Any change or maintenance of a constant speed of the electric drive ensures targeted regulation of the torque developed by the motor. The moment is formed as a result of the interaction of the flux (flux linkage) created by one part of the motor with the current in the other part and is determined by the vector product of these two spatial moment-generating vectors. Therefore, the magnitude of the moment developed by the engine is determined by the modules of each vector and the spatial angle between them.
When building scalar control systems only the numerical values (modules) of the moment-forming vectors were controlled and regulated, but their spatial position was not controlled. Vector control principle lies in the fact that the control system controls the numerical value and position in space relative to each other of the moment-forming vectors. Hence, the task of vector control is to determine and force the instantaneous values of currents in the motor windings in such a way that the generalized vectors of currents and flux links occupy a position in space that ensures the creation of the required electromagnetic torque.
Electromagnetic torque generated by the motor:
where m is the design factor; , 2 - spatial
vectors of currents or flux links forming a moment; X- spatial angle between moment-generating vectors.
As follows from (6.53), the minimum values of the currents (flux links) that form the moment will be for the required value of the moment if the vectors X and 2 are perpendicular to each other, i.e. X = °.
In vector control systems, there is no need to determine the absolute spatial position of the vectors, and 2 in relation to the axes of the stator or rotor. It is necessary to determine the position of one vector relative to another. Therefore, one of the vectors is taken as base, and the position of the other controls the angle x.
Based on this, when constructing vector control systems, it is advisable to proceed from the mathematical description of electromagnetic and electromechanical processes expressed in coordinates tied to the base vector (coordinates And- v). Such a mathematical description is given in § 1.6.
If we take as the base vector and direct the coordinate axis And along this vector, then, based on (1.46), we obtain the following system of equations:
in these equations? v = , since the vector coincides with the coordinate axis And.
On fig. 6.31 shows a vector diagram of currents and flux linkages in the axes And- v ^ coordinate orientation And according to the rotor flux vector. It follows from the vector diagram that
Rice. B.31. Vector diagram of flux links and currents in axes u-v at M
With constancy (or slow change) n otocoupling rotor d "V u / dt \u003d resulting in i and = And Г = yji u + i v = i v
In this case, the rotor current vector G perpendicular to the rotor flux linkage. Since the rotor leakage flux 0 is significantly less than the flux in the machine gap H, t then at a constant flux linkage of the rotor, we can assume that the projection of the stator current vector on the coordinate axis v i v is equal to |/"| or /
The advantage of the adopted coordinate system u-v to build a system of vector control of the torque and speed of an induction motor is that the motor torque (6.54) is defined as the scalar product of two mutually perpendicular vectors: the rotor flux linkage * P and the active component of the stator current. Such a definition of torque, typical, for example, for DC motors independent excitation, it is most convenient for building an automatic control system.
Vector control system. The block diagram of such management is built on the basis of the following principles:
- ? a two-channel control system consists of a channel for stabilizing the rotor flux linkage and a channel for controlling the speed (torque);
- ? both channels must be independent, i.e. changing the adjustable values of one channel should not affect the other;
- ? the speed (torque) control channel controls the stator current component / v . The algorithm of operation of the torque control loop is the same as in the systems of slave speed control of DC motors (see § 5.6) - the output signal of the speed controller is a reference for the motor torque. By dividing the value of this job by the flux linkage modulus of the rotor And we get the task for the stator current component i v (Fig. 6.32);
- ? each channel contains an inner loop of currents / v and i and with current regulators that provide the necessary quality of regulation;
- ? received current values i v and i and through coordinate transformations are translated into the values i a and / p of a two-phase fixed coordinate system a - (3 and then in setting real currents in the stator windings in a three-phase coordinate system a-b-c;
- ? the signals of speed, rotor rotation angle, currents in the stator windings, necessary for calculations and formation of feedbacks, are measured by the corresponding sensors and then, using inverse coordinate transformations, are converted into the values of these quantities corresponding to the coordinate axes u-v.
Rice.
Such a control system provides fast control of the torque, and, consequently, the speed in the widest possible range (over 10,000:1). In this case, the instantaneous values of the moment of the asynchronous motor can significantly exceed the passport value of the critical moment.
In order to make the control channels independent of each other, it is necessary to introduce cross compensating signals e K0MPU and e compm to the input of each channel (see Fig. 6.32). The value of these signals can be found from the equations of the stator circuit (6.54). Expressing and CHK 1y in terms of the corresponding currents and inductances (1.4) and taking into account that when the axis is oriented And along the vector of the rotor flux linkage H / |y = 0 we get:
Where do we find
Where scattering coefficient.
Substituting (6.55) into (6.54) and taking into account that in the considered control system d x V 2u /dt = 0, we get
or 
new time constants; e i i e v - EMF of rotation along the axes u-v
To set independent quantities i and and /v needs to be offset e and And e v by introducing compensating stresses:
To implement the principles of vector control, it is necessary to directly measure or calculate (estimate) the module and the angular position of the rotor flux linkage vector using a mathematical model. The functional diagram of the vector control of an asynchronous motor with direct measurement of the flow in the air gap of the machine using Hall sensors is shown in fig. 6.33.
Rice. B.33. Functional diagram of direct vector control of an induction motor
The scheme contains two control channels: a control channel (stabilization) of the rotor flux linkage *P 2 and a speed control channel. The first channel contains an external loop of the rotor flux linkage, containing a PI flux-linkage controller RP and a flux-linkage feedback, the signal of which is formed using Hall sensors that measure the flow in the machine gap X? T along the axes ai(3. The real values of the flow are then recalculated in the PP block into the values of the rotor flux linkage along the a and p axes, and using the VF vector filter, the modulus of the rotor flux vector is found, which is fed as a negative feedback signal to the flux linkage controller RP and is used in as a divider in the speed control channel.
