Control Arrangements for Inverter Fed Drives

Control Arrangements for Inverter Fed Drives

For speed control manufacturers offer options ranging in sophistication from a basic open-loop scheme which is adequate when precise speed holding is not essential, through closed-loop schemes with tacho or encoder feedback, up to vector control schemes which are necessary when optimum dynamic performance is called for. The variety of schemes is much greater than for the fully matured d.c. drive, so we will look briefly at some examples in the remainder of this section.

The majority of drives now provide a digital interface so that the user can input data such as maximum and minimum speeds, acceleration rates, maximum torque, etc. General purpose inverters that are not sold with a specific motor may have provision for motor parameters such as base frequency, full-load slip and current, leakage reactance and rotor resistance to be entered so that the drive can self-optimise its control routines.

Perhaps the ultimate are the self-commissioning drives that apply test signals to the motor when it is first connected in order to determine the motor parameters, and then set themselves to deliver optimum performance.

Open Loop Speed Control

control arrangements for inverter fed drives
Fig. 1

In the smaller sizes the simple ‘constant V/f ’ control is the most popular, and is shown in Figure 1. The output frequency, and hence the no-load speed of the motor, is set by the speed reference signal, which in an analogue scheme is either an analogue voltage (0–10 V) or current (4– 20 mA). This set-speed signal may be obtained from a potentiometer on the front panel, or remotely from elsewhere.

In the increasingly common digital version the speed reference will be set on the keypad. Some adjustment of the V/f ratio and low-speed voltage boost will be provided. Typical steady-state operating torque–speed curves are shown in Figure 2.

For each set speed (i.e. each frequency) the speed remains reasonably constant because of the stiff torque–slip characteristic of the cage motor. If the load is increased beyond rated torque, the internal current limit (not shown in Figure 1) comes into play to prevent the motor from reaching the unstable region beyond pull out. Instead, the frequency and speed are reduced, so that the system behaves in the same way as a d.c. drive.

Sudden changes in the speed reference are buffered by the action of an internal frequency ramp signal, which causes the frequency to be gradually increased or decreased. If the load inertia is low, the acceleration will be accomplished without the motor entering the current-limit regime. On the other hand if the inertia is large, the acceleration will take place along the torque–speed trajectory shown in Figure 2.

Fig. 2

Suppose the motor is operating in the steady state with a constant load torque at point (a), when a new higher speed (corresponding to point (d)) is demanded. The frequency is increased, causing the motor torque to rise to point (b), where the current has reached the allowable limit.

The rate of increase of frequency is then automatically reduced so that the motor accelerates under constant current conditions to point (c), where the current falls below the limit: the frequency then remains constant and the trajectory follows the curve from (c) to settle finally at point (d).

A typical deceleration trajectory is shown by the path aefg in Figure 2. The torque is negative for much of the time, the motor operating in quadrant 2 and regenerating kinetic energy to the inverter.

Most small inverters do not have the capability to return power to the a.c. supply, and the excess energy therefore has to be dissipated in a resistor inside the converter. The resistor is usually connected across the d.c. link, and controlled by a chopper.

When the link voltage tends to rise, because of the regenerated energy, the chopper switches the resistor on to absorb the energy. High inertia loads, which are subjected to frequent deceleration can therefore pose problems of excessive power dissipation in this ‘dump’ resistor.

Speed reversal poses no problem, the inverter Wring sequence being reversed automatically at zero speed, thereby allowing the motor to proceed smoothly into quadrants 3 and 4.

Some schemes include slip compensation, whereby the drive senses the active component of the load current, which is a measure of the torque; deduces the slip (which at full flux is proportional to the torque); and then increases the motor frequency to compensate for the slip speed of the rotor and thereby maintain the same speed as at no load. This is similar to the ‘IR’ compensation used in open-loop d.c. drives.

Closed Loop Speed Control

Where precision speed holding is required a closed-loop scheme must be used, with speed feedback from either a d.c. or a.c. tachogenerator, or a digital shaft encoder. Many different control strategies are employed, so we will consider the typical arrangement shown in Figure 3.

