Method and apparatus for controlling PWM inverter

In the control of a PWM inverter, there are various requirements such as decreasing a harmonic loss and acoustic noises, improving control response, optimizing switchings of the branches of the inverter in any condition, and simplification in circuit construction. In the present invention, the branches of the inverter are controlled in such that an evaluation function on the whole combination of the inverter and the load connected to the AC side of the inverter is made to be minimized.

TECHNICAL FIELD 
This invention relates to a method and apparatus for controlling a pulse 
width modulation (PWM) inverter. 
This invention is utilized in a case where an AC servo motor is required to 
operate with a low harmonic loss, low acoustic noise, fast torque response 
and high efficiency, or in a case where, in the current controlling system 
using a PWM inverter, the control error is required to be minimum under 
the limited switching frequencies. 
BACKGROUND ART 
According to one of the conventional methods, in the current control, a 
deviation of output current from a calculated current command value (or 
vector value) is inputted to a comparator, and then an output of the 
comparator indicating a comparison result is used to determine the 
switching pattern of the PWM inverter, i.e. on/off of the branches of the 
inverter. 
In other words, in the conventional method, there is only one state 
variable or state vector to determine the switching. 
However, according to the method, the optimum switching is not always 
accomplished because the switching method is determined by only one state 
variable. 
For example, some high frequency currents and acoustic noises have been 
observed. Moreover, there exists another problem in which the structure of 
the circuits for obtaining a command value are complicated because the one 
command value is used to control the whole system. 
It is the object of the present invention to solve the above-mentioned 
problems. 
DISCLOSURE OF INVENTION 
The present invention is characterized in that each arm of an inverter is 
adequately switched in such manner that an evaluation function on a state 
between the inverter and the system connected to the AC side of the 
inverter is minimized.

BEST MODE FOR CARRYING OUT THE INVENTION 
In FIG. 1 showing a preferred embodiment of the invention, reference 
numeral 1 denotes a rectifier circuit, 2 a PWM inverter (a voltage type 
inverter is shown but a current type inverter may also be used), 3 a load 
connected to the inverter (e.g. an AC motor or a power supply), 4 a 
detection and arithmetic circuit for state variables x1, x2, . . . , 5 
denotes an arithmetic operation circuit which calculates optimum command 
values x1, x2, x3, . . . which correspond to x1, x2, x3, . . . according 
to external commands. 6 denotes an address circuit which has, for analogue 
input signals, a conversion circuit which converts an analogue input 
signal to the digital form and includes a comparator or an A/D converter, 
or which has, for digital input signals, a conversion circuit for 
converting the inputted digital signals into a suitable form when they are 
inputted into an optimum switching table to be described later. The 
optimum switching table 7 is programmed in such manner that the PWM 
inverter minimizes the error of a state variable xi--xi using the 
designated evaluation function. 
Now, assuming that the inverter is composed of three branches respectively 
including switching elements S.sub.a, S.sub.b, S.sub.c, and that the 
instantaneous voltage vector v(S.sub.a, S.sub.b, S.sub.c) can take the 
following 8 vector values according to the state 1 or 0 (1 denotes the 
upper position and 0 denotes the lower position) of the switching 
elements: v(0,0,0), v(1,0,0), v(0,1,0), v(1,1,0), v(0,0,1), v(1,0,1), 
v(0,1,1), v(1,1,1). 
In these vectors, v(0,0,0) and v(1,1,1) are zero vectors because the output 
voltages are zero. 
Considering a flux linkage vector .PSI. which is obtained by a time 
integration of instaneous voltage vector v, in order to control the 
magnitude of .PSI. to a substantially constant value, the vector v shown 
in FIG. 2 may be selected. That is, the voltage vector v may be selected 
such that the absolute value .vertline..PSI..vertline. of .PSI. can be 
maintained between the lower value .PSI..sub.min and upper value 
.PSI..sub.max. For example, a case in which .PSI. rotates clockwisely in a 
range of -.pi./6&lt;.theta..ltoreq..pi./6 will be considered, where .theta. 
is an angle between the primary flux linkage vector .PSI. and an axis d. 
If .PSI. reaches the upper limit value .PSI..sub.max at point P.sub.1, 
.PSI. is rotated using v(0,1, 0) of the eight vectors in order to lower 
the absolute value. On the contrary, if .PSI. reaches the lower limit 
value .PSI..sub.min at point P.sub.2, the absolute value is increased by 
using v(1,1,0). 
Similarly, in a case where .theta. is in a different range, the absolute 
value of the primary flux linkage vector can be maintained within the 
predetermined range by detecting that .vertline..PSI..vertline. has 
reached .PSI..sub.max or 1/8.sub.min and by selecting proper voltage 
vector v(S.sub.a,S.sub.b,S.sub.c) according to the value of .theta.. 
In the case of a motor, for example, the rotating velocity of vector .PSI. 
coincides, with the rotating velocity of the rotating magnetic field. 
As a vector .PSI., any one of the above-mentioned eight vectors may be 
selected. If the locus of .PSI. is made to depict a loop, for example, the 
harmonic loss and the acoustic noise will be increased. However, by 
varying the magnitude of vector v and the rotating velocity, the torque 
control and efficiency of an induction motor can be improved. 
