WO2005119900A1

WO2005119900A1 - On-line parameter adaptation in ac motors

Info

Publication number: WO2005119900A1
Application number: PCT/SE2005/000827
Authority: WO
Inventors: Ragnar JÖNSSON
Original assignee: Individual
Current assignee: Individual
Priority date: 2004-06-01
Filing date: 2005-06-01
Publication date: 2005-12-15
Anticipated expiration: 2006-12-01
Also published as: SE0401401D0

Abstract

A method and system of controlling an AC induction motor for sensorless field oriented control. The motor comprises a stator, a rotor, at least two stator windings and at least two rotor windings. The control system comprising first (uq) and second (ud) control signals from which output voltages are calculated and fed to the motor for the operation and control of the motor in four quadrants. The first control signal (uq) essentially controls the torque and said second control signal (ud) essentially controls the magnetizing current or flux of the motor. The first control signal (uq) is passed through a highpass filter in order to filter out and remove low frequency components of the control voltage. A corresponding theoretically generated highpass filtered control signal including actual parameter values of the motor (RSm, RRm, LSm) is compared with the actual generated highpass filtered control signal in order to produce an error signal. Finally, the parameter values are adjusted so that said error signal is minimized. The break frequency (ω2) of the highpass filter is lower than a characteristic frequency ω1 = (RS+RR) / σLS of said motor.

Description

TITLE: ON-LINE PARAMETER ADAPTATION IN AC MOTORS

AREA OF INVENTION The present invention relates to a method and control system for an AC induction motor and more specifically for sensorless field oriented control. The motor comprises a stator, a rotor, at least two stator windings and at least two rotor windings. The control system comprises first and second control signals, from which output voltages are calculated and fed to the motor for the operation and control of the motor. The first control signal essentially controls the torque of the motor and the second control signal essentially controls the magnetizing current or flux of the motor. A major feature of the invention is that it permits sensorless control, i.e. without a mechanical sensor on the motor shaft. BACKGROUND OF INVENTION The present invention is based on the inventions disclosed in EP-B-0515469 and in a pending Swedish patent application 0400596-3 filed 2004-03-10, which are owned by applicant of the present invention. Said patent documents disclose a method and control system for an AC induction motor for control thereof in four quadrants, i.e. both as motor and generator. The system has been named "Natural Field Orientation" NFO, because of the fact that the control strategy is simple and based on "natural" phenomena in the motor itself. It is a well-known fact that sensorless control is especially difficult at low motor speeds, close to zero speed. The calculation of control signals relies on measured electrical quantities (voltages and currents) and an accurate knowledge of the motor parameters. Especially the stator resistance has a dominating role in the equations. It can be concluded that it is very important to know the true value of the stator resistance in order to get good performance of the control system at low speeds. The stator resistance depends on the temperature of the motor windings, i.e. on the temperature of the motor. A modern motor with isolation class F can be operated at 40 degrees Celsius ambient temperature and with an internal temperature rise of 105 degrees. When the motor heats up from normal ambient temperature of 20 degrees to maximum permissible temperature of 145 degrees the copper resistance will increase approximately 50 %. This large variation explains why it is so important to monitor and measure the true stator resistance during motor operation, i.e. "on-line". In the following, the term "adaptation" is used to describe the process of automatic measurement of the resistance when the motor is used in normal operation. In EP-B-0515469, on-line adaptation of the stator resistance when the motor operates at low speed is described. This will not be considered or described in the present specification. However, the present invention relates to the adaptation of the stator resistance when the motor operates at high speed. At first sight, it may not be necessary to adapt the value of the stator resistance at high speed. The stator resistance has almost negligible influence on the control performance at high speed. It may happen, however, that the motor operates at high speed with heavy load during a long time. Then it heats up. Suddenly it may be required to make a stop, or quickly go down to low speed. In such a case it will be too late for adaptation of the stator resistance if it has not been done already at high speed. DISCLOSURE OF THE INVENTION An object of the present invention is to adapt the true value of the stator resistance when the motor operates at high speed. The description is made for an AC induction motor but the invention can be used with other motor types as well. According to an aspect, there is provided a method of controlling an AC induction motor for sensorless field oriented control, comprising a stator, a rotor, at least two stator windings and at least two rotor windings, said control system comprising first and second control signals from which output voltages are calculated and fed to the motor for the operation and control of the motor in four quadrants, wherein said first control signal essentially controls the torque of the motor and said second control signal essentially controls the magnetizing current or flux of the motor. The method comprises passing said first control signal through a highpass filter in order to filter out and remove low frequency components of said control voltage; and comparing said higpass filtered control signal with a corresponding theoretically generated highpass filtered control signal including actual parameter values of the motor in order to produce an error signal. The parameter values may be adjusted so that said error signal is minimized. The break frequency of said highpass filter may be lower than a characeristic frequency of said motor. The break frequency of said highpass filter may be above a value which is dependent of the inertia of the motor so that the counter electromotive force of the motor is effectively removed by the highpass filter. According to another aspect, there is provided a control system for an AC induction motor, for sensorless field oriented control, comprising a stator, a rotor, at least two stator windings and at least two rotor windings, said control system comprising first and second control signals from which output voltages are calculated and fed to the motor for the operation and control of the motor in four quadrants, wherein said first control signal essentially controls the torque of the motor and said second control signal essentially controls the magnetizing current or flux of the motor. The system comprises a highpass filter for filtering said first control signal in order to filter out and remove low frequency components of said control voltage; and a means for comparing said higpass filtered control signal with a corresponding theoretically generated highpass filtered control signal including actual parameter values of the motor in order to produce an error signal. The system may further comprise a means for adjusting said parameter values so that said error signal may be minimized. A break frequency of said highpass filter may be lower than a characeristic frequency of said motor. The break frequency of said highpass filter may be above a value which is dependent of the inertia of the motor so that the counter electromotive force of the motor is effectively removed by the highpass filter.

