Vector motor control. Modern problems of science and education

• Tutorial

- What is vector control?
- Keep the current at 90 degrees.

The term “vector control” of electric motors is familiar to anyone who has been at least somewhat 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 near the end, consisting of a bunch of hairy formulas with references to all the other chapters of the book. Why don’t you want to understand this issue at all? And even the simplest explanations still go through differential equilibrium equations, vector diagrams and a bunch of other mathematics. Because of this, attempts like this appear to somehow turn on the engine without using the hardware. But in fact, vector control is very simple if you understand the principle of its operation “on your fingers”. And then it will be more fun to deal with formulas if necessary.

Operating principle of a synchronous machine

Let's consider the operating principle of the simplest AC motor - a permanent magnet synchronous machine. 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 fluid that dampens the oscillations of the needle), the rotor is always oriented along the stator field. If we hold a compass and rotate the Earth under it, the needle will spin along with it, doing work to mix 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 move following the rotating magnetic field. In a real synchronous motor, the stator field is created by electromagnets - coils with current. The winding circuits there are complex, but the principle is the same - they create a magnetic field with the stator, directed in the desired direction and having the required amplitude. Let's look at the following figure (Figure 1). In the center there is a magnet - the rotor of a synchronous motor (the "arrow" of the compass), and on the sides there are two electromagnets - coils, each creating its own magnetic field, one in the vertical axis, the other in the horizontal.

Figure 1. Operating principle of a synchronous electric machine

The magnetic flux of the coil is proportional to the current in it (to a 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 perpendicularly located 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 I α And I β, creating magnetic fluxes along the α and β axes, respectively. Total stator current vector Is creates a co-directed stator magnetic flux. Those. in fact Is symbolizes the external magnet that 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 rotate according to the stator magnetic flux, i.e. by vector Is(the position of the rotor in this case is shown by the dotted line). Accordingly, if you apply current only to the phase α , let's say I α= 1A, the rotor will stand horizontally, and if in β, vertically, and if you apply I β= -1 And then it will flip 180 degrees. If you supply current I α according to the law of sine, and I β according to the law of cosine 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 a two-phase machine 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 Is 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 here with the signs of moment and angle, which is why the characteristic is often drawn inverted relative to the horizontal axis).

To obtain 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 rotate to the appropriate position, which must be taken as zero. Then, through the torque sensor, you need to turn the rotor “by hand”, fixing the angle on the graph at each point θ , which was 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 Mmax 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 measurement of torque), if we apply 2A, we get M max = 2 N∙m.

From this characteristic it follows 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 obtain the highest 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 always set the current vector at 90° to the magnetic field of the rotor, i.e. perpendicular to the magnet in Figure 1. We need to change everything the other way around - the rotor does not move towards 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 motor torque by the amplitude of the current. The greater the amplitude, the higher the torque. But the rotation frequency, the frequency of the current in the windings is no longer “our” business - what happens, how the rotor rotates, so it will be - we control the torque on the shaft. Oddly enough, this is exactly 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, to the point that vector control generally refers to any control laws where “vectors” are involved, but usually vector control refers to precisely the above control method.

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 you have something to measure 90° relative to. The easiest way to do this is by installing the position sensor itself on the rotor shaft. Then you need to figure out how to create a current vector, maintaining the desired currents in 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 you will need phase current sensors. Next, you need to assemble a vector control structure in the form of a program on a microcontroller that will do the rest. So that this explanation does not look like an instruction on “how to draw an owl,” let’s continue the dive.
You can maintain the current with the microcontroller using a software PI (proportional-integral) current regulator and PWM. For example, a structure with a current regulator for one phase α is shown below (Figure 3).

Figure 3. Current-closed control structure for one phase

Here is the current setting i α_back– a certain constant, the current that we want to maintain for this phase, for example 1A. The task is sent 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. I can only recommend some of this. The output current regulator sets the phase voltage U α. The voltage is supplied to the PWM block, which calculates the duty cycle settings (comparison settings) for the PWM timers of the microcontroller, generating PWM on a bridge inverter of four switches to generate this U α. The algorithm can be different, for example, for positive voltage the PWM of the right rack is proportional to the voltage setting, the lower switch is closed on the left, for negative PWM the left one, the lower switch is closed on the right. Don't forget to add dead time! As a result, such a structure makes the software a “current source” at the expense of a voltage source: we set the value we need i α_back, and this structure implements it with a certain speed.