In the first channel, the internal current circuit is subordinated to the flux linkage circuit i and, containing a PI current controller RT1 and feedback on the actual value of the current / 1i, calculated from the real values of the currents of the stator phases using the phase converter PF2 and the coordinate converter KP1. The output of the current regulator RT1 is the voltage reference Ulu, to which the compensation signal of the second channel is added e kshpi(6.57). The resulting voltage reference signal is converted by means of the coordinate KP2 and phase PF2 converters into the specified values and voltage phases at the output of the frequency converter.
The rotor flux linkage control channel ensures that the flux linkage H* 2 remains constant in all modes of drive operation at the level of the set value x P 2set. If it is necessary to weaken the field, F*^ can vary within certain limits with a small rate of change.
The second channel is designed to control the speed (torque) of the engine. It contains an external velocity circuit and an internal current circuit / y subordinate to it. The speed reference comes from the intensity generator of the RFG, which determines the acceleration and the required speed value. Speed feedback is implemented by means of a DS speed sensor or a rotor angular position sensor.
The speed controller PC is adopted proportional or proportional-integral depending on the requirements for the electric drive. The output of the speed controller is the task for the moment developed by the engine L / ass. Since the moment is equal to the product of the current and the flux linkage of the rotor H / 2, then, dividing the value of the torque setting in the DB division block M rear on H / 2, we get the value of the current reference, which is fed to the input of the current regulator RT2. Further signal processing is similar to the first channel. As a result, we obtain a task for the motor supply voltage by phases, which determines the value and spatial position at each moment of time of the generalized stator voltage vector!? Note that the signals related to variables in the - coordinates are direct current signals, and the signals reflecting currents and voltages in air coordinates are alternating current signals that determine not only the modulus, but the frequency and phase of the corresponding voltage and current.
The considered vector control system is currently implemented in digital form on the basis of microprocessors. Various block diagrams of vector control have been developed and are widely used, differing in details from the one under consideration. So, at present, the actual values of flux linkages are not measured by magnetic flux sensors, but are calculated using a mathematical model of the engine, based on the measured phase currents and voltages.
In general, vector control can be assessed as the most efficient way to control AC motors, providing high accuracy and speed of control.
vector control
vector control is a control method for synchronous and asynchronous motors, which not only generates harmonic currents (voltages) of the phases (scalar control), but also provides control of the rotor magnetic flux. The first implementations of the vector control principle and algorithms of increased accuracy require the use of rotor position (speed) sensors.
In general, under vector control" is understood as the interaction of the control device with the so-called "space vector", which rotates with the frequency of the motor field.
Mathematical apparatus of vector control
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See what "Vector control" is in other dictionaries:
Kalka with him. vectorregelung. A method of controlling the rotation speed and/or torque of an electric motor by means of the action of the electric drive converter on the vector components of the electric motor stator current. In Russian-language literature in ... Wikipedia
The solution of the problem of optimal control of mathematical theory, in which the control action u=u(t) is formed as a function of time (thereby it is assumed that during the process no information, except for that given at the very beginning, enters the system ... ... Mathematical Encyclopedia
- (frequency controlled drive, VFD, Variable Frequency Drive, VFD) control system for the rotor speed of an asynchronous (or synchronous) electric motor. It consists of the actual motor and frequency converter ... Wikipedia
This term has other meanings, see CNC (meanings). This page is proposed to be merged with CNC. Explanation of the reasons and discussion on the Wikipedia page: To unification / 25 f ... Wikipedia
Stator and rotor of an induction machine 0.75 kW, 1420 rpm, 50 Hz, 230 400 V, 3.4 2.0 A The induction machine is an AC electric machine ... Wikipedia
- (DPR) part of the electric motor. In collector electric motors, the rotor position sensor is a brush-collector assembly, which is also a current switch. In brushless motors, the rotor position sensor can be of different types ... Wikipedia
DS3 DS3 010 Basic data Country of construction ... Wikipedia
An asynchronous machine is an alternating current electric machine, the rotor speed of which is not equal (less than) the rotational speed of the magnetic field created by the stator winding current. Asynchronous machines are the most common electrical ... ... Wikipedia
- What is vector control?
- Keep the current at 90 degrees.
The term "vector control" of electric motors is familiar to everyone who is at least somehow interested in the question of how to control an AC motor using a microcontroller. However, usually in any book on electric drives, the chapter on vector control is somewhere towards the end, consists of a bunch of hairy formulas with references to all the other chapters of the book. Why do not want to understand this issue at all. And even the simplest explanations still make their way through differential equilibrium equations, vector diagrams, and a bunch of other math. Because of what, there are approximately such attempts to somehow spin the engine without using the mat.chasti. But in fact, vector control is very simple, if you understand the principle of its operation “on the fingers”. And there it will be more fun to deal with formulas if necessary.
The principle of operation of a synchronous machine
Consider the principle of operation of the simplest AC motor - a synchronous machine with permanent magnets. A convenient example is a compass: its magnetic needle is the rotor of a synchronous machine, and the Earth's magnetic field is the magnetic field of the stator. Without an external load (and there is none in the compass, except for friction and liquid that dampens the vibrations of the arrow), the rotor is always oriented along the stator field. If we hold the compass and rotate the Earth under it, then the arrow will spin after it, doing the work of mixing the liquid inside the compass. But there is a slightly simpler way - you can take an external magnet, for example, in the form of a rod with poles at the ends, the field of which is much stronger than the Earth's magnetic field, bring it to the compass from above and rotate the magnet. The arrow will follow the rotating magnetic field. In a real synchronous motor, the stator field is created by electromagnets - current-carrying coils. The winding schemes there are complex, but the principle is the same - they create a magnetic field with the stator, directed in the right direction and having the right amplitude. Let's look at the following figure (Figure 1). In the center is a magnet - the rotor of a synchronous motor (the "needle" of the compass), and on the sides are two electromagnets - coils, each creating its own magnetic field, one in the vertical axis, the other in the horizontal.
