WO1995008452A1

WO1995008452A1 - Control method and circuit for an induction motor

Info

Publication number: WO1995008452A1
Application number: PCT/NL1994/000231
Authority: WO
Inventors: Tim Gerald BLÖMER; Peter Theodorus Rutgers; Erik Cornelis Maria Verhoeven; Dirk Jan De Groot
Original assignee: Stichting Voor De Technische Wetenschappen
Priority date: 1993-09-23
Filing date: 1994-09-23
Publication date: 1995-03-30

Abstract

Control method and circuitry to control a linear or rotating induction motor wherein Reynolds number R is substantially constant and the ratio between dissipated power and force (Ptot/F) reaches a substantially minimum value by selecting said Reynolds number R to have a value of 0.5 « R « 5.0. When Reynolds number R substantially equals 0.8 the sensitivity of the ratio Ptot/F to parameter variations is minimal, whereas when Reynolds number R substantially equals 1.0 the sensitivity of force (F) to parameter variations is minimal.

Description

Control method and ci-cuit for an induction motor

The present invention is related to a method and a control circuit to control an induction motor wherein Reynolds number R is substantially constant, as is known from the publication W. Deleroi, "Einfluss der Standerwicklungsanordnung auf das Betriebs- verhalten von asynchronen Linearmotoren", Elektrotechnische Zeit- schrift - ETZ Vol.95, No. 11, 2 July 1974, 601-606.

Linear servo-motors are actuators capable of executing a linear movement of limited travel. They are widely used in indus¬ trial applications since a linear movement is directly obtained without intervening means, which are necessary in rotating motors to obtain linear movements and which introduce inaccuracy, back¬ lash, inefficiency, additional mass and reduction of strength. How- ever, the relationship between the generated force and the motor current in linear induction motors is non-linear and the behaviour of linear induction motors is speed dependent. Therefore, control of linear induction motors is difficult.

The dynamics of induction motors in general are described by a set of non-linear differential equations. Since most control algorithms presuppose a linear model, in practice, the induction motor is made linear using a non-linear state feedback, generally known as flux-oriented control. However, in most arrangements according to the state of the art such linearizing results in a poor efficiency because, among other things, the known linearizing methods introduce dissipation of power during periods the linear induction motor is not generating any force.

The control method and circuit according to the publication of W. Deleroi mentioned above, are directed to reduce the influence of the so-called entry effect at high speed, which is especially important when applied with trains and the like. This object of the known method and circuitry is obtained by selecting Reynolds number equal to 10. Then, also optimal efficiency, couple and power is obtained. However, no control method or control circuitry is dis- closed wherein the ratio between dissipated power and force of servo motors designed to generate varying forces at varying speeds is substantially minimal.

A further control method and circuitry to control linear induction motors is disclosed in U. Feldmann, "Steuerung von asyn- chronen Linear otoren mit grossen magnetischen Reynoldszahlen", Elektrotechnische Zeitschrift, ETZ - Vol. 96, No. 7, 5 February, 1975, 311-316. Also in this publication criteria to be optimized are efficiency, couple and power. Moreover, the main object is to obtain an optimal slip which has to be kept constant. To obtain this object it is concluded that Reynolds number has to be large. No indication is given that to obtain the desired object Reynolds number needs to be constant. Moreover, also here no control method or control circuitry is disclosed wherein the ratio between dissi¬ pated power and force of servo motors designed to generate varying forces at varying speeds is substantially minimal.

The object of the invention is to provide a control method and circuitry by which an optimal value of power dissipation of an induction motor is obtained.

In order to obtain this object the control method as defined in the preamble of claim 1 is characterized in that the ratio between dissipated power and force (P_{t t}/F) reaches a sub¬ stantial minimum value by selecting said Reynolds number R to have a value of 0.5 ≤ R ≤ 5.0.

By selecting a constant Reynolds number within this range not only the dissipated power will be zero if no force is generated by the induction motor but also the dissipated power will be sub¬ stantially minimal for any force generated which is a very advant- ageous feature when varying forces at varying speeds are required.