Further, perhaps some readers have already thought that the vector control structure is only a small matter away - you need to install two current regulators, one regulator for each phase, and form a task on them depending on the angle from the rotor position sensor (RPS), i.e. e. make 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_back And i β_back will be sinusoidal, i.e. the task for the current regulators will change all the time. The speed of the controller is not infinite, so when the task changes, it does not immediately process it. If the task is constantly changed, then the regulator will always catch up with it, never reaching it. And as the engine rotation speed increases, the lag of the real current from the given one will become larger and larger, 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. That's why they do it differently. The correct structure is as follows (Figure 5):

Figure 5. Vector sensor control structure for 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, BOD_1 turns to + ϴ , and BKP_2 on - ϴ . That's all the difference between them. In foreign literature they are called Park transformations. BKP_2 performs 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 engine rotor (using the rotor position angle ϴ ). And BKP_1 makes the reverse transformation, from setting the voltage along the axes d And q makes the transition to the axes α And β . I don’t provide any formulas for converting 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, tied to the rotor

That is, instead of “rotating” the settings of the regulators (as was the case in the previous structure), their inputs and outputs rotate, and the regulators themselves operate in static mode: currents d, q and the outputs of the controllers in steady state are constant. Axles d And q rotate together with the rotor (as they are rotated by a signal from the rotor position sensor), while the axis regulator q regulates exactly the current that at the beginning of the article I called “perpendicular to the rotor field”, that is, it is a torque-generating current, and the current d is aligned with the “rotor magnet”, so we don’t need it and we set it equal to zero. This structure is free 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 have adjusted each of their currents, reached the specified voltage - and that’s it, like the rotor, don’t run away from them, they don’t even know about it: all the work of turning is done by coordinate transformation blocks.

To explain “on the fingers” you can give some analogy.

For linear traffic, let it be, for example, a city bus. It constantly accelerates, then slows down, then goes backwards and generally behaves as it wants: it is an engine rotor. Also, you are 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 should also change the speed accordingly and monitor it all the time. But now we’ll do “vector control” for you. You climbed inside the bus, stood in the middle and held on to the handrail - like the bus, don’t 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 actually 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 make it, such as compensation for cross-connections, various restrictions, field weakening, etc. But this is the basic principle.

And if you need to regulate not the drive torque, but still the speed (the correct angular speed, rotation frequency)? Well then we install another PI controller - a speed controller (RS). We apply a speed command to the input, and at the output we have a torque command. Since the axis current q is proportional to the torque, then to simplify it, the output of the speed controller can be fed directly to the input of the axis current controller q, like this (Figure 7):

Figure 7. Speed ​​controller for vector control
Here the SI, the intensity setter, 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 taken from the rotor position sensor handler, since ω this is the derivative of the angular position ϴ . Well, or you can simply measure 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. Vector sensor control structure for three-phase synchronous machine

Three-phase currents, just like two-phase ones, serve one purpose - to create a stator current vector Is, directed in the desired direction and having the desired amplitude. Therefore, three-phase currents can simply be converted into two-phase, and then leave the same control system that has already been assembled for a two-phase machine. In English-language literature, such a “recalculation” is called Clarke transformation (Edith Clarke is her), in our country it is called phase transformations. In the structure in Figure 8, accordingly, this operation is performed by a phase transformation block. They are done again using the school geometry course (Figure 9):

Figure 9. Phase conversions - from three phases to two. For convenience, we assume that the amplitude of the vector I s is equal to the amplitude of the current in the phase

I think no comments are needed. A few words about the current of phase C. There is no need to install a current sensor there, since the three phases of the motor are connected in a star, and according to Kirchhoff’s law, everything that flows through two phases must flow out of the third (unless, of course, there is a hole in your motor insulation, and half did not leak somewhere onto the housing), therefore the current of phase C is calculated as the scalar sum of the currents of phases A and B with a minus sign. Although a third sensor is sometimes installed to reduce measurement error.

A complete rework of the PWM module is also required. Typically, a three-phase six-switch inverter is used for three-phase motors. In the figure, the voltage command still arrives in two-phase axes. Inside the PWM module, using reverse phase transformations, this can be converted into voltages of phases A, B, C, which must be applied to the motor at this moment. But what to do next... Options are possible. A naive method is to set a duty cycle for each inverter rack proportional to the desired voltage plus 0.5. This is called sine wave PWM. This is exactly the method that the author used in habrahabr.ru/post/128407. Everything is good in this method, 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 do the math. Let you have a classic frequency converter, powered by an industrial three-phase network 380V 50Hz. Here 380V is the linear (between phases) effective voltage. Since the converter contains a rectifier, it will rectify this voltage and the DC bus will have a voltage equal to the amplitude linear voltage, i.e. 380∙√2=540V DC voltage (at least without load). If we apply a sinusoidal calculation algorithm in the PWM module, then the amplitude of the maximum phase voltage that we can achieve will be equal to half the voltage on the DC bus, i.e. 540/2=270V. Let's convert into effective phase: 270/√2=191V. And now to the current linear: 191∙√3=330V. Now we can compare: 380V came in, but 330V came out... And you can’t do anything else with this type of PWM. To correct this problem, the so-called vector type PWM is used. Its output will again be 380V (ideally, without taking into account all voltage drops). The vector PWM method has nothing to do with vector control of an electric motor. It's just that its rationale again uses a little school geometry, which is why it's called vector. However, his work cannot be explained on the fingers, so I will refer the reader to books (at the end of the article) or to Wikipedia. I can also give you a picture that slightly hints at the difference in the operation of sinusoidal and vector PWM (Figure 10):