BREIF DESCRIPTION OF THE DRAWINGS Further objects features and advantages of the invention will appear from the following detailed description of embodiments of the invention with reference to the appended drawings, in which: Fig. 1 is a block diagram of a control system according to prior art; Figs. 2A and 2B are schematic circuit diagrams of a motor model; Fig. 3 is a block schema similar to Fig 2A or 2B; Fig. 4 is a block schema similar to Fig. 3 with a current control added; Fig. 5 is a diagram showing the transfer function and break frequencies; Fig. 6 is a block diagram of an embodiment of the invention .

DETAILED DESCRIPTION OF EMBODIMENTS Figure 1 is a block diagram of a typical, modern control system for field oriented control of an AC induction motor. The motor itself is schematically shown in the lower part of the figure. The motor is connected to three terminals with the voltage outputs u_SR , u_ss and u_sτ . Motor currents i_SR , i_ss and i_sτ are measured and fed back to the system. Almost all professional motor control systems use current control loops. The current control loop should be as fast as possible. This gives a quick response on control signals. Further on, the current control loop protects the circuit, because the current control loop keeps the motor current at the same value as the commanded current. Thanks to this it is possible to have an accurate current limit on the commanded value. Figure 1 shows two current control loops, one for the q-channel and one for the d-channel . Although not shown in Figure 1 it is assumed that the complete system is designed and built as a "pulse width modulated" (PWM) control system. This is common practice for motor drives. A modern control system is normally digital and the sampling frequency is normally the same as the PWM frequency. Practically all modern motors are designed and built as three-phase motors. This is for practical reasons. It is, however, clear from figure 1 that the real control system operates in two coordinates only, defined as d- and q-coordinates . A conversion of the control voltages is made from two to three coordinates (or phases) before the voltages are connected to the motor. In a similar way, the measured currents in three phases are converted from three to two coordinates before they are used in the control system. The conversion between two and three coordinates has no importance for the theory. It only changes some scaling factors as is well known. Consequently, the following description will be made for a two-phase system. Equations and symbols in the following are based on:

W. Leonhard, Control of Electrical Drives, Third edition,

Springer Verlag 2001. A detailed description of the whole theory for field oriented control will not be given in this specification. Only those parts of the system that are relevant for the present invention will be described. Figure 2 A shows the classical "equivalent circuit" of one motor phase with the stator components to the left and the rotor components to the right. The airgap between stator and rotor is not indicated.

R_s = the resistance in the stator winding, normally made of copper σ_sL₀ = the leakage inductance on the stator side L₀ = the main inductance on the stator side σ_RL₀ = the leakage inductance on the rotor side

R_R I slip symbolizes the rotor circuit according to classical theory Figure 2 B shows a slightly modified circuit that is the basis for the present description. It should be noted, however, that the present invention would work equally well in a system according to Figure 2 A. Figure 2 B defines a so-called "rotor flux model" with all leakage inductance concentrated on the stator side.