This inverter has separate control of the a.c. output voltage (via phase-angle control in the input rectifier) and frequency (via the switching in the inverter), and this makes understanding how the control system operates easier than when voltage and frequency are controlled together, as in a PWM inverter.

Fig. 3

Here, we will assume that the control variables are continuous analogue signals, though of course the majority of implementations will involve digital hardware. The arrangement of the outer speed-control loop (see Figure 3) is identical with that of the d.c. drive: the actual speed (represented by the voltage generated by the tachogenerator) is compared with the target or reference speed and the resulting speed error forms the input to the speed controller. The output of the speed controller provides the input or reference to the inner part of the control system, shown shaded in Figure 3.

In both the d.c. drive and the induction motor drive, the output of the speed controller serves as a torque reference signal, and acts as the input to the inner (shaded) part of the system. We will now see that, as in the d.c. drive, the inner system of the inverter-fed drive is effectively a torque-control loop that ensures that the motor torque is directly proportional to the torque reference signal under all conditions.

We have seen that if the magnitude of the flux wave in an induction motor is kept constant, the torque in the normal operating region is directly proportional to the slip speed. (We should recall that ‘normal operating region’ means low values of slip, typically a few per cent of synchronous speed.) So the parameter that must be controlled in order to control torque is the slip speed.

But the only variable that we can directly vary is the stator frequency (and hence the synchronous speed); and the only variable we can measure externally is the actual rotor speed. These three quantities (see Figure 3) are represented by the following analogue voltages:

Slip speed = ωslip

Synchronous speed = ωsynch

Rotor speed = ω

Where ωsynch = ω + ωslip (equation 1)

Equation (1) indicates how we must vary the stator frequency (i.e. the synchronous speed) if we wish to obtain a given slip speed (and hence a given torque): we simply have to measure the rotor speed and add to it the appropriate slip speed to obtain the frequency to be supplied to the stator.

This operation is performed at the summing junction at the input to the shaded inner section in Figure 3: the output from the summing junction directly controls the inverter output frequency (i.e. the synchronous speed), and, via a shaping function, the amplitude of the inverter output voltage.

The shaping function, shown in the call-out in Figure 3, provides a constant voltage–frequency ratio over the majority of the range up to base speed, with ‘voltage-boost’ at low frequencies. These conditions are necessary to guarantee the ‘constant flux’ condition that is an essential requirement for us to be able to claim that torque is proportional to slip speed.

(We must also accept that as soon as the speed rises above base speed, and the voltage–frequency ratio is no longer maintained, a given slip speed reference to the inner system will yield less torque than below base speed, because the flux will be lower.)

We have noted the similarities between the structures of the induction motor and d.c. drives, but at this point we might wish to pause and reflect on the differences between the inner loops.

In the d.c. drive the inner loop is a conventional (negative feedback) current control where the output (motor current) is measured directly; the torque is directly proportional to current and is therefore directly controlled by the inner loop.

In contrast, the inner loop in the induction scheme provides torque control indirectly, via the regulation of slip speed, and it involves a positive feedback loop. It relies for its success on the linear relationship between torque and slip, and thus is only valid when the flux is maintained at full value and the slip speed is low; and because it involves positive feedback there is the potential for instability if the loop gain is greater than one, which means that the tachogenerator constant must be judged with care.

Returning now to the outer speed loop and assuming for the moment that the speed controller is simply a high-gain amplifier, understanding the operation of the speed-control loop is straightforward.

When the speed error increases (because the load has increased a little and caused the speed to begin to fall, or the target speed has been raised modestly) the output of the speed controller increases in proportion, signalling to the inner loop that more torque is required to combat the increased load, or to accelerate to the new speed. As the target speed is approached, the speed error reduces, the torque tapers off and the target speed is reached very smoothly.

If the gain of the speed error amplifier is high, the speed error under steady-state conditions will always be low, i.e. the actual speed will be very close to the reference speed.