Figure 10. Change in phase potentials for scalar and vector PWM

Types of position sensors

By the way, what position sensors are used for vector control? There are four types of sensors most commonly used. These are a quadrature incremental encoder, a Hall element-based encoder, an absolute position encoder, and a synchronous encoder.
Quadrature encoder does not indicate the absolute position of the rotor - by its impulses it only allows you to determine how far you have traveled, but not where and from where (how 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. Its reference mark (index) saves the situation a little - there is only one per mechanical revolution, if you reach it, then the absolute position becomes known, and from it you can already count how much you have driven using a quadrature signal. But how to get to this mark at the beginning of work? In general, this is not always convenient.
Hall element sensor- This 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 value, but with low accuracy. Accuracy is usually enough to keep the angle of the current vector so that the motor at least moves 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. construct a linearly varying angle from a rough discrete angle. This is done based on the assumption that the motor rotates at approximately constant speed, something like this (Figure 11):

Figure 11. Operation of a Hall element position sensor for a three-phase machine and extrapolation of its signal

Often a combination of an encoder and a Hall effect sensor is used for servo motors. In this case, you can make a single software module for processing them, eliminating the disadvantages of both: do the angle extrapolation given above, but not by time, but by marks from the encoder. Those. An encoder operates inside the Hall sensor from edge to edge, and each Hall edge clearly initializes the current absolute angular position. In this case, only the first movement of the drive will be non-optimal (not at 90°), until it reaches some front of the Hall sensor. A separate problem in this case is the processing of non-idealities of both sensors - rarely does anyone arrange the Hall elements symmetrically and evenly...

In even more expensive applications they use absolute encoder with a digital interface (absolute encoder), which immediately provides the absolute position and allows you to avoid the problems described above.

If the electric motor is very hot, and also when increased accuracy of angle measurement is required, use “analog” synchronous sensor(resolver, rotating transformer). This is a small electrical machine used as a sensor. Imagine that in the synchronous machine we 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 into the phase stator coil α , if vertical - then only in β , if you turn it 180, the phase of the signal will change, and in intermediate positions it is induced both here and there according to the sine/cosine law. Accordingly, by measuring the signal amplitude in two coils, the position can also be determined from the ratio of this amplitude and the phase shift. 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 making. There, any physical phenomena are used just to find out the position as accurately as possible. We will not consider them.

Simplifying vector control

As you understand, vector control is quite demanding - give it position sensors, current sensors, PWM vector control, and no microcontroller to calculate all this mathematics. Therefore, for simple applications it is simplified. To begin with, you can eliminate the position sensor by making 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 job on a PWM module) and about the currents in the motor from sensors. Inside the observer there is a model of an electric motor, 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, completely simplified. There are countless types of observers like these. Every graduate student specializing in electric drives tries to invent his own, which is somehow better than others. The basic principle is monitoring the EMF of the electric motor. Therefore, most often, a sensorless control system is operational only at relatively high rotation speeds, where the EMF is large. It also has a number of disadvantages compared to the presence of a sensor: you need to know the engine parameters, the speed of the drive is limited (if the rotation speed changes sharply, the observer may not have time to track it and “lie” for some time, or even “fall apart” completely) , setting up an observer is a whole procedure; for its high-quality operation, you need to know exactly the voltage on the motor, accurately measure its currents, etc.

There is another simplification option. For example, you can do so-called “auto-switching”. In this case, for a three-phase motor, they abandon the complex PWM method, abandon the complex vector structure and begin to simply turn on the motor phases using a position sensor on 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 try to make sure that the average current vector is still at 90 degrees to the “rotor magnet” by choosing the moment when the phases are turned on. At the same time, turning on the phase under voltage, it is not known when the current will increase in the motor phase. At a low rotation speed it does this faster, at a high speed, where the EMF of the machine interferes, it does it more slowly; the rate of increase in current also depends on the inductance of the motor, 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 advance or lag relative to the optimal 90 degrees. Therefore, in such systems, a “switching advance” setting is introduced - essentially just the time, how much earlier voltage needs to be applied to the motor phase, so that in the end the phase of the current vector is closer to 90 degrees. Simply put, this is called “setting timings.” Since the current in an electric motor during autocommutation is not sinusoidal, then if you take the sinusoidal machine discussed above and control it in this way, the torque on the shaft will pulsate. Therefore, in motors designed for autocommutation, 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 autocommutation mode. Synchronous machines optimized for autocommutation are called brushless direct current motors (BLDC) or in English BLDC (Brushless Direct Current Motor). The auto-commutation mode is also often called the valve mode, and motors operating with it are valve-type. But these are all just different names that do not affect the essence in any way (but seasoned electric drive operators often suffer from CPGS in matters related to these names). There is a good video illustrating the principle of operation of such machines. It shows an inverted motor, 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 go for even greater simplification. Switch the windings so that one phase is always “free” and no PWM is applied to it. Then it is possible to measure the EMF (voltage induced in the phase coil), and when this voltage passes through zero, use this as a signal from the rotor position sensor, because the phase of this induced voltage depends precisely on the position of the rotor. This results in sensorless auto-commutation, which is widely used in various simple drives, for example, in “regulators” for aircraft model propellers. It must be remembered that the EMF of the machine appears only at a relatively high rotation speed, therefore, to start, such control systems simply slowly cycle through the phases, hoping that the motor rotor will follow the supplied current. As soon as the EMF appears, the auto-commutation 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 they make even greater simplifications. You can completely abandon the microcontroller, keys, position sensors and other things by switching phases with a special mechanical switch (Figure 13):