σ = a combined leakage factor for the stator and rotor inductance

L_s = the total stator inductance R_R l(l + σ_R ) = the resistance in the rotor circuit for a rotor flux model

EMF = the "Electro Motive Force" = the induced voltage in the rotor winding, that is proportional to the rotor speed. Sometimes called the "speed voltage".

*_m« ⁼ the magnetizing current that creates the common magnetic flux in the motor

(l + σ_R )ϊ_R = the rotor current that creates the motor torque The supply voltage is a voltage vector: u_s = u_d + ju_(/ . The two currents are indicated as vector components i_mR and i_R . The vector notation is important, because the two currents are orthogonal to each other. There is 90 degrees phase shift between the magnetizing current and the rotor current. This is a condition for correct "field orientation". The upper part of Figure 1 shows two separate control channels, the q-channel and the d-channel. The q-channel controls the torque. Only this channel will be considered in the following. The following simplified symbols will be used for the q-channel : Supply voltage = u_q Rotor current = i Rotor resistance = R_R EMF = e The motor has a homogenous design and all three phase windings are equal. It is not possible to describe one phase winding as a d-phase and another phase as a q-phase . All phases operate both with d- and q-components of the voltages and currents. In spite of this it is possible to control the d-channel and the q-channel separately, as is shown in Figure 1. This requires a thorough theoretical explanation. This will not be given here, but it is noted that this favorable feature is a result of the concept "field oriented control". Figure 3 is similar to Figure 2 A but with simplified symbols and indication of the individual d- and q- components of voltage and current. The q-channel according to Figure 3 will be studied in the following. An electric motor is not equivalent with a normal electric circuit. The mechanical operation of the motor has influence on the voltages and currents. One way of describing this phenomenon is to say that the motor has a "mechanical impedance" that is connected or added to the "electrical impedance". Normally it is impossible to separate the mechanical impedance from the electrical impedance as long as only electrical measurements are made. It is the purpose of the present invention to solve this problem and measure the stator resistance in the presence of the mechanical impedance. Figure 3 shows the counter EMF as an electric voltage e. This is where the mechanical impedance of the motor has influence on the electrical system. The voltage e is proportional to the magnetic flux and the rotor speed. The flux is normally kept constant and consequently the analysis can concentrate on the rotor speed. Figure 4 is similar to Figure 3 but without the components from the d-channel, i.e. only components in the q-channel are shown. A current control circuit has been added. Compare with figure 1. In reality, there is a vector rotator for the output voltage u_q and a vector rotator for the measured current . These two vector rotators cancel each other and consequently they need not be shown in Figure 4. The control part of figure 4 is a conventional PI- controller. The proportional gain is defined by the value of R₀. The integral gain is defined by the time constant

T Two equations can be written for figure 4 : l + sT_n

«, =( -'» sT_n u_q - e ι_n = ^■ R_s + R_R + sσL_s

s = Laplace operator Develop the second equation:

σL,

Define :

Make use of a classical design rule for a current controller .

Choose: ^σ° ^so = T₀ -".SO ⁺ -^ΛO

The extra index "0" tells that these are the nominal (or theoretical) parameter values for the motor. They are not exactly the same as the real values in the actual motor. Now it is possible to write an expression for the "open loop gain" Y₀ of the current control loop:

r ^L.o-A-"-o^{1 +} sτ^, ₀ ^ϊl (R_s + R ' i+sr,) Rearrange the expression:

In this expression for the open loop gain it is acceptable to make an approximation: Then:

Calculate the "closed loop gain" Y_c :

R_n where ω₀ = ^{1+ y}« I₊,Γ„^±^ 1 +-^- τ₀(R_s + R_R ) R_n ω_n

The transfer function for the current loop controller is

ω_n

Observe that the "speed voltage" e is present all the time. It can be described as a disturbance in the system but it has no influence on the transfer function itself. Classical control theory tells that the maximum possible "bandwidth" ω₀ of the current control loop depends on the sampling frequency in the digital control system. (The sampling process is not shown in Figure 4.) A rule of thumb says that a suitable bandwidth is 1/10 of the sampling frequency. A typical PWM controller in a motor drive system operates with 5 kHz switching frequency and the data sampling is made with the same frequency.