In the method according to the invention Reynolds number R may substantially equal 0.8 since then the sensitivity of the ratio between dissipated power and force (P_{t t}/F) to variations of the translator/rotor time constant of the motor is minimized. When Reynolds number R is selected to substantially equal 1.0 the sensi¬ tivity of the force to variations of the translator/rotor time constant of the motor is minimal.

In a first embodiment, the induction motor is a linear in¬ duction motor, wherein the Reynolds number R is selected to be con- stant by making

2πf - vπ/τ = constant where: f = stator current frequency [Hz] v = translator speed [m/s] τ = pole pitch [m]

In a further embodiment of the invention with respect to linear induction motors the stator current frequency f is selected to meet the condition 2πf_g >> vπ/τ. Then, a constant stator fre¬ quency can be chosen to cause the Reynolds number to be substanti¬ ally constant allowing a simple analog motor control loop design. In a second embodiment, the induction motor is a rotating induction motor wherein Reynolds number R is selected to be con¬ stant by making

ωs - ωr.n/2 = constant

where: ω Ξ = angular velocity of stator current [rad/s] ωr = angular velocity of rotor [rad/s] n = number of magnetic poles of the stator

The control circuit according to the invention is charac¬ terized in that the control circuit is arranged in such a way that the ratio between dissipated power and force (P_tot/F) reaches a substantial minimum value by selecting said Reynolds number R to h. -^* a value of 0.5 ≤ R ≤ 5.0. Such a control circuit shows the same advantages as does the control method according to the inven¬ tion.

Preferably, in the control circuit according to the inven¬ tion Reynolds number R substantially equals 0.8 or 1.0. When Rey¬ nolds number R is 0.8 or 1.0, respectively, the sensitivity of the ratio between dissipated power and force (P_tot/F) or of the force itself, respectively, to variations of the translator/rotor time constant of the motor is minimal.

In a first embodiment such a control circuit is designed for a linear induction motor and comprises at least: a. a control unit having an input connected to a first sum¬ ming device, the first summing device having an inverting and a non-inverting input, in which the inverting input is to receive a feedback signal from the motor and the non-inverting input is to receive a predetermined signal; b. oscillating means to generate at least one sinus wave with a frequency f ; c. means to take a square root having an input connected to an output of the control unit; d. at least one multiplying means having a first input con¬ nected to the oscillating means, a second input connected to the means to take a square root, and an output to supply a current signal to the motor; e. a second summing device having n-1 inverting inputs, each of said inverting inputs being connected to the output of one of the multiplying means, respectively, and one output to supply a current signal to the motor, wherein, in order to select a constant Reynolds number, the frequency f is selected to meet the condition:

2πf_s - vπ/τ = constant

where: f_s = stator current frequency [Hz] v = translator speed [m/s] τ = pole pitch [m]

Preferably, in the control circuit defined above the fre¬ quency f is selected to meet the condition 2πf_s >> vπ/τ. The present invention also relates to a control circuit for a rotating induction motor, comprising at least: a. a control unit having an input connected to a first sum¬ ming device, the first summing device having an inverting and a non-inverting input, in which the inverting input is to receive a feedback signal from the motor and the non-inverting input is to receive a predetermined signal; b. oscillating means to generate at least one sinus wave with a frequency f_s; c. means to take a square root having an input connected to an output of the control unit; d. at least one multiplying means having a first input con¬ nected to the oscillating means, a second input connected to the means to take a square root, and an output to supply a current signal to the motor; e. a second summing device having n-1 inverting inputs, each of said inverting inputs being connected to the output of one of the multiplying means, respectively, and one output to supply a current signal to the motor, wherein, in order to select a constant Reynolds number, the following condition is met:

a) S - ωr.n/2 = constant

where: ωs = angular velocity of stator current [rad/s] ω_r angular velocity of rotor [rad/s] n = number of magnetic poles of the stator

The invention also relates to a preamplifier unit to be used in any of the control circuits defined above, comprising at least: a. oscillating means to generate at least one sinus wave with a frequency f_s; b. means to take a square root having an input to be con¬ nected to an output of the control unit; c. multiplying means having a first input connected to the oscillating means, a second input connected to the means to take a square root, and an output to supply a current signal to the motor. The present invention will be explained by reference to the accompanying drawings, in which:

Figure 1 shows the relationship between total power dissi¬ pation per generated force unit and the Reynolds number of induc¬ tion motors; Figure 2 shows an embodiment of a preamplifier unit accord¬ ing to the invention;

Figure 3 shows a linear induction motor control loop com¬ prising the preamplifier according to figure 2.

