ON THE QUESTION OF INCREASING RESPONSE SPEED AND IMPROVING CONTROL QUALITY IN MUS-D SYSTEMS WITH PPU

V. A. SEVASTYANOV

(Recommended by the scientific seminar of the Department of EPP of the Tomsk Polytechnic Institute)

Reliability in operation, and the static and dynamic accuracy of regulation, determine the quality of a modern automated electric drive for heavy metal-cutting machine tools. To a significant degree, fulfillment of these requirements depends on the characteristics of the converter and of the actuating electric motor of the automatic control system. In MUS-D drives with PPU, the question of investigating ways to increase response speed deserves attention. A certain combination of semiconductor diodes and triodes with the control windings of the magnetic amplifier, associated with complication of the circuit because of separate control of the chokes and reduction of the power gain coefficient, led to the creation of a new type of fast-acting magnetic amplifiers (BMU)—semiconductor-magnetic commutators, distinguished by stability of the gain coefficient and frequency characteristics [2].

The investigations carried out showed that the use of intermediate semiconductor amplifiers (PPU) together with ordinary self-saturating magnetic amplifiers (MUS), under certain conditions, makes it possible to obtain the same optimal dynamic characteristic as in the BMU, with a simpler circuit solution in a multiphase MUS, and makes it possible to use standard PPUs.

The three main causes of the inertia of a MUS determine its response speed [1]: the occurrence of short-circuited loops in the electrical circuits; half-period delay; and inertia caused by the coupling between changes in the fluxes in the cores of the MUS circuit through the common control circuit. This coupling leads to an increase in the change of flux of the controlled choke at the expense of the EMF induced in the control winding of another choke that is in the “interrogation” state—by the operating voltage, i.e., at the expense of the change of flux in another core. In this case the output voltage will be determined not only by the value of the control signal in this controlling half-period, but will also depend on the magnitude of the control signal in the preceding half-period. As a result, inertia arises, which is usually represented by a first-order element with the time constant \(T_{\text{mu}}\).

Under these conditions the transfer function of the MUS, in the linear approximation, according to [1], can be represented as:

\[ W(p)=\frac{K_{\mathrm{mu}}}{T_{\mathrm{mu}}p+1}\,e^{-p\tau}. \tag{1} \]

Here \(K_{\mathrm{mu}}\) is the static voltage gain coefficient of the MUS,
\(T_{\mathrm{mu}}\) is the time constant of the MUS caused by the third source of inertia,
\(\tau\) is the half-period delay time, which cannot be neglected, since it determines the stability of operation of the ACS.

It follows from (1) that a reduction of the principal inertia of the MUS can be achieved by decreasing the time constant \(T_{\mathrm{mu}}\). Since the latter and the power gain coefficient \(K_{\mathrm{mp}}\) of the magnetic amplifier are interrelated, in practice, in deeply regulated MUS-D drives with a PPU, this can be accomplished by redistributing the power gain coefficients \(K_{\mathrm{sr}}\) and \(K_{\mathrm{pr}}\) of the power MUS and the PPU; at the same time their voltage gain coefficients \(K_{\mathrm{mu}}\) and \(K_{\mathrm{pu}}\), which determine the static accuracy of regulation, may remain the same. On the basis of these considerations, in view of the small values of the operating voltages of the thyrodes (20–30 V), in MUS-D drives with a wide speed-control range it is expedient to use a class-D PPU with pulse-width-modulation elements, with transition to the current control winding of the MUS.

Fig. 1. Schematic diagram of the converter: output stage of the PPU-MUS.

Figure 1 shows the schematic diagram of such a converter, including the output stage of a class-D PPU in the form of a thyrode PT operating on the control winding of the power MUS. The power section of the MUS is assembled according to a circuit with internal negative feedback and has no closed loops in the power circuit. The output PT is normally (in the absence of a control signal) brought into saturation by the base-bias circuit. When a control signal is present, owing to the specific operation of a class-D PPU, the output PT, operating on the combined control-bias winding connected in series in the collector circuit, switches to cutoff mode with repetition frequency \(f_k = 100\) Hz and with pulse duty ratio \(\gamma\) regulated as a function of the input signal. The PT is protected against overvoltages by the discharge circuit \(D\)--\(OY\)--\(R_d\).