Consequently, the bandwidth of the current control loop can be 500 Hz. In other words ω₀ - 2π500 « 3000 rad/s. The exact bandwidth of the current control loop is not important for the description of the present invention. It is enough to know that the bandwidth ω₀ is much higher than the frequency c . A typical value for the frequency ω_] is 150 rad/s or 25 Hz. In the following analysis the current loop controller is considered to be a "current source" that creates a current i in the motor winding. This is true up to the bandwidth limit ω₀. By help of Figure 4 it is possible to write an expression for the voltage u_q :

", = *, (^Rs + ^sσLs +^R _R)+^e + e

ω_n

Finally: 1 + ^ u_q = i_{qR /}{^Rs + ^RR) ^- + ^e 1 + — ω₀

This transfer function can be plotted in a Bode diagram. This is a logarithmic diagram that shows the amplitude of _ as a function of the excitation frequency ^lqR_ef ω . See Figure 5. The transfer function for is represented by three asymptotic lines (if e is neglected) u . .

Low frequency: = (R_S+R_R) ^lqKef ij T

Medium frequency: — — = (R_S+R_R)— = (R_S + R_R)₇ ^—r = sσL_s ',Re «. {^RS ^{+ R}R)

High frequency: — — = (R_s + R_R )— 5- ^lqKtf ^ω\ So far the equations describe an existing system. It is time to add the extra functions according to the present invention . It was said earlier that the "mechanical impedance" of the motor had influence on the system and the speed voltage represents this influence e . It is necessary to eliminate the influence of the voltage e . The rotor speed can not change as fast as the electrical signal because of the inertia in the motor itself and in the load. Consequently, the voltage e can not change as fast as the voltage u and this makes it possible to separate the electrical properties from the mechanical. One possible solution is to use a high pass filter for the voltage signal . ω, High pass filter: 1 + ω. See Figure 5 where the high pass filter function is shown as a dotted line. Essentially all variations in e are supposed to occur at frequencies below the frequency ω₂ . The value of the frequency ω₂ may be chosen depending on the application. The resistance adaptation can be made in the frequency region from ω₂ to ω_l . A low value of ω₂ gives a larger frequency range for the resistance adaptation. The value of ω₂ can be lower if the inertia is high . Figure 6 shows a possible system design according to the present invention. The upper part of Figure 6 shows the real current controller and the real motor according to the description above. The lower part of Figure 6 shows a "model system" that is an accurate representation of the real system. The whole model system is designed as a digital system in the microprocessor. If both systems are identical and operate on the same control signal i_{q Ref} they will create the same voltage u_q in the upper and the lower channel. The high pass filters are shown as separate blocks in the figure. The outputs from the high pass filters are

^U _qmotor . ^and ",mode/ ^• Observe that the speed voltage e is included in the model system. This is not the real speed voltage. The estimated speed voltage from the motor control system should be used in this place. Alternatively, the speed voltage is omitted from the model system. The high pass filter is intended to eliminate most of the influence from the speed voltage anyway. The difference signal u_qmolor - u_{q moάel} = ε can now be used as an information source for adjusting the parameter values (R_s + R_R) and σL_s in the model system. The adjustment should be made until the value of ε is zero. This serves as an indication that the real system and the model system are identical. The resistance adjustment can be made essentially in the frequency region from ω₂ to ω . If the leakage inductance should be adjusted, it can be made essentially in the frequency region from ω_l to ω_Q . The leakage inductance can be considered to be stable with a fixed value and it is not necessary to adjust this parameter . The adjusted resistance values (and possibly the leakage inductance value) in the model system should be used in the motor control algorithm for the real system. It was said above that the stator resistance could be adapted at low speed, according to known theory, for example as described in EP-B-0515469. However, such an adaptation is made in the d-channnel. It is also possible to adapt the stator inductance in the d-channel, however at high speed. The present invention describes a scheme for adaptation of the series resistance (R_S + R_R ) in the q- channel at all speeds. A combination of the different methods may be used. The series resistance (R_S + R_R ) is measured at all speeds, and this gives indirect information about the temperature changes in the stator resistance R_s . It can be assumed that the stator and rotor windings heat up to the same extent, and consequently the temperature increase of R_s is similar to that of R_R . In reality the rotor is slightly warmer than the stator and this can be taken into account. The actual value of the stator resistance at ambient temperature is measured in advance, and consequently the compensation for temperature change can be added to the actual value. The adaptation of stator resistance in the d-channel at low speed may still be used. Thanks to the present invention the adaptation can start from an almost correct value . The adaptation of the series resistance (R_s + R_R ) gives information also about the rotor resistance R_Λ . The rotor speed is estimated by help of equations including the rotor resistance and consequently the speed estimation can be made more accurate, thanks to the present invention. Good parameter values are essential for good motor control. Field oriented control can operate more accurately if the parameter values are accurate. This results in improved field orientation. An accurate field orientation helps to make the channels orthogonal and thus separate the d- and the q-channel from each other and this makes possible a good parameter adaptation. The invention may be embodied in software and connected to inverters connected to a motor. The software may be executed by a DSP (Digital Signal Processor) or a conventional CPU (Central Processing Unit) . Alternatively, the method and system may be embodied in an ASIC (Application Specific Integrated Circuit) or any other hardware or combination of hardware and software. The method and system may also be performed by analogue circuitry. The invention can be implemented in any suitable form including hardware, software, firmware or any combination of these. The elements and components of an embodiment of the invention may be physically, functionally and logically implemented in any suitable way. The functionality may be implemented in a single unit, in a plurality of units or as part of other functional units. The invention may be implemented in a single unit, or may be physically and functionally distributed between different units and processors. In the claims, the term "comprises/comprising" does not exclude the presence of other elements or steps. Furthermore, although individually listed, a plurality of means, elements or method steps may be implemented by e.g. a single unit or processor. Additionally, although individual features may be included in different claims, these may possibly advantageously be combined, and the inclusion in different claims does not imply that a combination of features is not feasible and/or advantageous. In addition, singular references do not exclude a plurality. The terms "a", "an", "first", "second" etc do not preclude a plurality. Reference signs in the claims are provided merely as a clarifying example and shall not be construed as limiting the scope of the claims in any way. Above, the invention has been described in relation to certain embodiment shown on the drawings. However, such embodiments do not limit the invention but are only for illustrating the invention. The invention may be modified and completed in different manners as occurs to a person reading the specification and such modifications are intended to be within the scope of the invention. The invention is only limited by the appended patent claims.