Figure 1. The principle of operation of a synchronous electric machine
The magnetic flux of the coil is proportional to the current in it (in the first approximation). We will be interested in the magnetic flux from the stator in the place where the rotor is located, i.e. in the center of the figure (we neglect edge effects, scattering, and everything else). The magnetic fluxes of two perpendicular coils are added vectorially, forming one common flux for interaction with the rotor. But since the flux is proportional to the current in the coil, it is convenient to draw the current vectors directly, aligning them with the flux. The figure shows some currents Iα And Iβ, which create magnetic fluxes along the axes α and β, respectively. Total stator current vector I s creates a co-directional stator magnetic flux. Those. in fact I s symbolizes an external magnet, which we brought to the compass, but created by electromagnets - coils with current.
In the figure, the rotor is located in an arbitrary position, but from this position the rotor will tend to turn according to the stator magnetic flux, i.e. by vector I s(the position of the rotor in this case is shown by the dotted line). Accordingly, if current is applied only to the phase α
, say Iα\u003d 1A, the rotor will stand horizontally, and if in β, vertically, and if you apply Iβ= -1A then it will flip 180 degrees. If you supply current Iα according to the law of sine, and Iβ according to the cosine law of time, a rotating magnetic field will be created. The rotor will follow it and spin (like a compass needle follows the rotation of a magnet by hand). This is the basic principle of operation of a synchronous machine, in this case two-phase with one pair of pluses.
Let's draw a graph of the motor torque depending on the angular position of the rotor shaft and the current vector I s stator - angular characteristic of a synchronous motor. This dependence is sinusoidal (Figure 2).
Figure 2. Angular characteristic of a synchronous machine (there is some historical confusion with the signs of moment and angle, which is why the characteristic is often drawn inverted relative to the horizontal axis).
To get this graph in practice, you can put a torque sensor on the rotor shaft, then turn on any current vector, for example, simply apply current to phase α. The rotor will turn to the corresponding position, which must be taken as zero. Then, through the torque sensor with “hands”, you need to turn the rotor, fixing the angle on the graph at each point θ , which they turned, and the moment that the sensor showed. Those. you need to stretch the "magnetic spring" of the engine through the torque sensor. The largest moment will be at an angle of 90 degrees from the current vector (from the beginning). The amplitude of the resulting maximum torque M max is proportional to the amplitude of the applied current vector. If 1A is applied, we get, say, M max = 1 N∙m (newton * meter, unit of torque), if we apply 2A, we get M max = 2 N∙m.
It follows from this characteristic that the motor develops the greatest torque when the rotor is at 90° to the current vector. Since, when creating a control system on a microcontroller, we want to get the maximum torque from the motor with a minimum of losses, and losses, first of all, are the current in the windings, it is most rational to set the current vector always at 90 ° to the magnetic field of the rotor, i.e. perpendicular to the magnet in Figure 1. It is necessary to change everything the other way around - not the rotor goes to the current vector we set, but we always set the current vector at 90 ° to the rotor, no matter how it rotates there, i.e. "nail" the current vector to the rotor. We will regulate the moment of the engine by the amplitude of the current. The larger the amplitude, the higher the moment. And the frequency of rotation, the frequency of the current in the windings is no longer “our” business - what happens, how the rotor will rotate, it will be so - we control the moment on the shaft. Oddly enough, this is what is called vector control - when we control the stator current vector so that it is at 90 ° to the rotor magnetic field. Although some textbooks give broader definitions, up to such that vector control is generally called any control laws where “vectors” are involved, but usually vector control is understood as the above method of control.
Building a vector control structure
But how is vector control achieved in practice? Obviously, first you need to know the position of the rotor so that there is something to measure 90 ° relative to. This is easiest to do by installing, in fact, the position sensor on the rotor shaft. Then you need to figure out how to create a current vector, maintaining the desired currents in the phases α
And β
. We apply voltage to the motor, not current ... But since we want to support something, we need to measure it. Therefore, for vector control, phase current sensors are needed. Next, you need to assemble the vector control structure in the form of a program on the microcontroller that will do everything else. So that this explanation does not look like an instruction "how to draw an owl", let's continue the dive.
You can maintain the current by the microcontroller using a software PI (proportional-integral) current controller and PWM. For example, the current regulator structure for one phase α is shown below (Figure 3).
Figure 3. Current-loop control structure for one phase
Here the current setting i α_set- a certain constant, the current that we want to maintain for this phase, for example 1A. The task goes to the current regulator adder, the disclosed structure of which is shown above. If the reader does not know how the PI controller works, then, alas, ah. I can only recommend some of this. The output current regulator sets the phase voltage Uα. The voltage is supplied to the PWM block, which calculates the duty cycles (comparison settings) for the microcontroller's PWM timers, forming a PWM on a four-key bridge inverter to form this Uα. The algorithm can be different, for example, for a positive PWM voltage, the right rack is proportional to the voltage setting, the bottom switch is closed on the left, for a negative PWM, the left one, and the bottom one is closed on the right. Don't forget to add dead time! As a result, such a structure makes a software “current source” due to the voltage source: we set the value we need i α_set, and the given structure implements it with a certain speed.