To investigate the behavior of the PPU-MUS converter in dynamics as an element of the ACS and to determine its influence on the response speed

values of the output power of the PPU, the PWM frequency, circuit solutions, etc., the following was done. Initially the output stage of the PPU was placed under the operating conditions:

\[ E_k = 20\ \text{V};\quad I_{cy}=0.3\ \text{A};\quad R_l=50\ \Omega;\quad f_k=100\ \text{Hz}. \]

The parameters of the combined control-bias winding were taken as:

\[ W_{oy}=200\ \text{turns},\quad R_{oy}=15\ \Omega;\quad P_{\max}=E_k I_{oy}=20\cdot 0.3=6\ \text{W}. \]

The power circuit of a series MUS of type UM. 3P—32.45.31, \(P_n=4.5\ \text{kW}\), \(U_n=340\ \text{V}\), \(K_{\text{dyn}}=13\cdot 10^3\ \text{s}^{-1}\), was assembled according to a circuit with external c.f. Then the expected time constant can be calculated, with sufficient accuracy, from the known formula:

\[ T_{\text{MU}}=\frac{K_{\text{mp}}}{K_{\text{dyn}}} =\frac{750}{13\cdot 10^3}=0.058\ \text{s}, \]

where the MUS power gain is determined by the ratio

\[ K_{\text{mp}}=\frac{P_n}{P_{\max}} =\frac{4.5\cdot 10^3}{6}=750, \]

and the dynamic gain \(K_{\text{dyn}}\) of the MUS is taken from the catalog. To assess the correctness of the choice of the switching frequency \(f_k=100\ \text{Hz}\), the case of a limiting step of the control signal was taken, when the duty ratio of the control pulses \(\gamma\) varied from 0 to 0.7. In this case the load current was regulated from \(I_{xx}=0.6\ \text{A}\) to \(I_{\text{st}}=18\ \text{A}\).

From the oscillogram in Fig. 2a it follows that the time constant of the transient process when the load current increases is 0.25 s, instead of the expected 0.058 s, and when it decreases, 0.1 s. In this case the currents of the working circuit and of the control circuit contain a sharply expressed 100 Hz component. Similarly, for a limiting step of the control signal (with \(\gamma\) changing from 0 to 1) and other conditions equal, the following values of the time constants were obtained: when the load current increases, 0.05 s; when it falls, as before, 0.1 s (oscillogram in Fig. 2b). Consequently, operation of the class-D PPU at a PWM frequency \(f_k=100\ \text{Hz}\) causes undesirable modulation of the MUS output voltage and prolongs the transient time, acting as an equivalent disturbance (the disturbance reduces the response speed). The value of the transient time constant when the load current decreases to \(I_{xx}\) remains approximately the same and is determined by the inertia of the circuits that close during the transient process in the power circuit, which is characteristic of a circuit with external c.f. of the MUS.

The upper limit of \(f_k\) is restricted by an increase in thermal losses in the PT when it operates in switching mode, as well as by the comparative complexity of circuits for increased-frequency sources. Therefore, taking into account the discrete nature of MUS operation, from the standpoint of response speed it is expedient to adopt a PPU PWM frequency of 300 Hz and a circuit with bridge c.f.

To verify the correctness of the above proposals and to determine the possibility of transferring the MUS to the BMU mode, the output PT (Fig. 1) was placed in operation under the following conditions:

\[ E_k=20\ \text{V};\quad I_{oy}=3\ \text{A};\quad R_{cy}=6.5\ \Omega;\quad f_k=300\ \text{Hz}. \]

Fig. 2. Oscillograms of the transient process in the PPU–MUS converter:
a — for a circuit with remote negative feedback at \(f_k = 100\ \text{Hz}\); \(\gamma = 0\div 0.7\); \(P_{\max}=6\ \text{W}\),
b — the same for \(\gamma = 0\div 1\),
c — for a bridge negative-feedback circuit at \(f_k = 300\ \text{Hz}\); \(\gamma = 0\div 0.7\); \(P_{\max}=60\ \text{W}\).

