Current and speed digital control of commutationless DC drives

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Current and speed digital control of commutationless DC

drives

Citation for published version (APA):

Duarte, J. L., Aubry, J. F., & Iung, C. (1989). Current and speed digital control of commutationless DC drives.

IEEE Transactions on Industrial Electronics, 36(4), 480-484. https://doi.org/10.1109/41.43006

DOI:

10.1109/41.43006

Document status and date:

Published: 01/01/1989

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480 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 36, NO. 4, NOVEMBER 1989

Current and Speed Digital Control of

Commutationless dc Drives

J. L. DUARTE, J. F. AUBRY, AND C . IUNG

A bstracl-Whole direct digital control of commutationless dc drives may be reached successfully by a minimal hardware structure. This paper deals with the presentation of a low-cost monochip microcomputer-based control system for speed regulation and current limitation that bas no current measurement of a dc motor fed by thyristors in discontinuous current-mode operation. With this system, the speed of the drive is controlled by a classical algorithm using the z transform. The thyristor firing is synchronized with the power supply and controlled by internal interrupts of the microcomputer. The current limitation is elaborated by an estimation algorithm using an experimental simplified model.

NOMENCLATURE

Power Supply

w supply angular frequency

V, peak supply voltage

t time

n index related to the nth control cycle or the nth sample instant

Motor and Load

R , L

J,

f

r

load torque

K back emf constant

1 armature current

n

speed

P,Cp’,Y Ae = wL/R

Qm steady-state speed

r,

steady-state load torque

pm,p

L,

y

L

steady-state angles

armature resistance, self inductance moment of inertia, friction coefficient

U voltage at motor’s terminals

I@

armature current arch crest value firing, exctintion, and conduction angles reduced electric time constant

I. INTRODUCTION

IGH-POWER density and low inductance in the armature

H

circuit are typical features of modem dc machines. If these machines are fed by line-commutated converters (single phase) without any additional smoothing reactance, discontinuous conduction occurs during the whole working range. In

Manuscript received May 5 , 1988; revised March 22, 1989.

J. L. Duarte is with the Electromechanics and Power Electronics Group, Eindhoven University of Technology, Eindhoven, the Netherlands.

J. F. Aubry and C. lung are with the Centre de Recherches en Automatique de Nancy, Nancy, France.

IEEE Log Number 8930407.

such converter drives, commutating processes between thyristors cannot occur, so they are called commutationless dc drives.

A look over existing published literature reveals approaches to the problem of digital speed control of commutationless dc drives where speed is treated alone [ 13, whereas in other cases, an internal current loop is associated with the speed loop [2], [3]. The internal current loop allows better safety where maximum current value is concerned, but on the other hand, it increases the system’s order, leading to an extra effort in practical implementation.

This paper attempts to describe a microprocessor-based speed control for commutationless dc drives, including a new approach for current limitation. The control algorithm has no current loop and is synchronized with the ac power supply voltage zero crossings. At each control cycle, the firing angle is calculated by a PI algorithm. Before enabling the firing pulses, the firing angle that gives a previously specified maximum current arch crest value for the cycle is also forecast. The calculated firing angle is then compared with this estimated angle and, if necessary, suitably modified. In contrast with classical dc drives, this unconventional approach allows current limitation without measuring this process variable.

For a 1-kW dc drive, practical results will be presented and discussed in greater detail.

11. SYSTEM DESCRIPTION AND IMPLEMENTATION The system herein consists of a dc motor drive fed by a single-phase full-wave thyristor bridge in discontinuous operation. The thyristors are fired by pulses generated from a digital impulse generator included in a microprocessor. Using discrete control equations and speed measurements, the same microprocessor performs speed and current control by calculating the firing angle for each cycle and converting these angles into time delays. The basic system structure is shown in Fig. 1.

Because the set motor-converter always operates in discontinuous conduction, a very limited number of components are required in order to implement the suggested system structure. (See [ 11 for the purpose of having a minimal hardware choice based on monochip microcomputers.)

Speed information is obtained by measuring the motor’s back emf when there is no current flow. This procedure avoids specific speed sensors.

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DUARTE et al. : CURRENT AND SPEED DIGlTAL CONTROL OF DC DRIVES R I I e z u t & I 48 1

I '

1

Fig. 1. Basic system structure.