Claims

PATENT CLAIMS 1. A method of controlling an AC induction motor for sensorless field oriented control, comprising a stator, a rotor, at least two stator windings and at least two rotor windings, said control system comprising first (u_q) and second (U_d) control signals from which output voltages are calculated and fed to the motor for the operation and control of the motor in four quadrants, wherein said first control signal (u_q) essentially controls the torque of the motor and said second control signal (u_d) essentially controls the magnetizing current or flux of the motor, characterized by passing said first control signal (u_q) through a highpass filter in order to filter out and remove low frequency components of said control voltage; and comparing said higpass filtered control signal with a corresponding theoretically generated highpass filtered control signal including actual parameter values of the motor (R_Sπ R_RΓT σL_Sm) in order to produce an error signal. 2. The method of claim 1, characterized by adjusting said parameter values (R_Sm/ RRΠI, σL_Sm) so that said error signal is minimized. 3. The method of claim 1 or 2, characterized in that a break frequency (ω₂) of said highpass filter is lower than a characeristic frequency C0ι = (R_S+R_R) /σL_s of said motor . 4. The method of any one of the previous claims, characterized in that said break frequency (ω₂) of said highpass filter is above a value which is dependent of the inertia of the motor so that the counter electromotive force (EMK, e) of the motor is effectively removed by the highpass filter. 5. A control system for an AC induction motor for performing the method according to claim 1, for sensorless field oriented control, comprising a stator, a rotor, at least two stator windings and at least two rotor windings, said control system comprising first (u_q) and second (u_d) control signals from which output voltages are calculated and fed to the motor for the operation and control of the motor in four quadrants, wherein said first control signal (u_q) essentially controls the torque of the motor and said second control signal (u_d) essentially controls the magnetizing current or flux of the motor, characterized by a highpass filter for filtering said first control signal (u_q) in order to filter out and remove low frequency components of said control voltage; and a means for comparing said higpass filtered control signal with a corresponding theoretically generated highpass filtered control signal including actual parameter values of the motor (R_Sm^ R_RΠ σL_Sm) in order to produce an error signal. 6. The system of claim 5, characterized by a means for adjusting said parameter values so that said error signal is minimized. 7. The system of claim 5 or 6, characterized in that a break frequency (ω₂) of said highpass filter is lower than a characeristic frequency α>ι = (R_S+R_R) /σL_s of said motor . 8. The system of any one of claims 5 to 7, characterized in that said break frequency (ω₂) of said highpass filter is above a value which is dependent of' the inertia of the motor so that the counter electromotive force (EMK, e) of the motor is effectively removed by the highpass filter. 9. A computer program product comprising computer program code means for executing at least one of the method steps according to any of claims 1 to 4 , when said computer program code means are run by an electronic device having computer capabilities.