Here the combined current control-bias winding has the parameters:

\[ W_{\text{oy}} = 20 \text{ turns}; \quad R_{\text{oy}} = 0.2 \ \Omega; \quad P_{\max} = 20 \cdot 3 = 60 \text{ W}. \]

The power section was assembled according to a circuit with bridge current feedback. In this case the expected time constant of the MUS, calculated in the manner indicated above, is 0.006 sec, i.e., optimal speed of response of the converter is expected.

Figure 2 shows an oscillogram of the transient process, recorded in the open-loop PPU–MUS system for the case under consideration. It follows from it that, under the adopted conditions, the operating mode of the MUS, in its dynamic properties, is almost no different from that of a BMU. In this case the transient-process time is minimal and is \(t = 0.01\) sec, and the transfer function, without significant error, may be represented in linear approximation as:

\[ W(p) = K_m e^{-p \tau}, \tag{2} \]

i.e., it is in no way different from that of a BMU. However, the realization of the obtained dynamic parameters of the PPU–MUS converter in a closed-loop automatic control system, because of the presence in it of a link with a constant delay, becomes more complicated: the stability of drive operation deteriorates, stabilization becomes difficult and, in the general case, represents a complex problem. The delay causes an unfavorable character of the amplitude–phase frequency characteristic of the converter; as the frequency increases, the delay angle \(\varphi = \omega \tau\) increases linearly, while the modulus remains practically constant. This complicates stabilization, since not every correcting device is capable of ensuring a reduction of the gain coefficient of the automatic control system, concentrated mainly in the converter, in the frequency region of the system cutoff to the value required by the stability condition. Thus, for example, as investigations have shown, the possibility of stabilizing a drive according to the MUS-D system with a PPU with a speed-control range greater than \(200 : 1\) by means of the widely used parallel correction is difficult and in a number of cases makes it necessary to change over to series correction or to another method of increasing the stability of drive operation, for example, by improving the damping from the side of the electric-motor shaft.

The dynamic characteristics of the actuating electric motor and its speed of response depend on the values of the ratio of the time constants

\[ T_{\text{я}} = \frac{L_{\text{я}}}{R_{\text{я}}} \quad \text{and} \quad T_{\text{м}} = \frac{GD^2 R_{\text{я}}}{375 C_e C_{\text{м}}}. \]

In speed-stabilization systems, where the smallest possible dynamic change in rotational speed under disturbing actions is required, it is desirable to increase \(GD^2\). This improves damping from the side of the electric-motor shaft and the quality of the drive transient process under disturbing actions. Under a control action at low rotational speeds the influence of \(GD^2\) is insignificant, while at high speeds, where current limiting operates, its increase leads to a proportional increase in the transient-process time. For systems of tracking-controlled electric drive, the question of increasing \(GD^2\) is contradictory and must be resolved with allowance for the specific conditions. In all cases, an increase in \(GD^2\) leads to a proportional increase in losses during the transient process and to deterioration of the drive speed of response.

As applied to machines of the new P series, it should be noted that, in view of the execution of motors of frame sizes 1 and 3 as two-pole induc-

the inductance of their armature winding is comparatively large, while large values of the ratio of the armature diameter to its length have led to increased values of the electromechanical time constants \(T_m\). The absence of a design version of series P machines with built-in tachogenerators makes it necessary to couple them to the motor shaft under production conditions and leads, in connection with this, to rotational pulsation of the tachogenerator voltage, which worsens the dynamics of the drive.