Further, perhaps, some readers have already thought that before the vector control structure, the matter is small - you need to put two current regulators, for each phase of the regulator, and form a task on them depending on the angle from the rotor position sensor (RPS), i.e. e. do something like this structure (Figure 4):
Figure 4. Incorrect (naive) vector control structure
You can't do that. When the rotor rotates, the variables i α_set And i β_set will be sinusoidal, i.e. the current regulator setting will change all the time. The speed of the controller is not infinite, therefore, when the task is changed, it does not immediately work it out. If the task is constantly changing, then the regulator will catch up with it all the time, never reaching it. And with an increase in the speed of rotation of the engine, the lag of the real current from the given one will be more and more, until the desired angle of 90 ° between the current and the rotor magnet ceases to be similar to it at all, and the vector control ceases to be so. Therefore, they do it differently. The correct structure is as follows (Figure 5):
Figure 5. The structure of vector sensor control for a two-phase synchronous machine
Two blocks have been added here - BKP_1 and BKP_2: blocks of coordinate transformations. They do a very simple thing: they rotate the input vector by a given angle. Moreover, BPK_1 turns to + ϴ , and BKP_2 on - ϴ . That's the whole difference between them. In foreign literature they are called Park transformations. BKP_2 makes coordinate transformation for currents: from fixed axes α And β , tied to the motor stator, to the rotating axes d And q tied to the motor rotor (using the rotor position angle ϴ ). And BKP_1 does the reverse transformation, from setting the voltage along the axes d And q makes a transition to the axes α And β . I do not give formulas for transforming coordinates, but they are simple and very easy to find. Actually, there is nothing more complicated than school geometry (Figure 6):
Figure 6. Coordinate transformations from fixed axes α and β, tied to the motor stator, to rotating axes d And q attached to the rotor
That is, instead of "rotating" the task of the regulators (as it was in the previous structure), their inputs and outputs rotate, and the regulators themselves operate in a static mode: currents d, q and the outputs of the regulators in the steady state are constant. axes d And q rotate together with the rotor (this is how the signal from the rotor position sensor rotates them), while the axis controller q regulates exactly the current that at the beginning of the article I called “perpendicular to the rotor field”, that is, this is a torque-generating current, and the current d co-directed with the "rotor magnet", so we do not need it and we set it to zero. Such a structure is spared from the disadvantage of the first structure - the current regulators do not even know that something is spinning somewhere. They work in a static mode: they adjusted each of their currents, reached a given voltage - and that’s it, don’t run away from them like a rotor, they won’t even know about it: coordinate transformation units do all the work on turning.
To explain "on the fingers" you can give some analogy.
For linear traffic, let it be, for example, a city bus. It accelerates all the time, then slows down, then goes back and generally behaves as it wants: this is the rotor of the engine. You are also in a car nearby, driving in parallel: your task is to be exactly in the middle of the bus: “keep 90 °”, you are the current regulators. If the bus changes speed all the time, you must also change the speed accordingly and keep track of it all the time. But now let's make "vector control" for you. You climbed inside the bus, stood in the middle and hold on to the handrail - just like a bus, do not run away, you can easily cope with the task of "being in the middle of the bus." Similarly, current regulators, "rolling" in the rotating axes d, q of the rotor, live an easy life.
The above structure really works and is used in modern electric drives. Only it lacks a whole bunch of small "improvements", without which it is no longer customary to do it, such as compensation for cross-coupling, various restrictions, field weakening, etc. But the basic principle is just that.
And if you need to regulate not the drive torque, but still the speed (according to the correct angular velocity, rotational speed)? Well, then we put another PI controller - the speed controller (RS). At the input we give the speed reference, and at the output we have the torque reference. Since the axis current q is proportional to the torque, it is possible to simplify the output of the speed controller directly to the input of the axis current controller q, like this (Figure 7):
Figure 7. Speed controller for vector control
Here, ZI is the intensity adjuster, smoothly changes its output so that the engine accelerates at the desired pace, and does not drive at full current until the speed is set. Current speed ω
is taken from the handler of the rotor position sensor, since ω
is the derivative of the angular position ϴ
. Well, or you can just detect the time between sensor pulses ...
How to do the same for a three-phase motor? Well, actually, nothing special, we add another block and change the PWM module (Figure 8).
Figure 8. The structure of vector sensor control for a three-phase synchronous machine
Three-phase currents, just like two-phase ones, serve one purpose - to create a stator current vector I s, directed in the desired direction and having the desired amplitude. Therefore, three-phase currents can simply be converted into two-phase ones, and then leave the same control system that has already been assembled for a two-phase machine. In the English-language literature, such a “recalculation” is called the Clarke transformation (Edith Clarke is her), in our case - phase transformations. In the structure in Figure 8, respectively, this is done by the block of phase transformations. They are made again using the school geometry course (Figure 9):
Figure 9. Phase conversions - from three phases to two. For convenience, we accept the equality of the amplitude of the vector I s to the amplitude of the current in the phase
I don't think comments are needed. A few words about the current of phase C. You don’t need to put a current sensor there, since the three phases of the engine are connected in a star, and according to Kirchhoff’s law, everything that has flowed through two phases must flow out of the third (unless, of course, your engine has a broken insulation, and half did not leak somewhere on the body), so the current of phase C is calculated as a scalar sum of the currents of phases A and B with a minus sign. Although the third sensor is sometimes installed to reduce the measurement error.