Figure 13. Mechanical switch for switching windings

When rotating, the rotor itself switches its parts of the windings, changing the voltage applied to them, while an alternating current flows in the rotor. 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 drives, there is even the concept of a “generalized electric machine”, to which the work of others is reduced. The “hands-on” explanations shown in the article can in no way serve as a practical guide to writing microcontroller code. The article discusses well if one percent of the information that is required to implement real 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, etc. This can be done in the latest book “Anuchin A.S. Electric drive control systems. MPEI, 2015”, as well as in “Kalachev Yu. N. Vector regulation (practice notes)”. The reader should be warned against diving into the formulas of “old” textbooks on drives, where the main emphasis 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 motors in this case is described by complex formulas and dependencies, but for the problem of vector control they are of almost no use (if only studied for self-development). You should be especially careful about the recommendations of old textbooks, where, for example, it is said that a synchronous machine should not operate at its maximum torque, since the operation there is unstable and threatens to tip over - all this is “bad advice” for vector control.

On which microcontroller you can make 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: in particular, there are two boring videos posted there, which show in practice how to set up a PI current controller, as well as how a current-closed and vector sensorless control structure works. In addition, you can purchase a debugging kit with a ready-made sensor vector control structure on a domestic microcontroller.

Continuation of the article, which talks about asynchronous motors.

P.S.
I apologize to the experts for the not entirely correct handling of some terms, in particular the terms “flow”, “flux linkage”, “magnetic field” and others - simplicity requires sacrifice...

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Scalar control(frequency) - a method of controlling brushless alternating current, which consists of maintaining a constant voltage/frequency ratio (V/Hz) throughout the entire operating speed range, while only controlling the magnitude and frequency of the supply voltage.

The V/Hz ratio is calculated based on the rating (and frequency) of the AC motor being monitored. By keeping the V/Hz ratio constant, we can maintain a relatively constant magnetic flux in the motor gap. 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 motor supply voltage 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 electric motors.

As applied to asynchronous motors

With the scalar control method, the speed is controlled by setting the stator voltage and frequency, so that the magnetic field in the gap is maintained at the desired value. To maintain a constant magnetic field in the gap, the V/Hz ratio must be constant at different speeds.

As the speed increases, the stator supply voltage must also increase proportionally. However, the synchronous frequency of an asynchronous motor is not equal to the shaft speed, but depends on the load. Thus, a scalar open-loop control system cannot accurately control speed when a load is present. To solve this problem, speed feedback, and therefore slip compensation, can be added to the system.

Disadvantages of Scalar Control

Method scalar control relatively simple to implement, but has several significant disadvantages:
• firstly, if a speed sensor is not installed, you cannot control the shaft rotation speed, since it depends on the load (the presence of a speed sensor solves this problem), and in the case of a change in load, you can completely lose control;
• secondly, it cannot be controlled. Of course, this problem can be solved using a torque sensor, but the cost of installing it is very high, and will most likely be higher than the electric drive itself. In this case, 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 tasks in which an electric drive is used with an engine speed control range of up to 1:10.

When maximum speed is required, the ability to regulate over a wide speed range and the ability to control the torque of the electric motor is used.

Any change or maintenance of a constant speed of the electric drive provides targeted regulation of the torque developed by the engine. The torque is formed as a result of the interaction of the flow (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 torque-generating vectors. Therefore, the magnitude of the torque 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 torque-generating 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 torque-generating vectors. Hence, the task of vector control is to determine and forcefully establish instantaneous current values ​​in the motor windings in such a way that the generalized vectors of currents and flux linkages 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 linkages that form torque; X- spatial angle between moment-generating vectors.