When operating at the lower limit of the range, i.e., in the principal operating mode of a deeply controlled electric drive, the operation of the actuating electric motor is also affected by secondary factors which, in drive design, are usually undeservedly neglected. These are the periodic components of the load torque, caused by mechanical inaccuracies of the kinematic chain, the presence of dry-friction sections or inhomogeneities of the material being processed, poor coupling quality of the tachogenerator with the motor, and their magnetic asymmetry. In view of the large gain coefficient of the closed-loop automatic control system, even a slight disturbance strongly affects its behavior, creating the appearance of unstable operation of the drive. The change in the speed of the actuating electric motor also has a periodic character with frequencies that are multiples of those of the disturbance. In this case the amplitude and phase of the oscillations are determined by the frequency properties of the closed-loop automatic control system. Under unfavorable conditions of coincidence of the disturbance frequencies and the cutoff of the automatic control system, resonance phenomena are possible.

The quality of the coupling of the attached tachogenerator with the motor determines the degree of nonuniformity of its rotational speed. In the region of medium speeds, with a sufficiently rigid connection of the shafts in this coupling, the presence of eccentricity causes the appearance in the output voltage of the tachogenerator of an alternating component of the rotational frequency

\[ f_{\text{ob}}=\frac{n}{60}\ \text{Hz}. \]

Additional asymmetry associated with mechanical runout of the bearings of the motor or tachogenerator, or with runout of the magnetic core—

Fig. 3. Graph of the dependence of the frequency of forced oscillations of the speed of a controlled electric drive (P-32 motor).

of the tachogenerator output leads to yet another component with double the frequency relative to the rotational frequency (oscillogram in Fig. 4a). The frequencies of rotational oscillations are proportional to the speed of rotation of the electric motor and are processed by the ACS in the form of forced oscillations in that speed zone in which \(f_{\mathrm{ob}}\) or \(2 f_{\mathrm{ob}}\) lie within the passband of the ACS [3].

Figure 3 gives graphs, calculated for the P-32 motor, of the dependence \(f(n)\) of the frequency of forced oscillations \(f\) of the electric drive as a function of the rotational speed \(n\) of the electric motor. With an ACS passband of about \(2 \div 6\) Hz, the speed zone associated with rotational oscillations (shown by hatching) is \(50 \div 400\) rpm. As the rotational speed of the electric motor increases, the frequencies of the rotational pulsations of the tachogenerator rapidly increase, and the electric drive practically does not reproduce these oscillations. However, if the electric-drive system contains an intermediate amplifier with signal conversion at a carrier frequency (50 Hz) or a class-D amplifier with a source of constant frequency for internal commutation (\(50 \div 100\) Hz), low-frequency oscillations may arise. The beat frequency appearing at rotational speeds close to 1500 and 3000 rpm is equal to the difference between the disturbance frequencies and the PPU commutation frequency.

Under the conditions of the permissible thermal load, calculated for prolonged operation at low rotational speeds, the current in the excitation winding is taken to be somewhat less than the nominal value. When operating with a weakened field at the upper speeds, the well-known effect of demagnetization and distortion of the motor’s operating characteristics arises [4]. The distorted mechanical characteristic does not have a definite stiffness and, accordingly, the stability of operation of the electric drive changes.

At the lower end of the control range, at very low motor rotational speeds, the influence on the quality of control of its magnetic asymmetry becomes apparent; this asymmetry is caused by slot pulsations of the excitation flux and the dependent pulsations of the motor torque. The frequency of tooth pulsations of the motor rotational speed depends on the number of armature slots \(z\).

\[ f_z = \frac{zn}{60} \]

Figure 3 gives the dependence of the frequency of tooth pulsations on rotational speed for a two-pole motor of type P-32; these pulsations appear, with an ACS passband of \(2 \div 6\) Hz, in the speed interval \(5 \div 25\) rpm. The latter is confirmed by the oscillogram in Fig. 4b of the start-up and subsequent no-load operation of a P-32 motor in an electric-drive system, and also by the oscillogram in Fig. 4a. The zone of tooth pulsations, for the required range of \(200:1\), can be shifted beyond its limits by using an actuator electric motor with a larger number of slots, i.e., a machine with \(P > 1\).

Thus, low-frequency forced oscillations in the ACS may arise practically over the entire speed-control range, creating the impression of unstable operation of the drive.