You also need a complete rework of the PWM module. Usually for three-phase motors, a three-phase six-switch inverter is used. In the figure, the voltage reference is still received in two-phase axes. Inside the PWM module, using inverse phase transformations, this can be converted into voltages of phases A, B, C, which must be applied at this moment to the motor. But what to do next ... Options are possible. The naive method is to give each inverter rack a duty cycle proportional to the desired voltage plus 0.5. This is called sinusoidal PWM. It is this method that the author used in habrahabr.ru/post/128407. In this method, everything is fine, except that this method will underutilize the voltage inverter - i.e. the maximum voltage that will be obtained will be less than what you could get if you used a more advanced PWM method.
Let's count. Let you have a classic frequency converter powered by an industrial three-phase network 380V 50Hz. Here 380V is the linear (between phases) operating voltage. Since there is a rectifier in the converter, it will rectify this voltage and the DC bus will have a voltage equal to the amplitude linear voltage, i.e. 380∙√2=540VDC (at least no load). If we apply the sinusoidal calculation algorithm in the PWM module, then the amplitude of the maximum phase voltage that we can make will be equal to half the voltage on the DC bus, i.e. 540/2=270V. Let's recalculate into the current phase: 270/√2=191V. And now into the current linear: 191∙√3=330V. Now we can compare: we got 380V, and 330V came out ... And more with this type of PWM is impossible. To correct this problem, the so-called vector type PWM is used. In it, the output will again be 380V (in the ideal case, without taking into account all voltage drops). Vector PWM has nothing to do with vector motor control. It's just that a bit of school geometry is again used in its justification, which is why it is called vector. However, his work on the fingers cannot be explained, so I will send the reader to the books (at the end of the article) or to Wikipedia. I can also give a picture that hints a little at the difference in the operation of sinusoidal and vector PWM (Figure 10):
Figure 10. Change of phase potentials for scalar and vector PWM
Types of position sensors
By the way, what position sensors are used for vector control? Four types of sensors are most commonly used. These are a quadrature incremental encoder, a Hall element encoder, an absolute position encoder, and a selsyn encoder.
Quadrature encoder does not give out the absolute position of the rotor - by its impulses, it only allows you to determine how much you have traveled, but not where and from where (as the beginning and end are related to the location of the rotor magnet). Therefore, it is not suitable for vector control of a synchronous machine by itself. Its fiducial mark (index) saves the situation a little - it is one per mechanical revolution, if you get to it, then the absolute position becomes known, and from it you can already count how much you have traveled with a quadrature signal. But how to get to this label at the beginning of work? In general, this is not always inconvenient.
Hall element sensor is a rough sensor. It produces only a few pulses per revolution (depending on the number of Hall elements, for three-phase motors there are usually three, i.e. six pulses), allowing you to know the position in absolute terms, but with low accuracy. The accuracy is usually enough to keep the angle of the current vector so that the motor at least drives forward and not backward, but the torque and currents will pulsate. If the engine has accelerated, then you can start programmatically extrapolating the signal from the sensor over time - i.e. build a linearly varying angle from a rough discrete angle. This is done based on the assumption that the motor rotates at a roughly constant speed, something like this (Figure 11):
Figure 11. The operation of the position sensor on the Hall elements for a three-phase machine and extrapolation of its signal
Often a combination of an encoder and a Hall sensor is used for servo motors. In this case, it is possible to make a single software module for their processing, removing the disadvantages of both: to extrapolate the angle given above, but not by time, but by marks from the encoder. Those. inside, from front to front of the Hall sensor, an encoder works, and each Hall front clearly initializes the current absolute angular position. In this case, only the first movement of the drive will be suboptimal (not under 90 °), until it reaches some front of the Hall sensor. A separate problem in this case is the processing of the non-ideality of both sensors - symmetrically and uniformly Hall elements are rarely available ...
In even more expensive applications, absolute encoder with a digital interface (absolute encoder), which immediately gives the absolute position and allows you not to experience the problems described above.
If the motor is very hot, and also when increased angle measurement accuracy is required, use "analogue" selsyn sensor(resolver, rotating transformer). It is a small electrical machine used as a sensor. Imagine that in the synchronous machine we have considered in Figure 1, instead of magnets, there is another coil to which we apply a high-frequency signal. If the rotor is horizontal, then the signal will be induced only in the phase stator coil α
, if vertically, then only in β
, if you turn it over by 180, then the phase of the signal will change, and in intermediate positions it is induced back and forth according to the sine / cosine law. Accordingly, by measuring the amplitude of the signal in two coils, the ratio of this amplitude and the phase shift can also determine the position. By installing such a machine as a sensor to the main one, you can find out the position of the rotor.
There are many more exotic position sensors, especially for ultra-high precision applications such as electronic chip fabrication. There, any physical phenomena are already used in order to only find out the position most accurately. We will not consider them.
Simplifying vector control
As you understand, vector control is quite demanding - set position sensors to it, and current sensors, and vector PWM to it, and the microcontroller is not anyhow to calculate all this mathematics. Therefore, for simple applications, it is simplified. To begin with, you can eliminate the position sensor by making a sensorless vector control. To do this, use a little more mathematical magic, located in the yellow rectangle (Figure 12):
Figure 12. Sensorless vector control structure
An observer is a block that receives information about the voltage applied to the motor (for example, from a task for the PWM module) and about currents in the motor from sensors. An electric motor model works inside the observer, which, roughly speaking, tries to adjust its currents in the stator to those measured from a real motor. If she succeeded, then we can assume that the position of the rotor simulated inside the shaft also coincides with the real one and can be used for the needs of vector control. Well, this is, of course, quite simplified. The types of such observers cannot be counted. Each graduate student in the specialty "electric drive" is trying to invent his own, which is somehow better than others. The basic principle is tracking the EMF of the electric motor. Therefore, most often a sensorless control system is operable only at a relatively high speed, where the EMF is large. It also has a number of disadvantages compared to the presence of a sensor: you need to know the parameters of the engine, the speed of the drive is limited (if the speed changes dramatically, the observer may not have time to track it and “lie” for some time, or even “fall apart” completely) , setting up the observer is a whole procedure, for its high-quality work, you need to know the voltage on the motor exactly, accurately measure its currents, etc.