As follows from (6.53), the minimum values ​​of currents (flux linkages) forming the torque will be for the required torque value 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 stator or rotor axes. It is necessary to determine the position of one vector relative to another. Therefore, one of the vectors is taken to be 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 a 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.

In Fig. Figure 6.31 shows a vector diagram of currents and flow linkages in the axes And- v ^coordinate orientation And along the rotor coupling vector. From the vector diagram it follows that

Rice. B.31. Vector diagram of flux linkages and currents in axes u-v at M

With constant (or slow change) p rotor clutch d"V u /dt= 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, if the rotor flux linkage is constant, we can assume that the projection of the stator current vector onto the coordinate axis v i v equals |/"| or /

The advantage of the adopted coordinate system u-v for constructing a system of vector control of torque and speed of an asynchronous 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. This definition of torque is typical, for example, for DC motors independent excitation, most convenient for constructing an automatic control system.

Vector control system. The structural diagram of such management is based on the following principles:

• ? a two-channel control system consists of a rotor flux linkage stabilization channel and a speed (torque) control channel;
• ? both channels must be independent, i.e. changing the regulated values ​​of one channel should not affect the other;
• ? the speed (torque) control channel controls the stator current component /v. The algorithm for the operation of the torque control loop is the same as in systems of slave speed control of DC motors (see § 5.6) - the output signal of the speed controller is a reference to the motor torque. By dividing the value of this task by the rotor flux linkage module And we get the task for the stator current component i v (Fig. 6.32);
• ? each channel contains an internal circuit of currents /v and i and with current regulators that provide the required quality of regulation;
• ? obtained current values i v and i and through coordinate transformations are converted into values i a and / p of a two-phase fixed coordinate system a - (3 and then in the task of real currents in the stator windings in a three-phase coordinate system a-b-c;
• ? The signals of speed, rotor rotation angle, and currents in the stator windings necessary for calculations and feedback formation are measured by appropriate 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 high-speed control of torque, and, consequently, speed in the widest possible range (over 10,000:1). In this case, the instantaneous torque values ​​of an asynchronous motor can significantly exceed the nominal value of the critical torque.

In order to make the control channels independent of each other, it is necessary to introduce cross compensating signals e K0MPU and e compm at the input of each channel (see Fig. 6.32). We find the value of these signals from the stator circuit equations (6.54). Having expressed and CHK 1y through the corresponding currents and inductances (1.4) and taking into account that when the axis is oriented And along the rotor flux linkage vector Х / |у =0 we obtain:

Where do we find it from?

Where dissipation coefficient.

Substituting (6.55) into (6.54) and taking into account that in the control system under consideration d x V 2u /dt = 0, we get

or

new time constants; e and e v - EMF of rotation along the axes u- v

To set independent quantities i and and /v needs to be compensated e and And e v introduction of compensating voltages:

To implement the principles of vector control, it is necessary to directly measure or calculate using a mathematical model (estimate) the module and angular position of the rotor flux linkage vector. The functional diagram of 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.ZZ. Functional diagram of direct vector control of an asynchronous motor

The circuit contains two control channels: a control (stabilization) channel for the rotor flux linkage *P 2 and a speed control channel. The first channel contains an external rotor flux linkage loop containing a PI flux linkage controller RP and flux linkage feedback, the signal of which is generated using Hall sensors that measure the flow in the machine gap X? T along the axes ai(3. The real flux values ​​are then recalculated in the PP block into the values ​​of the rotor flux linkage along the axes a and p and using the vector filter VF, the modulus of the rotor flux linkage vector is found, which is supplied as a negative feedback signal to the flux linkage regulator 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 regulator PT1 and feedback on the actual value of the current / 1i, calculated from the real values ​​of the stator phase currents using the phase converter PF2 and the coordinate converter KP1. The output of the current regulator PT1 is the voltage setting Ulu, to which the compensation signal of the second channel is added e kshpi(6.57). The received voltage setting signal is converted by means of coordinate KP2 and phase PF2 converters into specified values ​​and voltage phases at the output of the frequency converter.

The rotor flux linkage control channel ensures that the flux linkage Ch* 2 remains constant in all drive operating modes at the level of the specified value x P 2set. If it is necessary to weaken the field, H*^ can vary within certain limits with a small rate of change.

The second channel is designed to regulate the speed (torque) of the engine. It contains an external speed loop and a subordinate internal current loop / 1у. The speed command comes from the intensity generator, which determines the acceleration and the required speed value. Speed ​​feedback is implemented via a DS speed sensor or a rotor angular position sensor.