IJJ. SYSTEM

LINEAR MODEL

The main system signals are shown in Fig. 2. Starting from

a) the mechanical time constant is large compared with the time delay between firing instants;

b) the dynamics of the electrical part of the system is very fast when compared with the mechanical one; c) the load torque presents only step changes;

d) only small perturbations around a steady-state operating point are considered.

the following realistic assumptions:

It is possible to work out the system's nonlinear electrome- chanical equations in order to set up a linear discrete recurrence relation for speed at the nth and the (n

+

1)th firing instants as a function of the firing angles [4]. This relation can be written as follows, where

x(n), u(n),

and ~ ( n )

are, respectively, the variations of the speed, the firing angle, and the torque:

x(n+

l)=Sox(n)+ Gou(n)+Lo~(n) (1)

with

x(n

+

1) =

Q(n

+

1)

-

a,;

x(n) =

Q(n)

-

Q,

= cp(n) - (0-

v(n) =

r

(n)

-

r,

where Q(n), cp(n), and

r ( n )

are, respectively, the speed, the firing angle, and the torque at the nth sampling instant, and

Q,,

cp,,

r,

are their steady state values. The expressions of coefficients So, Go, and LO are given by

*

W J R

[",-3

_K sin cp,

1

[l-exp [-yJA,]] 1

Lo=- lr.

W J

Equation (l), taking into account perturbations around a steady-state operating point specified by

a,,

r,,

cp,, and y,, is established in the Appendix.

IV.

SPEED CONTROL

ALGORITHM

Fig. 3 shows the controller structure that allows the drive system to follow a step change in the speed reference and adapt

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V LO 1 - so controller canverler+drive % z - s o reference

Fig. 3. Controller block diagram.

itself to a load torque step change, both with zero error. The controller equation is

u(n)=u(n- 1)+ W l € ( n ) + WoE(n- 1) or

&)=&I- 1 ) + W l € ( n ) + Wo€(n- 1). ₍₂₎ This controller contains an integral action to avoid the static error. The two coefficients WO and Wl are necessary to

achieve an arbitrary pole placement [8].

Then, at each control cycle, the speed control strategy consists of calculating the digital speed error in the microprocessor and then in calculating the firing instant for the cycle. The time delay for the firing instant is established considering the last power supply voltage zero crossing.

Coefficients Wl and

W O

are related to system stability. The characteristic equation of the closed loop set up by (1) and (2) is, after applying the z transform

(Z-l)(Z-So)+Go( WIZ+ Wo)=O. (3) Hence, in order to get a desired dynamic response for the speed loop, one must choose the controller coefficients as

W1= [ 1

+

So - (Z1+ &)]/Go

WO =

-

[ So

-

21Z2] / Go (4)

where ZI and Z2 represent the desired roots for (3). Meanwhile, considering variable speed applications, it may occur that the load torque or the speed reference can change abruptly. In these cases, the controller algorithm can react in such a way that the armature current becomes harmful for the dc motor and the thyristor. Accordingly, it is necessary to keep the current overload beneath a limited value.

V. CURRENT LIMITATION

During each cycle, once the firing angle is settled and before firing pulses are enabled, we can forecast such current characteristics as the average value, extinction angle, or peak value, without any current measurement. This is made possible because the drive system always works in discontinuous current operation, so only the firing angle and the speed are independent variables.

However, the current characteristics are related to the firing angle and speed by strong nonlinear expressions that would take too long to solve on line bv a micromocessor. These

TABLE I

TEST DRIVE SYSTEM

DC motor, 1 H P I 170 V 1 7 A / 3000 rpm K = 0,477 Vdrad R = l , O o h m L = 0,0078 H 0=314,16rad/s f = 0,0010 Nmdrad J = 0,0025 kgm2 V, = 310 V 'peak ( A ) 40 3 0 2 0 IO 0 110 I30 I50 170 ( " ) 90

Fig. 4. Current peak value as a function of the firing angle.

difficulties are bypassed here by approximate calculations, as suggested below.

Based on experimental tests of the system detailed in Table I, Fig. 4 shows the relation between current arch peak values and firing angles, speed being the level parameter. Fig. 5 was set up by changing the level parameter, as suggested by the arrows in Fig. 4. Then, Fig. 5 gives the minimal firing angle as a function of speed so that it will not cross over a desired maximal current arch peak value (see I& max level parameter

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I

483

DUARTE et al. : CURRENT AND SPEED DIGITAL CONTROL OF DC DRIVES

min

I

I50

-

I40 a, .-I b I 3 0 m b d 2 I20 r l

2

C d I10 I O 0

1

TABLE II

NUMERICAL VALUES FOR Am,n AND pmln

15 1 ,a3 10-3 2.618 25 1 ,83 x 10-3 2,443 35 2,io 10-3 2,295 20 1.83 x 10-3 2,531 ' + , 0 ₁₀₀₀ _{2 000} ₃₀₀₀ Speed ( r p r n ) function of speed.

in Fig. 5 ) . Curves shown in Fig. 5 may be approximated by straight lines to get the following expression for the minimal firing angle at each control cycle:

Fig. 5 . Firing angle value corresponding to the current peak value as a

O A -50 rns (a) lo

^I

l

f

l

p m i n ( n ) = P m i n - h n i n Q(n). ( 5 )

Equation (5) is easily computed by a microprocessor. Some values for pmin and

A h

are given in Table II.