There is another simplification option. For example, you can do the so-called "auto-switching". In this case, for a three-phase motor, the complex PWM method is abandoned, the complex vector structure is abandoned, and the motor phases are simply turned on by the position sensor on the Hall elements, even sometimes without any current limitation. The current in the phases is not sinusoidal, but trapezoidal, rectangular, or even more distorted. But they are trying to make sure that the average current vector is still at 90 degrees to the "rotor magnet" by choosing the moment of switching on the phases. In this case, including the energized phase, it is not known when the current will increase in the motor phase. At a low speed, it does it faster, at a high speed, where the EMF of the machine interferes, slower, and the rate of current rise depends on the motor inductance, etc. Therefore, even including the phases at exactly the right time, it is not at all a fact that the average current vector will be in the right place and with the right phase - it can either lead or lag relative to the optimal 90 degrees. Therefore, in such systems, the “commutation advance” setting is introduced - in fact, it’s just time, how much earlier it is necessary to apply voltage to the motor phase, so that as a result the phase of the current vector is closer to 90 degrees. In a simple way, this is called "tuning the timings." Since the current in the electric motor during auto-switching is not sinusoidal, then if we take the sinusoidal machine discussed above and control it in this way, the moment on the shaft will pulsate. Therefore, in motors designed for auto-switching, the magnetic geometry of the rotor and stator is often changed in a special way to make them more suitable for this type of control: the EMF of such machines is made trapezoidal, due to which they work better in auto-switching mode. Synchronous machines optimized for autocommutation are called brushless direct current motors (BLDC) or in English BLDC (Brushless Direct Current Motor). The auto-switching mode is also often called the valve mode, and the motors working with it are valve ones. But these are all just different names that do not affect the essence in any way (but seasoned electric drives often suffer from SPGS in matters related to these names). There is a good video illustrating the principle of operation of such machines. It shows a motor reversed, with the rotor on the outside and the stator on the inside:
But there is a course of articles on such engines and the hardware of the control system.
You can even go for an even greater simplification. Switch the windings so that one phase is “free” all the time and no PWM is applied to it. Then you can measure the EMF (voltage induced in the phase coil) in it, and when this voltage passes through zero, use it as a rotor position sensor signal, because the phase of this induced voltage depends precisely on the position of the rotor. It turns out sensorless auto-switching, which is widely used in various simple drives, for example, in "regulators" for aircraft model propellers. At the same time, it must be remembered that the EMF of the machine appears only at a relatively high speed, therefore, to start, such control systems simply slowly sort out the phases, hoping that the motor rotor will follow the supplied current. As soon as the EMF appears, the auto-switching mode is activated. Therefore, a sensorless system (so simple, and most often complex too) is not suitable for tasks where the engine must be able to develop torque at near-zero speeds, for example, for a traction drive of a car (or its model), a servo drive of some mechanism, etc. P. But the sensorless system is successfully suitable for pumps and fans, where it is used.
But sometimes even more simplification is made. You can completely abandon the microcontroller, keys, position sensors and other things by switching the phases with a special mechanical switch (Figure 13):
Figure 13. Mechanical switch for switching windings
During rotation, the rotor itself switches its parts of the windings, changing the voltage applied to them, while the current in the rotor flows alternating. The commutator is positioned in such a way that the magnetic flux of the rotor and stator is again close to 90 degrees in order to achieve maximum torque. Such motors are naively called DC motors, but completely undeservedly: inside, after the collector, the current is still alternating!
Conclusion
All electric machines work in a similar way. In the theory of electric drive, there is even the concept of a “generalized electric machine”, to which the work of others is reduced. The “on the fingers” explanations shown in the article can in no way serve as a practical guide to writing microcontroller code. The article considered well if one percent of the information that is required for the implementation of this vector control. To do something in practice, you need, firstly, to know TAU, at least at the level of understanding how the PI controller works. Then you still need to study the mathematical description of both the synchronous machine and the synthesis of vector control. Also study vector PWM, find out what pole pairs are, get acquainted with the types of machine windings, and more. This can be done in the recent book “Anuchin A.S. Electric drive control systems. MPEI, 2015", as well as in "Kalachev Yu. N. Vector regulation (practice's notes)". The reader should be warned against diving into the formulas of the "old" textbooks on the drive, where the main focus is on considering the characteristics of electric motors when powered directly from a three-phase industrial network, without any microcontrollers and position sensors. The behavior of the engines in this case is described by complex formulas and dependencies, but for the problem of vector control they are almost of no use (if only studied for self-development). You should be especially careful with the recommendations of old textbooks, where, for example, it is said that a synchronous machine should not work at the maximum of its moment, since the work there is unstable and threatens to overturn - for vector control, all this is “bad advice”.
On which microcontroller you can make a full-fledged vector control, read, for example, in our article New domestic motor-control microcontroller K1921VK01T JSC "NIIET", and how to debug it in the article Methods for debugging microcontroller software in an electric drive. Also visit our website: there, in particular, two boring videos are posted, where they show in practice how to set up a current PI controller, as well as how a current-closed and vector sensorless control structure works. In addition, you can purchase a debug kit with a ready-made sensor vector control structure on a domestic microcontroller.