The PC speed controller is adopted as proportional or proportional-integral, depending on the requirements for the electric drive. The output of the speed controller is the command for the torque developed by the L/R engine. Since the torque is equal to the product of the current by the rotor flux linkage H / 2, then by dividing the torque setting value in the DB division block M back on Ch / 2, we obtain the value of the current setting, which is supplied to the input of the current regulator PT2. Further signal processing is similar to the first channel. As a result, we obtain a task for the motor supply voltage by phase, which determines the value and spatial position at each moment of time of the generalized stator voltage vector!? Note that the signals relating to variables in the - coordinates are direct current signals, and the signals reflecting currents and voltages in the air coordinates are alternating current signals that determine not only the module, 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 structural vector control schemes have been developed and are widely used, differing in detail from the one under consideration. Thus, at present, the actual values ​​of flux linkages are not measured by magnetic flux sensors, but are calculated using a mathematical model of the motor, based on measured phase currents and voltages.

In general, vector control can be assessed as the most effective way to control AC motors, providing high accuracy and speed of control.

1

When designing frequency control of an electric drive, there is a need to build adequate models that fully take into account the specifics of the ongoing electromechanical processes in the engine. To test models, it is necessary to compare them with a physically implemented process on real equipment; in this regard, there is a need to determine the parameters of real electric motors to check the model for adequacy. The article describes a mathematical model of vector control of an asynchronous electric motor. The model allows you to monitor electromechanical processes in an electric motor during its operation. Graphs of mechanical and electrical transient processes characterizing the start-up of an electric motor were obtained. A mechanical characteristic of the electric motor with vector control has been constructed, clearly showing the increase in the load range. The adequacy of the model was assessed. Mathematical experiments and model creation were performed in the graphical simulation environment Simulink, an application to the Matlab package.

inverter

mathematical model

mechanical characteristics

vector control

asynchronous motor

1. Vinogradov A.B. Vector control of AC electric drives / Ivanovo State Energy University named after V.I. Lenin". – Ivanovo, 2008. – 297 p.

2. Likhodedov A.D. Construction of the mechanical characteristics of an asynchronous motor and its testing // Modern problems of science and education. – 2012. – No. 5. – URL: http://www..09.2012).

3. Usoltsev A.A. Vector control of asynchronous motors: a textbook on disciplines of the electromechanical cycle. – St. Petersburg, 2002.

4. Shuvalov G.A. Saving electricity using a frequency converter // Electrical equipment: operation and repair. – 2012. – No. 2.

5. Blaschke, F. Das Prinzip der Feldorientierung, die Grundlage für die Transvector-Regelung von Drehfeldmaschinen (in German), Siemens-Zeitschrift 45, Heft 10, 1971.

6. PLC - it's easy!! Vector control. – URL: http://plc24.ru/vektornoe-upravlenie/ (date of access: 09/12/2012).

Development of asynchronous electric drive with vector control

It is customary to distinguish between two main methods of controlling AC electric drives that use semiconductor frequency converters as energy converters: frequency and vector.

With frequency control, one of the static laws of frequency control is implemented in the electric drive (for example, , etc.). At the output of the control system, a task is generated for the frequency and amplitude of the output voltage of the inverter. The scope of application of such systems: asynchronous electric drive, which does not have increased static and dynamic requirements, fans, pumps and other general industrial mechanisms.

With vector control, control is carried out based on the instantaneous values ​​of the variables. In digital vector systems, control can be performed using equivalent (averaged over the control discrete interval) variables.

In 1971, Blaschke proposed the principle of constructing a control system for an asynchronous motor, which used a vector model of the motor with the orientation of the coordinate system along the rotor flux linkage. This principle is also called direct torque control. Vector control allows you to significantly increase the control range, control accuracy, and increase the speed of the electric drive. This method provides direct control of motor torque.

The torque is determined by the stator current, which creates an exciting magnetic field. When directly controlling the torque, it is necessary to change, in addition to the amplitude, the phase of the stator current, that is, the current vector. This is where the term “vector control” comes from.

To control the current vector, and, consequently, the position of the stator magnetic flux relative to the rotating rotor, it is necessary to know the exact position of the rotor at any time. The problem is solved either using an external rotor position sensor, or by determining the rotor position by calculations using other engine parameters. The currents and voltages of the stator windings are used as these parameters.

Less expensive is a variable frequency drive with vector control without a speed feedback sensor, but vector control requires a large volume and high speed of calculations from the frequency converter. In addition, for direct torque control at low, close to zero rotation speeds, operation of a variable frequency electric drive without speed feedback is impossible. Vector control with a speed feedback sensor provides a control range of up to 1:1000 and higher, speed control accuracy is hundredths of a percent, torque accuracy is a few percent.

The power supply of the IM and SM in vector control mode is carried out from an inverter, which can provide the required amplitude and angular position of the stator voltage (or current) vector at any time. The amplitude and position of the rotor flux linkage vector are measured using an observer (a mathematical apparatus that allows one to restore unmeasured parameters of the system). Depending on the operating conditions of the electric drive, it is possible to control the electric motor both in modes with normal accuracy and in modes with increased accuracy of processing the speed or torque task. For example, a frequency converter provides an accuracy of maintaining the rotation speed of ±2-3% in U/f mode, with vector control without a speed sensor of ±0.2%, with full vector control with a speed sensor an accuracy of ±0.01% is provided.