The force F generated by a linear induction motor may be expressed in the following way:

F = C(R).I_S ² - F_trans(T_t) (1) where: F = the force generated by the motor [Ν]

C(R) = a variable dependent on R [Ν/A²]

R = Reynolds number

I = the amplitude of the stator current [A]

^Ftrans ⁼ ^^ne transient force [Ν]

T_t = translator time constant [s]

The first part of the equation, C(R).I_s ², is the steady- state force, whereas the second part of the equation, the transient force F.trans' causes the generated force F not to reach its end value instantly. Therefore, F ' tra„n„s limits the band width of the lin- earized system. The time during which Ftrans acts is proportional to the translator time constant T . However, T_t may be selected to be very short in order to make F_trans negligible relative to the steady state force. If so, equation (1) may be written as:

F =- C(R).I ² (2)

Variable C in equations (1) and (2) depends on the Reynolds number R. If R is constant variable C will be constant and, accord- ing to equation (2) the generated force F will be proportional to the stator current I squared. For induction motors Reynolds number

R may be written as

T_t.(2πf_s - vπ/τ) (3)

where: T_t = translator time constant [s] f = stator current frequency [Hz] v = translator velocity [m/s] τ = pole pitch [m] If

2πf_s - vπ/τ = const (4)

then Reynolds number R will be constant and, consequently, variable C(R) will be constant.

To meet the condition of equation (4) the stator frequency f will have to vary around a predetermined value, the variation being dictated by the variation in the translator speed v. This un- desirable situation may be avoided by selecting:

2πf_s >> vπ/τ (5)

Then, the stator frequency f may be constant to cause Reynolds number to be substantially constant. A constant stator frequency is easy to implement by means of an analog preamplifier, as will become more clear from the description of figure 2 below.

The selection of a constant Reynolds number not only sim- plifies the control circuit of the linear induction motor but also offers the possibility of minimum dissipation control (MDC) . This can be shown by reference to figure 1 in which the relationship between the dissipation P_tot per generated force unit F and Rey¬ nolds number R for induction motors in general is depicted. From figure 1 it can be deduced that selecting a constant R, as described above, causes P_tot/F to be constant. Therefore, if no force F is generated no power P will be dissipated, thus, en¬ hancing the efficiency of the system. Moreover, as figure 1 shows, a value of Reynolds number R may be selected at which P_tot/F reaches an absolute minimum value. The curve of figure 1 is to be measured experimentally, either automatically or by hand. The value at which P /F reaches its minimum is also determined either auto¬ matically or by hand. Means to automatically measure the curve of figure 1 are known to a person skilled in the art, as are means to compute the absolute minimum of such a curve. A computer having measuring points of the curve stored in a memory may, for instance, be used to that purpose. In practice, it appears that P_tot/F has a substantially minimum value when Reynolds number R is selected to be constant within a range from 0.5 to 5.0. When Reynolds number R equals 0.8 the sensitivity of the ratio P_tot/F to variations of the translator/rotor time constant of the motor is minimal. When R equals 1.0 the sensitivity of the force F itself to these vari¬ ations is minimal.