P.S.
I apologize to experts for not quite correct handling of some terms, in particular with the terms "flow", "flux linkage", "magnetic field" and others - simplicity requires sacrifice ...
According to the latest statistics, approximately 70% of all generated electricity in the world consumes an electric drive. And this percentage is growing every year.
With a properly selected method of controlling the electric motor, it is possible to obtain maximum efficiency, maximum torque on the shaft of the electric machine, and at the same time the overall performance of the mechanism will increase. Efficiently running electric motors consume a minimum of electricity and provide maximum efficiency.
For electric motors powered by a frequency converter, the efficiency will largely depend on the chosen method of controlling the electric machine. Only by understanding the merits of each method can drive engineers and designers get the best performance out of each control method.
Content:
Control methods
Many people working in the field of automation, but not closely involved in the development and implementation of electric drive systems, believe that the control of an electric motor consists of a sequence of commands entered using an interface from a control panel or a PC. Yes, from the point of view of the general hierarchy of controlling an automated system, this is correct, but there are still ways to control the electric motor itself. It is these methods that will have the maximum impact on the performance of the entire system.
For asynchronous motors connected to a frequency converter, there are four basic control methods:
- U / f - volt per hertz;
- U/f with encoder;
- Open-loop vector control;
- Closed-loop vector control;
All four methods use PWM pulse width modulation, which changes the width of a fixed signal by varying the pulse width to create an analog signal.
Pulse width modulation is applied to the frequency converter by using a fixed DC bus voltage. by quickly opening and closing (more correctly, switching) generate output pulses. By varying the width of these pulses, a "sine wave" of the desired frequency is obtained at the output. Even if the form of the output voltage of the transistors is pulsed, the current is still obtained in the form of a sinusoid, since the electric motor has an inductance that affects the shape of the current. All control methods are based on PWM modulation. The difference between the control methods is only in the method of calculating the applied voltage to the motor.
In this case, the carrier frequency (shown in red) represents the maximum switching frequency of the transistors. The carrier frequency for inverters is usually in the range of 2 kHz - 15 kHz. The frequency reference (shown in blue) is the output frequency reference signal. For inverters applicable in conventional drive systems, as a rule, lies in the range of 0 Hz - 60 Hz. When the signals of two frequencies are superimposed on each other, a transistor opening signal will be issued (indicated in black), which supplies power to the electric motor.
V/F control method
Volt-per-hertz control, most commonly referred to as V/F, is perhaps the easiest way to regulate. It is often used in simple electric drive systems due to its simplicity and the minimum number of parameters required for operation. This control method does not require mandatory installation of an encoder and mandatory settings for a frequency-controlled electric drive (but it is recommended). This results in lower costs for auxiliary equipment (sensors, feedback wires, relays, etc.). U / F control is quite often used in high-frequency equipment, for example, it is often used in CNC machines to drive spindle rotation.
The constant torque model has a constant torque over the entire speed range at the same U/F ratio. The variable torque ratio model has a lower supply voltage at low speeds. This is necessary to prevent saturation of the electric machine.
V/F is the only way to control the speed of an induction motor that allows the control of multiple drives from a single frequency converter. Accordingly, all machines start and stop at the same time and operate at the same frequency.
But this method of control has several limitations. For example, when using the V/F control method without an encoder, there is absolutely no certainty that the shaft of an induction machine is rotating. In addition, the starting torque of the electric machine at a frequency of 3 Hz is limited to 150%. Yes, the limited torque is more than enough for most existing equipment. For example, almost all fans and pumps use a V/F control method.
This method is relatively simple due to its looser specification. Speed control is typically in the range of 2% - 3% of the maximum output frequency. The speed response is calculated for frequencies above 3 Hz. The response speed of the frequency converter is determined by the speed of its response to a change in the reference frequency. The higher the response speed, the faster the response of the drive to a change in the speed reference.
The speed control range when using the V/F method is 1:40. Multiplying this ratio by the maximum operating frequency of the electric drive, we obtain the value of the minimum frequency at which the electric machine can operate. For example, if the maximum frequency is 60 Hz and the span is 1:40, then the minimum frequency is 1.5 Hz.
The U/F pattern determines the ratio of frequency and voltage during the operation of a variable frequency drive. According to him, the curve for setting the rotation speed (frequency of the electric motor) will determine, in addition to the frequency value, the voltage value supplied to the terminals of the electric machine.
Operators and technicians can select the desired V/F regulation pattern with a single parameter in a modern frequency converter. The preset templates are already optimized for specific applications. There is also the possibility of creating your own templates, which will be optimized for a specific system of variable frequency drive or electric motor.
Devices such as fans or pumps have a load torque that depends on their rotational speed. The variable torque (figure above) of the V/F pattern prevents adjustment errors and improves efficiency. This regulation model reduces magnetizing currents at low frequencies by reducing the voltage on the electrical machine.
Constant torque machines such as conveyors, extruders and other equipment use the constant torque control method. With a constant load, full magnetizing current is required at all speeds. Accordingly, the characteristic has a direct slope in the entire speed range.
U/F control method with encoder
If it is necessary to improve the accuracy of speed control, an encoder is added to the control system. The introduction of speed feedback using an encoder allows you to increase the accuracy of regulation up to 0.03%. The output voltage will still be determined by the set V/F pattern.
This control method has not been widely used, since the advantages it presents compared to standard V/F functions are minimal. Starting torque, response speed and speed control range are all identical to standard V/F. In addition, with an increase in operating frequencies, problems may arise with the operation of the encoder, since it has a limited number of revolutions.
