows through the channel P1 at a speed of x (t), which depends directly on the position of the spool. Channel P2 at this time switches to drain. If the spool moves to the negative side from the neutral position, then in this case the channel P1 switches to a drain, and the flow of working fluid flows through the channel P2 at a speed x (t), directly proportional to the position of the spool. (In this case, the rate should be considered negative, coinciding in sign with the sign of the spool position). Channels P1 and P2 are connected to the actuator, and the flowing working fluid causes the actuator piston to move to the desired position.
Servovalve according to a certain law converts the control function u (t) into the function x (t). The flow rate of the working fluid x (t) depends on the control voltage u (t) and, as practice shows, this dependence is well described by a second-order linear differential equation with constant, strictly positive coefficients. The response x (t) to the control u (t) is the solution to the Cauchy problem:
Thus, from a mathematical point of view, the servovalve is a second-order differential dynamic link.
Knowledge of the law, which describes the dynamics of the servo valve, opens up unlimited possibilities for designers and developers of control systems. Equations allow for computer simulation and rapid mathematical analysis, for example, using software systems such as MatLab, MathCAD, etc.
Dynamic links are fully characterized by their dynamic parameters A, B, and C. Knowing them, you can construct any characteristics of a dynamic link and determine how the link will react to any input.
For specific technical devices, these parameters are often hidden while it is necessary for practical calculations to know their exact meaning. Such a situation arises, for example, during repair work. Link parameters may change after prolonged use. In such cases, the idea of testing comes to the rescue. Many real dynamic links allow for test validation. You can send an arbitrary test signal to the input of the link and measure the response to it.
There is a problem of identifying the parameters of the dynamic link. What test signal should be fed to the input of the link and how should the measurement results be processed to restore its parameters? Below I will try to give one of the methods of such identification.
a, b, d are defined as follows:
The figure shows that the method worked. Parameters identified.
I will give an example of a code which solves diffur. And the rest, “this is so”, if someone is interested, then he can program the above formulas himself.
At the end I would like to note the following. As a result of this work, methods have been developed to identify the parameters of the dynamic link. The results of the numerical experiment confirm the correctness of the theoretical reasoning and the above formulas for practical calculation. All experiments on computers are performed in the Matlab package, the main advantage of which is the possibility of modeling, analysis and visualization of various dynamic processes.
The article describes an example that clearly demonstrates the stabilization of the response to a single signal. It was also found that the response to the harmonic signal over time becomes almost harmonic.
For those who do not quite understand what is happening here, I will tell the following. Just imagine that a servovalve is installed in an excavator. Like all technology over time, servovalves tend to break. In fact, my research is needed to repair these broken devices. Imagine that with a certain device I can remove A, B and C indicators from a broken servo valve, compare them with the initial ones (when the device functions normally), and then tweak something (bolts, screws), after which the servo valve will be as good as new. From a mathematical point of view, I don `t know anything other than x (t) - solutions of diffura, and only by it and the angular frequency (w) can I determine the coefficients of this diffura itself. These are the wonders.
Introduction
Management of an object using technical means without human intervention is called automatic control. The main task of automatic control is to maintain a certain law of changing one or more physical quantities in the control object.
The objects of control of technical systems are kinematic mechanisms, electrical systems, thermal, chemical and other technological processes. The state of an object is characterized by state variables, which include angular and linear coordinates, velocities, and other mechanical variables describing the movements of kinematic mechanisms; currents or voltages of electrical circuit elements; temperature and density of substances in thermal and chemical processes, and any other physical quantities. To smoothly go to the mat. Servo valve models I will introduce the concept of dynamic link.
')
Dynamic link
At once I will make a reservation that the article will deal with dynamic links of the second order.
The dynamic link is a mathematical model of the simplest node, the functioning of which is described by differential equations.
In simple terms, a dynamic link is a device that receives an input signal and receives a response to an output signal.
The functioning of many real dynamic links is described by second-order linear differential equations with constant coefficients:
Servo valves
In 1955, Bill Moog designed the servovalve. This is an electro-hydraulic mechanical device that allows you to control the powerful hydraulic flow of the working fluid weak electrical signals. The design was very successful. Since then, servo valves have been used in various automatic control systems. They are used in rockets, airplanes, machine tools and many other technical objects.