A radical method of improving the quality of speed control under periodic load oscillations is to construct an ACS using correcting connections with respect to the principal disturbance—so-called combined systems [5]. However, at the present stage of development of automation in machine-tool building this is associated with unacceptable

by complicating the control circuits. As a practical method, often achieving the goal, for improving the dynamics one may recommend installing a motor of increased power, with a larger number of slots and a larger electromechanical time constant. Thus, in developing an electric drive according to the MUS-D system with PPU, with a speed-control range of 200:1, for the feed mechanism of a heavy carousel machine tool, the nominal data satisfied the following two variants of the executive electric motor:

Fig. 4. Oscillograms:
a—cogging and rotational pulsations of the rotation speed of the P-32 executive electric motor at speed settings of 18 and 60 rpm;
b—starting and operation of the P-32 motor at a speed of 19 rpm.

motor P-32, \(P_{\mathrm{n}} = 4.5\ \text{kW}\), \(n_{\mathrm{n}} = 3000\ \text{rpm}\), \(u_{\mathrm{n}} = 340\ \text{V}\), \(p = 1\), \(z = 18\), which met the permissible torque only with forced ventilation; motor P-41, \(P_{\mathrm{n}} = 6\ \text{kW}\), \(n_{\mathrm{n}} = 3000\ \text{rpm}\), \(u_{\mathrm{n}} = 340\ \text{V}\), \(p = 2\), \(z = 29\), which met the heating requirement under self-ventilation, although it was used at only half the nominal torque.

Tests of the motors in a closed automatic control system confirmed that, over the entire range of speed settings, the drive with the higher-power motor has the better dynamic characteristics.

From what has been said it follows that, in the best case, the dynamic and operating characteristics of drives with a wide speed-control range based on the MUS-D system with PPU can be obtained by using a special electric motor designed for operation under the conditions of machine-tool production, for example, PBST.

Conclusions

1. In automatic-control systems, the use of a PPU together with a power series MUS, under certain conditions of their matching, makes it possible to obtain a static converter with the same optimal dynamic characteristic as in a BMU, while using a simpler control circuit.

2. The half-period delay, which cannot be neglected in a closed ACS, worsens the stability of the drive and complicates the conditions for its stabilization.

3. The conditions for matching a PPU with a power MUS are satisfied by the use of a class-D PPU with PWM elements. From the standpoint of response speed and taking into account the discrete character of MUS operation, it is more expedient to choose a repetition frequency of 300 Hz; however, it should be noted that this leads to some complication of the converter circuit, which is not always justified.

4. The improvement of the drive dynamics, the nonuniformity of the rotational speed, and the quality of control in deeply regulated electric drives depend to a considerable extent on the type of drive motor. An improvement in the performance of the MUS-D drive with a class-D PPU, developed for the feed mechanism of heavy machine tools, is expected when a PBST electric motor is used.

Literature

1. M. A. Rosenblat. Magnetic Amplifiers. Gosenergoizdat, 1960.

2. Ya. S. Brovman, V. G. Kagan, F. D. Kochubievskii. Electric Drives with Semiconductor Control. Systems with Electric-Machine Converters (PMK-G-D). Energiya Publishing House, 1964.

3. Ya. S. Brovman, V. G. Kagan, F. D. Kochubievskii, V. A. Naidis. Electric Drives with Semiconductor Control. Direct-Current Systems with Electric-Machine Amplifiers. Energiya, 1964.

4. I. Z. Ageev. Unstable operation and self-oscillations in automatic-control systems of direct-current machines with nonlinear characteristics. Elektrichestvo, No. 5, 1964.

5. E. M. Smirnov, L. M. Smirnova, Z. B. Pozdeeva. Synthesis of correcting devices for an electric drive using the EMU-D system with combined control under harmonic load. Academy of Sciences of the USSR, Nauka Publishing House, 1964.

6. A. P. Ineshin, V. A. Sevast’yanov. On increasing response speed in systems with magnetic amplifiers. Scientific Notes of the Ulyanovsk State Pedagogical Institute, Vol. 20, Issue 4, 1965.