Open Loop Vector Control
Open Loop Vector Control (VU) is used for a wider and more dynamic speed control of an electrical machine. When starting from a frequency converter, motors can develop a starting torque of 200% of the rated torque at a frequency of only 0.3 Hz. This greatly expands the list of mechanisms where an asynchronous electric drive with vector control can be used. This method also allows you to control the machine torque in all four quadrants.
The torque is limited by the motor. This is necessary to prevent damage to equipment, machines or products. The value of the moments is broken down into four different quadrants, depending on the direction of rotation of the electric machine (forward or backward) and depending on whether the electric motor implements . Limits can be set for each quadrant separately, or the user can set the total torque in the frequency converter.
The motor mode of the asynchronous machine will be provided that the magnetic field of the rotor lags behind the magnetic field of the stator. If the rotor magnetic field begins to outpace the stator magnetic field, then the machine will enter the regenerative braking mode with energy return, in other words, the asynchronous motor will switch to the generator mode.
For example, a bottle capping machine may use a torque limit in quadrant 1 (forward with positive torque) to prevent over-tightening of the bottle cap. The mechanism makes a forward movement and uses positive torque to screw the cap on the bottle. On the other hand, a device such as an elevator with a counterweight heavier than an empty car will use quadrant 2 (reverse rotation and positive torque). If the car rises to the top floor, then the torque will be opposite to the speed. This is necessary to limit the lifting speed and prevent the counterweight from free-falling, as it is heavier than the cab.
The current feedback in these frequency converters allows you to set limits on the torque and current of the motor, since as the current increases, so does the torque. The output voltage of the inverter may increase if the mechanism requires more torque, or decrease if the limit is reached. This makes the vector control principle of an asynchronous machine more flexible and dynamic than the U/F principle.
Also frequency converters with open-loop vector control have a faster speed response - 10 Hz, which makes it possible to use it in mechanisms with shock loads. For example, in rock crushers, the load is constantly changing and depends on the volume and dimensions of the rock being processed.
Unlike the V/F control pattern, vector control uses a vector algorithm to determine the maximum effective operating voltage of the motor.
The VU vector control solves this problem due to the presence of feedback on the motor current. As a rule, the current feedback is generated by the internal current transformers of the frequency converter itself. Based on the obtained current value, the frequency converter calculates the torque and flux of the electrical machine. The basic motor current vector is mathematically split into a magnetizing current vector (I d) and a torque vector (I q).
Using the data and parameters of the electric machine, the inverter calculates the vectors of the magnetizing current (I d) and torque (I q). To achieve maximum performance, the frequency converter must keep I d and I q separated by 90 0 . This is significant because sin 90 0 = 1 and the value 1 represents the maximum torque value.
In general, the vector control of an induction motor provides tighter control. The speed regulation is approximately ±0.2% of the maximum frequency, and the regulation range reaches 1:200, which allows you to keep the torque when working at low speeds.
Vector feedback control
Closed-loop vector control uses the same control algorithm as the VU without feedback. The main difference is the presence of an encoder, which allows the variable frequency drive to develop 200% starting torque at 0 rpm. This item is simply necessary to create an initial moment when starting off elevators, cranes and other lifting machines in order to prevent the load from sinking.
The presence of a speed feedback sensor allows you to increase the response time of the system more than 50 Hz, as well as expand the speed control range up to 1:1500. Also, the presence of feedback allows you to control not the speed of the electric machine, but the moment. In some mechanisms, it is the value of the moment that is of great importance. For example, winding machine, blocking mechanisms and others. In such devices, it is necessary to regulate the moment of the machine.
Dmitry Levkin
Scalar control(frequency) - a method of controlling a brushless alternating current, which consists in maintaining a constant voltage / frequency ratio (V / Hz) over the entire operating speed range, while only the magnitude and frequency of the supply voltage are controlled.
The V/Hz ratio is calculated based on the rated values (and frequency) of the controlled AC motor. By keeping the V/Hz ratio constant, we can keep the magnetic flux in the motor gap relatively constant. If the V/Hz ratio increases then the motor becomes overexcited and vice versa if the ratio decreases the motor is in an underexcited state.
Changing the supply voltage of the electric motor with scalar control
At low speeds, it is necessary to compensate for the voltage drop across the stator resistance, so the V/Hz ratio at low speeds is set higher than the nominal value. The scalar control method is most widely used to control asynchronous motors.
Applied to asynchronous motors
With the scalar control method, the speed is controlled by setting the voltage and frequency of the stator so that the magnetic field in the gap is maintained at the desired value. To maintain a constant magnetic field across the gap, the V/Hz ratio must be constant at different speeds.
As the speed increases, the stator supply voltage should also increase proportionally. However, the synchronous frequency of an induction motor is not equal to the shaft speed, but depends on the load. Thus, an open loop scalar control system cannot accurately control the speed when there is a load. To solve this problem, speed feedback can be added to the system, and hence slip compensation.
Disadvantages of scalar control
- Method scalar control relatively simple to implement, but has several significant drawbacks:
- firstly, if a speed sensor is not installed, it is impossible to control the speed of rotation of the shaft, since it depends on the load (the presence of a speed sensor solves this problem), and in the case of when the load changes, you can completely lose control;
- Second, you can't manage. Of course, this problem can be solved using a torque sensor, but the cost of its installation is very high, and will most likely be higher than the electric drive itself. In this case, the torque control will be very inertial;
- it is also impossible to control torque and speed at the same time.
Scalar control is sufficient for most applications where an electric drive is used with a motor speed control range of up to 1:10.
When maximum speed is required, the ability to control a wide range of speeds and the ability to control the torque of the electric motor is used.