Figure 2 shows an embodiment of a preamplifier 30 which may be used in a control loop to control a (linear) induction motor in such a way as to obtain a constant Reynolds number and, therefore, a constant P_{t t}/F, preferably a substantial minimum value of P_tot/F. The control loop itself is shown in figure 3. The preamplifier 30 according to figure 2 for n phase motors comprises a phase-shift oscillator 1 generating output sig¬ nals 2(1 ) ...2(n-1 ) being 360°/n out of phase and being supplied to a switch 4. The switch 4 is operated by the input signal to the preamplifier 30, which input signal is present on line 11, and is split into lines 12 and 13. The input signal on line 11 is a con¬ trol signal proportional to the force F to be generated by the motor. Output lines 5( 1 ) ...5(n-1 ) , respectively, of the switch 4 carry signals 2(1 ) ...2(n-1 ) , respectively, or, inverted signals 2(1 ) ...2(n-1 ) , respectively, depending on the sign of the input signal present on line 12 to switch 4. Output lines 5(1 ) ...5(n-1 ) , respectively, are connected to multipliers 7(1 ) ...7(n-1 ) , respec¬ tively. The multipliers 7(1 ) ...7(n-1 ) each receive a further input signal through lines 17(1 ) ...17(n-1 ) , respectively, being output lines of a square root unit 16. The square root unit 16 receives an input signal via a line 15 which is connected to the output of a rectifier 14. The rectifier 14 receives an input signal via line 13 connected to input line 11.

Each multiplier 7(1 ) ...7(n-1 ) has one output 8(1 ) ...8(n-1 ) , which are directly connected to an end amplifier 31 (figure 3). Moreover, all outputs 8(1 ) ...8(n-1 ) of the multipliers 7(1)...7(n- 1) are connected to inverting inputs of a summing device 20. The output 8(n) of the summing device 20 is connected to the end ampli¬ fier 31. As can be seen in figure 3, the input line 11 to the pre¬ amplifier 30 is the output line of a control unit 34. The control unit receives an input signal Δx, which is the output of a summing device 35, which receives at a non-inverting input a signal repre¬ sentation of a desired position x_nom of a moving part of the motor 32 and at an inverting input a feedback signal representative of the actual position x of the moving part of the motor 32. Further¬ more, the end amplifier 31 supplies output signals to the motor 32 through output lines 36(1 ) ...36(n-1 ) .

During operation the stator current frequency f_s is deter- mined by the phase-shift oscillator 1 and is selected to meet the condition of equation (5). The output signals on output lines 8(1 ) ...8(n-1 ) of the multipliers 7(1 ) ...7(n-1 ) and on output line 8(n) of the summing device 20 are sinus wave signals 360°/n out of phase having an amplitude proportional to the square root of the absolute value of the input signal to the preamplifier 30, being present on line 11. The sign of the input signal on line 11 deter¬ mines the switching state of switch 4 and, therefore, the direction of the electromagnetic field within the motor 32 and the direction of the generated force F.

The combination of the preamplifier 30, the end amplifier 31, and the motor 32 results in a system 33, which behaves like a DC motor. Therefore, a standard P, PI, or PID control unit 34 may be used. A state-feedback control unit may be used instead.

Figures 2 and 3 show analog implementations of a control circuit for a linear induction motor. However, it is to be under¬ stood that also digital implementations are possible in which the analog units of figures 2 and 3 are replaced by their functional equivalents in a computer program.

The method and apparatus according to the invention may ad¬ vantageously be used in rather small induction motors where trans¬ lator time constants are small by nature, and in systems having a small band width, since they have a small transient force relative to the steady-state force.

It is to be understood that the principles of the present invention are also applicable to rotating induction motors that meet the same conditions as set out above. In rotating induction motors the Reynolds number may be defined as:

(ω_ •n/2) (6)

where: _r = rotor time constant [s] ω = angular velocity of the stator current [rad/s] ω_r = angular velocity of the rotor [rad/s] n = number of magnetic poles of the stator According to formula (6) the requirement to keep the

Reynolds number constant is met if

ω_s - ω_r.n/2 = C- (7)

where: C, = constant.

The circuits of figures 2 and 3 also apply in case of rotating induction motors. However, in rotating induction motors the feedback signal x represents the rotor angular position and the signal x_nom represents the nominal rotor angular position.

Claims

1. Method to control an induction motor wherein Reynolds number R is substantially constant characterized in that the ratio between dissipated power and force (P_{t t}/F) reaches a substantial minimum value by selecting said Reynolds number R to have a value of 0.5 ≤ R ≤ 5.0.