General principle of vector control of IM

In the future, we will use the following indices of coordinate systems: a-b - fixed coordinate system (), oriented along the axis of phase a of the stator winding; x-y - coordinate system rotating synchronously with the rotor () and oriented along the phase axis a of its winding; d-q - coordinate system rotating synchronously with the rotor flux linkage () and oriented in its direction; m-n is an arbitrarily oriented coordinate system rotating at an arbitrary speed.

The general principle of modeling and constructing an IM control system is that for this purpose a coordinate system is used, constantly oriented in the direction of any vector that determines the electromagnetic torque. Then the projection of this vector onto the other coordinate axis and the corresponding term in the expression for the electromagnetic torque will be equal to zero, and formally it takes a form identical to the expression for the electromagnetic torque of a DC motor, which is proportional in magnitude to the armature current and the main magnetic flux.

In the case of orientation of the coordinate system along the rotor flux linkage ( ) the moment can be represented as:

, (1)

where is the leakage inductance of the rotor circuit, is the inductance of the magnetization circuit, is the number of pole pairs, and is the projection of the stator currents on the axes of the coordinate system.

Using this expression, it is possible, provided that the rotor flux linkage is constant, to control the electromagnetic torque by changing the projection of the stator current onto the transverse axis. The choice of equation for constructing a control system plays a big role, because many quantities, especially for short-circuited blood pressure, cannot be measured. In addition, this choice significantly affects the complexity of the system transfer functions, sometimes increasing the order of the equations several times.

To build an IM vector control system, you need to select the vector relative to which the coordinate system will be oriented, and the corresponding expression for the electromagnetic torque, and then determine the quantities included in it from the equations for the stator and/or rotor circuit (2):

, (2, a)

, (2, b)

where is the voltage of the stator windings in vector form; - active resistance of the stator and rotor windings; components are associated with changes in flux linkage over time due to changes in currents over time and are called transformation EMF, by analogy with the processes of its excitation in the corresponding electric machine; components , - are associated with a change in flux linkage due to rotor rotation and are called rotational emf.

If we select the rotor flux linkage as a reference vector and orient the coordinate system along it so that its real axis coincides with the direction , then the angular frequency of rotation of the coordinate system will be equal to the angular frequency of the stator supply, since The flux vectors of the stator and rotor rotate at the same frequency. The use of the rotor flux linkage vector theoretically provides greater overload capacity of the IM.

In this case, the projections of the stator current vector, taking into account the fact that , are equal to:

(3)

where is the electromagnetic time constant of the rotor.

Let us express the flux linkage and angular frequency of the rotor:

(4)

Thus, using the projection of the stator current, the rotor flux linkage can be controlled, and the transfer function of this channel corresponds to an aperiodic link with a time constant equal to the rotor time constant; and with the help of projection it is possible to independently and inertia-free control the rotor frequency.

In this case, the electromagnetic torque of the IM can be determined by knowing the frequency of the rotor currents for a given flux linkage:

, (5)

Expressions - determine the relationship between the projections of the stator current on the coordinate axes, flux linkage, rotor frequency and electromagnetic torque of the IM. From the expression and equation of motion it follows that torque can be controlled inertia-free by two input signals: flux linkage and rotor frequency. These signals are related to the projections of the stator current vector by expressions. Therefore, the vector control device contains a coordinate decoupling unit (RC), which carries out transformations in accordance with expressions (3), as well as a rotator that rotates the stator current vector in the direction opposite to the rotation of the IM rotor. The input signals for the control device will be the linear network voltage and the frequency of the supply voltage, corresponding to the flux linkage and rotor frequency. The name of the coordinate decoupling block comes from its function of generating signals corresponding to independent (decoupled, separated) projections of the stator current vector (Figure 1).

Rice. 1. Block diagram of the coordinate decoupling block.

From the expression for the electromagnetic torque (5) and the general equation of motion, we can obtain the transfer function of the IM via the rotor frequency control channel:

where is the mechanical time constant. This transfer function is fully consistent with a DC motor, so the construction of electric drive systems with vector control of IM is no different from DC drives.

It should be noted that the control device can perform its functions only on the condition that the IM parameters included in the transfer functions of its links correspond to the true values, otherwise the flux linkage and rotor frequency in the IM and in the control device will differ from each other. This circumstance creates significant difficulties when implementing vector control systems in practice, because blood pressure parameters change during operation. This especially applies to the values ​​of active resistances.

Mathematical description of coordinate transformations

If the current vector is represented in a fixed coordinate system (a, b), then the transition to a new coordinate system (x,y), rotated relative to the original one by a certain angle (Figure 2a), is carried out from the following relation of the arguments of complex numbers:

Or (7)

Rice. 2. Generalized current vector in various coordinate systems.