One optimum vector at any instant within the eight vectors can be selected 
automatically if the evaluation function and the state function are 
determined. 
Therefore, if the values of vector v as functions of all the input values 
are stored in the form of tables, the optimum switching pattern (the 
combination of ON and OFF of the inverter branch) can be quickly and 
easily outputted. 
FIG. 3 shows an example of a control system to which the present invention 
is applied for high speed torque control and high efficiency operation. 
In FIG. 3, reference numeral 1 denotes a rectifier circuit, 2 a PWM 
inverter, and 3 an induction motor fed by the inverter. 12 and 13 denote 
respectively three phase/two phase converters, 14 a primary flux linkage 
calculation circuit, and 15 an instantaneous torque calculation circuit. 
The combination of circuits 14 and 15 corresponds to the circuit 4 in FIG. 
1. 
Reference numeral 16 denotes a primary flux linkage command calculation 
circuit which is composed of a nonlinear filter 20 having different time 
constants for a rise and a fall, and a nonlinear amplifier 21 whose 
input/output characteristic is shown in FIG. 3A. 
Reference numeral 17 denotes a calculation circuit which calculates a 
torque command value T.sub.ref in accordance with an external command. The 
circuit 17 is composed of P-I control circuit, etc. The combination of 
circuits 16 and 17 corresponds to the circuit 5 in FIG. 1. 
Reference numeral 18 denotes an address circuit which comprises comparators 
22 and 23, and an angle region detection circuit 24. 
The comparator 22 is inputted with the difference between the torque 
command T.sub.ref and an instantaneous torque value T, i.e. T=T.sub.ref 
-T, which is calculated by a substractor 25 and outputs a 2-bit signal 
corresponding to one of 1, 0, and -1 according to the input signal. The 
input/output characteristic of the comparator 22 has a hysteresis as shown 
in FIG. 3B. The output values 1 and -1 denote an excess and a shortage of 
the torque respectively. 
The comparator 23 is inputted with the difference between the primary flux 
linkage command .PSI..sub.ref and actual primary flux linkage 
.vertline..PSI..vertline. i.e. .DELTA..PSI.=.PSI..sub.ref 
-.vertline..PSI..vertline., which is calculated by a substractor 26, and 
outputs a 1-bit signal of 1 or 0 according to the input signal. The 
input/output characteristic of the comparator 23 has hysteresis as shown 
in FIG. 3C. The .PSI..sub.max and .PSI..sub.min of the hysteresis curve 
correspond to the .PSI..sub.max and .PSI..sub.min in FIG. 2 respectively. 
An angle region detector 24 is supplied with signals .PSI..sub.d, 
.PSI..sub.q and .vertline..PSI..vertline., for judging the angle of the 
primary flux linkage vector with reference to axis d line P in one of the 
6 regions, each having an angle of 60.degree. so as to output a 3-bit 
signal which denotes one of 6 regions I-VI. Regions I-VI are the ranges of 
the angle which satisfy the following equations. 
I: -.pi./6&lt;.theta..ltoreq..pi./6 
II: .pi./6&lt;.theta..ltoreq..pi./2 
III: .pi./2&lt;.theta..ltoreq.5.pi./6 
IV: 5.pi./6&lt;.theta..ltoreq.7.pi./6 
V: 7.pi./6&lt;.theta..ltoreq.3.pi./2 
VI: 3.pi./2&lt;.theta..ltoreq.11.pi./6(=-.pi./6) 
The judgement as to whether the angle .theta. is in one of regions I-VI is 
performed by comparing d axis component of .PSI..sub.d and q axis 
component of .PSI..sub.q with .+-..sqroot.3/2.vertline..PSI..vertline., 
.+-.(1/2).vertline..PSI..vertline. and 0. 
The optimum switching table 19 stores optimum switching patterns 
corresponding to the outputs (which are composed of a combination of 
output .tau. of the comparator 22, output .phi. of comparator 23 and 
output .theta. of the angle region detection circuit 24) of the address 
circuit 18. The optimum switching table 19 is composed of, for example, a 
read only memory (ROM) which uses the outputs of the address circuit 18 as 
its addresses, stores the corresponding switching patterns (which are 
composed of 3-bit data corresponding to states of S.sub.a, S.sub.b, 
S.sub.c, respectively) in the addresses and outputs corresponding data 
when an address data is inputted. The switching elements of the inverter 
are driven according to the output data. 
The evaluation function stored in the optimum switching table 19 is 
programmed so as to improve a transient response rather efficiently and to 
minimize the harmonic loss and acoustic noise. 
FIG. 4 illustrates an example of the optimum switching table. 
In the table, .tau. and .phi. denote the torque and primary flux linkage 
output from the comparator, respectively, and .theta.=I,II,III,IV,V,VI 
indicates the angle regions to which the flux vectors .PSI. belong. 
FIGS. 5A and 5B show test results of transient response of primary flux 
linkage .PSI. and torque T by digital simulation method. That is, three 
signals show a locus of primary flux linkage .PSI. and a variation in 
torque T when a torque command is changed in a step-wise fashion. 