The following figure shows in simplified form a servo valve together with an actuator.
The servo valve includes an electromagnet and a spool. In the channel P under high pressure flows the working fluid. Depending on the position of the spool, the working fluid flows through the channel P1 or through the channel P2. The control electrical voltage u (t) is applied to the electromagnet. The field of the electromagnet causes the spool to move in one direction or another from the neutral position, which in turn opens or closes the corresponding holes through which the working fluid flows. In the neutral position of the spool, both channels are closed. If the spool moves in a positive direction from the neutral position, the channel P1 opens and the flow of working fluid flows through the channel P1 at a speed of x (t), which depends directly on the position of the spool. Channel P2 at this time switches to drain. If the spool moves to the negative side from the neutral position, then in this case the channel P1 switches to a drain, and the flow of working fluid flows through the channel P2 at a speed x (t), directly proportional to the position of the spool. (In this case, the rate should be considered negative, coinciding in sign with the sign of the spool position). Channels P1 and P2 are connected to the actuator, and the flowing working fluid causes the actuator piston to move to the desired position.
Servo valve as a dynamic link
Servovalve according to a certain law converts the control function u (t) into the function x (t). The flow rate of the working fluid x (t) depends on the control voltage u (t) and, as practice shows, this dependence is well described by a second-order linear differential equation with constant, strictly positive coefficients. The response x (t) to the control u (t) is the solution to the Cauchy problem:
Thus, from a mathematical point of view, the servovalve is a second-order differential dynamic link.
Knowledge of the law, which describes the dynamics of the servo valve, opens up unlimited possibilities for designers and developers of control systems. Equations allow for computer simulation and rapid mathematical analysis, for example, using software systems such as MatLab, MathCAD, etc.
The task of identifying the parameters of the dynamic link
Dynamic links are fully characterized by their dynamic parameters A, B, and C. Knowing them, you can construct any characteristics of a dynamic link and determine how the link will react to any input.
For specific technical devices, these parameters are often hidden while it is necessary for practical calculations to know their exact meaning. Such a situation arises, for example, during repair work. Link parameters may change after prolonged use. In such cases, the idea of testing comes to the rescue. Many real dynamic links allow for test validation. You can send an arbitrary test signal to the input of the link and measure the response to it.
There is a problem of identifying the parameters of the dynamic link. What test signal should be fed to the input of the link and how should the measurement results be processed to restore its parameters? Below I will try to give one of the methods of such identification.
Method of identification of the parameters of the second-order linear dynamic link by the response to the sum of the harmonic and the single signal
a, b, d are defined as follows:
Simulation in Matlab
The figure shows that the method worked. Parameters identified.
Matlab code
I will give an example of a code which solves diffur. And the rest, “this is so”, if someone is interested, then he can program the above formulas himself.
A =
B =
C =
w =
t=linspace(0,100,100000).'; p=struct('a',1/A,'B',B,'C',C,'w',w);
F=@(t,xy,p) [xy(2); p.a+pa*(cos(pw*t)-pB*xy(2)-pC*xy(1))];
[tt,xy]=ode45(F,t,[0;0],odeset,p);
x=xy(:,1); y=xy(:,2);Conclusion
At the end I would like to note the following. As a result of this work, methods have been developed to identify the parameters of the dynamic link. The results of the numerical experiment confirm the correctness of the theoretical reasoning and the above formulas for practical calculation. All experiments on computers are performed in the Matlab package, the main advantage of which is the possibility of modeling, analysis and visualization of various dynamic processes.
The article describes an example that clearly demonstrates the stabilization of the response to a single signal. It was also found that the response to the harmonic signal over time becomes almost harmonic.
For those who do not quite understand what is happening here, I will tell the following. Just imagine that a servovalve is installed in an excavator. Like all technology over time, servovalves tend to break. In fact, my research is needed to repair these broken devices. Imagine that with a certain device I can remove A, B and C indicators from a broken servo valve, compare them with the initial ones (when the device functions normally), and then tweak something (bolts, screws), after which the servo valve will be as good as new. From a mathematical point of view, I don `t know anything other than x (t) - solutions of diffura, and only by it and the angular frequency (w) can I determine the coefficients of this diffura itself. These are the wonders.
Source: https://habr.com/ru/post/127919/
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