For a coordinate system rotating with a constant angular frequency, the angle is equal to .

The coordinate transformation can be written in expanded form as follows:

From here you can find the components of the vector in matrix form:

, (9)

where , are the instantaneous values ​​of the currents of the corresponding windings.

A necessary element of the IM vector control system is a rotator that transforms vector coordinates in accordance with expression (9).

To transform variables from the coordinate system (d,q) to the coordinate system (a, b), we use the following equations:

where γ is the field orientation angle. The block diagram of the rotator is shown in Figure 3.

Rice. 3. Block diagram of the rotator.

Mathematical model of blood pressure

The asynchronous motor is modeled in the coordinate system - α, β. The equations corresponding to this coordinate system are described by the system of equations:

(11)

where: , , , - components of the stator and rotor flux linkage vectors in coordinate systems; , - components of the stator voltage vector in coordinate systems; - active resistance of the stator and rotor windings; - total inductances of the stator and rotor windings (17), (18); - electromagnetic coupling coefficients of the stator and rotor (12), (13); p - number of pole pairs; - mechanical speed of the rotor; J is the moment of inertia of the motor rotor; - moment of resistance on the motor shaft.

The values ​​of the total inductances of the windings and the electromagnetic coupling coefficients of the stator and rotor are calculated using the formulas:

where: - leakage inductance; - inductance of the magnetization circuit,

where: - inductive leakage resistance of the stator and rotor windings; - inductive reactance of the magnetization circuit; f is the frequency of the voltage supplied to the stator.

By solving a system of differential equations in coordinates (11), it is possible to obtain a dynamic mechanical characteristic and time characteristics of state variables (for example, torque and speed), which give an idea of ​​the processes occurring in the engine. The components of the voltage supplied to the stator winding of the motor are calculated by the formula:

(19)

where U is the effective value of the voltage supplied to the stator.

Solving the equations comes down to integrating the left and right sides of each differential equation of the system:

(20)

Current dependences are calculated using the equations:

(21)

Passport data of AD DMT f 011-6у1 are given in the article.

Figure 4 shows a model of an IM controlled by stator current in a coordinate system oriented along the rotor flux linkage.

Rice. 4. IM vector control model in the Simulink environment:

AD - asynchronous motor;

УУ - control device, including: RK - coordinate decoupling unit, R - rotator;

N is the load, which also takes into account the resistance of the bearings.

The IM vector control model allows you to monitor electromagnetic processes occurring in an asynchronous motor during its operation.

The following graph (Figure 5) shows the mechanical characteristics of an electric motor with vector control, obtained by modeling, in comparison with the mechanical characteristics of an electric motor without a controller, obtained in a full-scale experiment.

Rice. 5. Comparison of mechanical characteristics.

As you can see from the graph, with vector control the mechanical characteristic of an asynchronous motor becomes rigid, as a result of which the overload range expands. The characteristic values ​​in the range from 0 to 153 Nm differ slightly, the error is only 1.11%, therefore, the resulting mathematical model adequately reflects the operation of a real engine and can be used for conducting experiments in engineering practice.

Conclusion

The use of vector control allows you to directly control the electromagnetic torque of the electric motor by changing the amplitude and phase of the supply voltage. To vector control an asynchronous motor, you must first reduce it to a simplified two-pole machine, which has two windings on the stator and rotor, according to which there are coordinate systems associated with the stator, rotor and field. Vector control implies the presence of a mathematical model of an adjustable electric motor in the control link.

The mechanical characteristics obtained from the operation of the described model confirm the theoretical information about vector control. The model is adequate and can be used for further experiments.

Reviewers:

Shvetsov Vladimir Alekseevich, Doctor of Technical Sciences, Professor of the Department of RES KamchatSTU, Petropavlovsk-Kamchatsky.

Potapov Vadim Vadimovich, Doctor of Technical Sciences, Professor of the Far Eastern Federal University branch, Petropavlovsk-Kamchatsky.

Bibliographic link

Likhodedov A.D., Portnyagin N.N. MODELING OF VECTOR CONTROL OF AN ASYNCHRONOUS ELECTRIC DRIVE // Modern problems of science and education. – 2013. – No. 1.;
URL: http://science-education.ru/ru/article/view?id=8213 (access date: 03/18/2019). We bring to your attention magazines published by the publishing house "Academy of Natural Sciences"

Vector control

Vector control is a method of controlling synchronous and asynchronous motors, not only generating harmonic currents (voltages) of the phases (scalar control), but also providing control of the rotor magnetic flux. The first implementations of the vector control principle and high-precision algorithms require the use of rotor position (speed) sensors.

In general, under " vector control" refers to the interaction of the control device with the so-called "spatial vector", which rotates with the frequency of the motor field.

Mathematical apparatus of vector control

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Books

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