As seen from these figures, the locus of the primary flux linkage .PSI. 
forms a minor loop in neither of the stable and transient states. This 
means that there exist little harmonic loss and little acoustic noise. 
Moreover, an experiment showed that the harmonic loss is decreased by one 
half and the acoustic noise is decreased by more than a few decibels. 
Moreover, the system has a very simple circuit configuration as well as a 
very simple adjustment portion for a coefficient R.sub.1 (which 
corresponds to a primary resistance) of a coefficient multiplier in the 
primary flux linkage calculation circuit 14 when compared with the 
conventional vector controller. 
Further, this system is free from any variation of constants, such as 
secondary resistance, because the system controls the torque directly. 
Because of optimization, the torque response is theoretically quicker than 
that obtained from the conventional vector control. 
FIG. 6 shows an example of a control system to which an optimum current 
control of inductive load having a back electromotive force is applied. 
In FIG. 6, reference numeral 1 denotes a rectifier circuit, 2 a PWM 
inverter, 33 an inductive load having a back electromotive force vector 
V.sub.E, 34A a current detector, and 34B a voltage detector, 35 denotes a 
voltage vector detector circuit for the digital output, 36 an A/D 
converter, 37 an angle detector circuit for a current error vector of the 
digital output, and 38 an optimum switching table for determining an 
optimum voltage vector. 
Furthermore reference numeral 39 denotes detection means for detecting 
back-electromotive force v.sub.E, 40 a coefficient multiplier which 
multiplies the back-electromotive force vector v.sub.E with a coefficient 
1/L (L means an inductance of a load 33), 41 an adder which adds the 
output of the coefficient multiplier 40, i.e. v.sub.E /L to the 
differentiated current command value I, i.e. dI.sub.r /dt, and 42 a 
substractor which forms a difference Ie between the current command Ir and 
an actual current I, i.e. I.sub.e =I.sub.r -I. 
The control method executed in the system shown in FIG. 6 is an example of 
an instantaneous current control method in which an evaluation function is 
made minimum. 
The equation described below is used as an evaluation function I. 
EQU I=n.sup.2 e.sup.2 /T.sup.2 
where, n means a number of change-over switchings when a next voltage 
vector is selected by changing the switches of an inverter, e.sup.2 a mean 
square error within a control interval, and T a time interval within a 
control interval, which determines good or bad when the switching 
frequency is relatively high. This value is calculated according to the 
following equation. 
##EQU1## 
where, I.sub.e is I.sub.r -I as shown in FIG. 6, and .phi. is an angle 
between I.sub.e and (dI.sub.e /dt)t=0 immediately after the switching. 
If the back-electromotive force vector and the inductance are assumed to be 
v.sub.E and L respectively, their relation is approximately expressed by 
##EQU2## 
Therefore it is sufficient to select a voltage vector v which can minimize 
the evaluation function v from all the voltage vectors determined by an 
inverter (8 for 3-phase bridge type inverter). 
This selection can be performed using, for example, an instantaneous 
sampling value or sampling values for a predetermined time interval when 
I.sub.e is larger than the predetermined value. 
In order to determine the voltage vector v which minimizes I, it is 
necessary to input angle .phi..sub.e of the vector I.sub.e, dI.sub.r 
/dt+v.sub.E /L and the present state of voltage vector v. 
FIG. 7 shows an output voltage waveform, current command values and an 
output current waveform. 
These waveforms were obtained when the circuit constants are L=10 mH, 
R=0.1.OMEGA. and V.sub.E =140 V and a d.c. input voltage into the inverter 
is 270 V. 
According to the present invention, the evaluation function has become one 
half of that obtained at the same switching frequency by the conventional 
method. This means that the harmonic loss is decreased to one half and the 
acoustic noise of a load is extremely reduced. 
Thus, the optimum control of the system is accomplished by determining the 
evaluation function. 
In the embodiments shown in FIGS. 6 and 7, no optimum switching table is 
indicated. However, the optimum switching patterns under any conditions 
could be made easily by one skilled in the art if the evaluation function 
is determined. 
In the above-mentioned embodiment, the optimum switching table is provided 
and switching patterns corresponding to respective input conditions are 
read out from the table, but the present invention is not limited to that 
embodiment. Switching patterns may be obtained by giving respective input 
conditions to a micro computer producing switching patterns as a result of 
calculations. 
As described above, according to the present invention, a switching for the 
optimization of an evaluation function which is composed of functions of 
state variables is made possible, and multi-variable control is easily 
performed because the errors caused by a commanded value are minimized 
simultaneously. 
Moreover, the present invention can contribute to an improvement of the 
system stability in motor control because a switching pattern which 
decreases harmonic loss and acoustic noises accompanying a switching of 
the PWM inverter can be selected, and the pattern can be selected to avoid 
voltage pulses having extremely narrow pulse widths. 
Further, from the viewpoint of hardware, no complex calculation is needed, 
digitalization is very easy and high speed operation is possible because 
the optimum switching pattern is obtained only by reading out memories 
directly. 
The present invention is suitable for use in PWM inverters connected to 
various AC loads or AC power supplies.