Finally, the microprocessor is able to perform current limitation on line without any current measurement on each control cycle. First, the firing angle p(n) is calculated by using

(2). Next, this angle must be compared to pmin (n), as given by

(5). If p(n) is smaller than pmin

(n),

the firing angle adopted for the cycle will be pmin (n). In this case, in order to avoid speed oscillations, the past speed error to be presented to the microprocessor at the next control cycle must be

734 t r b n

400 tr/mn

**~ * ( n ) =**

-[p(n- l ) - p ( n ) + W O E ( T Z - 1)]/W1 ₍₆₎ in order to have

p(n

+

1) = p,in(n)

+

W,€(n

+

1)

+

WoE*(n) ₍₇₎

and p(n

+

1) will be compared to pmin(n

+

1) and so on. VI. EXPERIMENTAL RESULTS

Fig. 6 illustrates a few experimental results. The drive system concerned is detailed in Table I. In Fig. 6(a), the system is not submitted to any constraint. In Fig. 6(b) the desired maximal current arch crest value is 20 A. It is clear that the current limitation smooths the speed response.

Other situations were tested but not shown here. For instance, once chosen for an average operating point, controller coefficients W , and

W O

can be kept constant over the whole working range (speed and load torque) in order to get suitable results. For that reason, the current limitation gets adaptive techniques out from the control strategy.

-50 ms (b)

current limitation (20-A maximal current arch crest).

Fig. 6. (a) Step response without current constraint; (b) step response with

VII. CONCLUSION

A very simple method for commutationless dc drive current limitation and speed control has been presented. The speed control is accomplished by a PI algorithm (2) that gives the firing angle on each cycle. This firing angle is bounded ( 5 ) in order to keep the armature current below a desired value.

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Experimental results confirm the effectiveness of this ap- Y ( e > = o

proach.

for 8 E [cp’(n), cp’(n+ l)]. APPENDIX

Derivation of (1) Then, the numerical equation is integrated

The linearized model of the system has been obtained by the Dirac impulse method 161, 171. The differential equations for

x ( n

+

1) =x[cp(n)

+

a ] =x[cp’(n)] = e-(fr/Jm)x(n)

~. . _

the variables x ( 8 ) = Q(8) - Qm(8) and y ( 8 ) = ii8)

-

are

x + - 6 p ( n )

A, Lo L

y = o

for 8 E [cp’(n), cp’(n+ 111

where Z(n) is the area of the difference of the voltage applied for cp = cpm and for cp = cp(n):

I(n)

= - [ V, sin cp(n) - K * Q(n)]

-

u(n)

and

d x K

f

v

dB Jw Jw Jo

- = - x

-_--.

Because x can be considered slowly varying in a period, we can use x ( n ) to integrate the electrical equation

developing

e-(f/-”%

as 1 - ( f / J w ) 8 and neglecting f / J in front of

R/L,

(1) is obtained.

REFERENCES

[1] J. F. Aubry et al., “Speed control of a dc motor: A low-cost system using a monochip microcomputer,” in Proc. LECI ’8I-IEEE, 1981 (San Francisco, CA), pp. 393-398.

J. F. Aubry et al., “Rtgulation de vitesse d’un moteur a courant continu avec contrale du courant par un microprocesseur monochip,” in Proc. CONCJMEL ’83, 1983 (Toulouse, France), pp. 111-20-111-25.

131 P. Magyar, “The dynamic behavior of the current control loop of a microprocessor-controlled dc drive in discontinuous current mode operation,’ ’ in Proc. Microelectron. Power Electron. Electrical Drive Syst. Conf., 1983, ETG/GMR (Darmstad, West Germany), pp.

183-188.

J. L. Duarte et al., “Digital incremental speed control of dc motor drives fed by thyristors,” IEE Publication 234 on Power Electronics and Variable Speed Drives, pp. 222-225.

J. L. Duarte, “Commande numtrique en courant et en vitesse sans capteur d’un moteur a courant continu,” T h b e de docteur ingknieur,

Institute National Polytechnique de Lorraine, Lorraine, France, Mar. 20, 1985.

R. Prajoux, “Etablissement d’un modble pour le comportement local d’un redresseur polyphast utilist en tant qu’amplificateur de puissance a rkponse rapide,” Comptes Rendus de I’Acadkmie des Sciences- (Paris tome 269 strie 4).

R. Prajoux et al., “Etablissement de modtles mathtmatiques pour rtgulateurs de puissance i modulation de largeur d’impulsions.”

E.S.A. Scientific Tech. Rev., pp. 2 5 4 2 , 1976.

F. M. Brasch and J. B. Pearson, “Pole placement using dynamic compensators.” IEEE Trans. Automat. Cont., vol. AC-15, pp. 34- 43, 1970. [2] [4] [5] [6] Paris: Gauthier-Villars, pp. 477-480. 171 [8]