2. Method according to claim 1 wherein Reynolds number R substantially equals 0.8 or 1.0.

3. Method according to claim 1 or 2 in which the induction motor is a linear induction motor, wherein Reynolds number R is selected to be constant by making

2πf_s - vπ/τ = constant

where: f = stator current frequency [Hz] v = translator speed [m/s] τ = pole pitch [m]

4. Method according to claim 3 in which the stator current frequency f_s is selected to meet the condition

2πf_s >> vπ/τ

5. Method according to claim 1 or 2 in which the induction motor is a rotating induction motor, wherein Reynolds number R is selected to be constant by making

ω - ω .n/2 = constant

where: ω = angular velocity of stator current [rad/s] ω = angular velocity of rotor [rad/s] n = number of magnetic poles of the stator

6. Control circuit to control an induction motor wherein Reynolds number R is substantially constant characterized in that the control circuit is arranged in such a way that the ratio between dissipated power and force (P_tot/F) reaches a substantial minimum value by selecting said Reynolds number R to have a value of 0.5 ≤ R < 5.0.

7. Control circuit according to claim 6 wherein Reynolds number R substantially equals 0.8 or 1.0.

8. Control circuit according to claim 6 or 7 connectable to a linear induction motor and comprising at least: a. a control unit (34) having an input connected to a first summing device (35), the first summing device (35) having an in¬ verting and a non-inverting input, in which the inverting input is to receive a feedback signal from the motor (32) and the non-in- verting input is to receive a predetermined signal; b. oscillating means (1) to generate at least one sinus wave with a frequency f_s; c. means (14, 16) to take a square root having an input connected to an output of the control unit (34); d. at least one multiplying means (7(1 ) ...7(n-1 ) ) having a first input connected to the oscillating means, a second input connected to the means (14, 16) to take a square root, and an out¬ put (8(1 ) ...8(n-1 ) to supply a current signal to the motor (32); e. a second summing device (20) having n-1 inverting in- puts, each of said inverting inputs being connected to the output (8(1 ) ...8(n-1 ) ) of one of the multiplying means (7(1 ) ...7(n-1 ) ) , respectively, and one output (8(n)) to supply a current signal to the motor (32) , wherein, in order to select a constant Reynolds number, the frequency £. is selected to meet the condition:

2πf - vπ/τ = constant

9. Control circuit according to claim 8, wherein the fre- quency f_s is selected to meet the condition:

2πf >> vπ/τ

10. Control circuit according to claim 6 or 7 connectable to a rotating induction motor, and comprising at least: a. a control unit (34) having an input connected to a first summing device (35), the first summing device (35) having an in¬ verting and a non-inverting input, in which the inverting input is to receive a feedback signal from the motor (32) and the non-in¬ verting input is to receive a predetermined signal; b. oscillating means (1) to generate at least one sinus wave with a frequency f ; c. means (14, 16) to take a square root having an input connected to an output of the control unit (34); d. at least one multiplying means (7(1 ) ...7(n-1 ) ) having a first input connected to the oscillating means, a second input connected to the means (14, 16) to take a square root, and an out¬ put (8(1 ) ...8(n-1 ) to supply a current signal to the motor (32); e. a second summing device (20) having n-1 inverting in¬ puts, each of said inverting inputs being connected to the output (8(1 ) ...8(n-1 ) ) of one of the multiplying means (7(1 ) ...7(n-1 ) ) , respectively, and one output (8(n)) to supply a current signal to the motor (32) , wherein, in order to select a constant Reynolds number, the following condition is met:

ωs - ωr.n/2 = constant

11. Preamplifier unit (30) to be used in a control circuit for an induction motor according to any of the claims 6 to 10 com¬ prising at least: a. oscillating means (1) to generate at least one sinus wave with a frequency f_s; b. means (14, 16) to take a square root having an input to be connected to an output of the control unit (34); c. multiplying means (7, 19) having a first input connected to the oscillating means, a second input connected to the means (14, 16) to take a square root, and an output to supply a current signal to the motor (32) .