In the discussion above, it was assumed that the speed controller remained in its linear region, i.e. the speed error was always small. But we know that in practice there are many situations where there will be very large speed errors.

For instance, when the motor is at rest and the speed reference is suddenly raised to 100%, the speed error will immediately become 100%. Such a large input signal will cause the speed error amplifier output to saturate at maximum value, as shown by the sketch of the amplifier characteristic in Figure 3.

In this case the slip reference will be at maximum value and the torque and acceleration will also be at maximum, which is what we want in order to reach the target speed in the minimum time. As the speed increases the motor terminal voltage and frequency will both rise in order to maintain maximum slip until the speed error falls to a low value and the speed error amplifier comes out of saturation.

Control then enters the linear regime in which the torque becomes proportional to the speed error, giving a smooth approach to the final steady-state speed. In relatively long-term transients of the type just discussed, where changes in motor frequency occur relatively slowly (e.g. the frequency increases at perhaps a few per cent per cycle) the behaviour of the standard inverter-fed drive is very similar to that of the two-loop d.c. drive, which as we have already seen has long been regarded as the yardstick by which others are judged.

Analogue control using a proportional and integral speed error amplifier can give a good transient response and steady-state speed holding of better than 1% for a speed range of 20:1 or more. For higher precision, a shaft encoder together with a phase-locked loop is used.

The need to fit a tacho or encoder can be a problem if a standard induction motor is used, because there is normally no shaft extension at the non-drive end. The user then faces the prospect of paying a great deal more for what amounts to a relatively minor modification, simply because the motor then ceases to be standard.


Where very rapid changes in speed are called for, however, the standard inverter-fed drive compares unfavourably with d.c. drive. The superiority of the d.c. drive stems firstly from the relatively good transient response of the d.c. motor, and secondly from the fact that the torque can be directly controlled even under transient conditions by controlling the armature current.

In contrast, the induction motor has inherently poor transient performance. For example, when we start an unloaded induction motor direct-online we know that it runs up to speed, but if we were to look in detail at what happens immediately after switching on we might be very surprised.

We would see that the instantaneous torque fluctuates wildly for the first few cycles of the supply, until the flux wave has built up and all three phases have settled into a quasi-steady-state condition while the motor completes its run-up. (The torque–speed curves found in this and most other textbooks ignore this phenomenon, and present only the average steady-state curve.)

We might also find that the speed oscillated around synchronous before finally settling with a small slip. For the majority of applications the standard inverter-fed induction motor is perfectly adequate, but for some very demanding tasks, such as high-speed machine tool spindle drives, the dynamic performance is extremely important and ‘vector’ or ‘field-oriented’ control is warranted. Understanding all the ins and outs of vector control is well beyond our scope, but it is worthwhile outlining how it works, if only to dispel some of the mystique surrounding the matter.

Some recent textbooks on electrical machines now cover the theory of vector control (which is still considered difficult to understand, even for experts) but the majority concentrate on the control theory and very few explain what actually happens inside a motor when operated under vector control.

Transient Torque Control

We have seen previously that in both the induction motor and the d.c. motor, torque is produced by the interaction of currents on the rotor with the radial flux density produced by the stator. Thus to change the torque, we must either change the magnitude of the flux, or the rotor current, or both; and if we want a sudden (step) increase in torque, we must make the change (or changes) instantaneously.

Since every magnetic field has stored energy associated with it, it should be clear that it is not possible to change a magnetic field instantaneously, as this would require the energy to change in zero time, which calls for a pulse of infinite power.

In the case of the main field of a motor, we could not hope to make changes fast enough even to approximate the step change in torque we are seeking, so the only alternative is to make the rotor current change as quickly as possible.

In the d.c. motor it is relatively easy to make very rapid changes in the armature (rotor) current because we have direct access to the armature current via the brushes. The armature circuit inductance is relatively low, so as long as we have plenty of voltage available, we can apply a large voltage (for a very short time) whenever we want to make a sudden change in the armature current and torque. This is done automatically by the inner (current-control) loop in the d.c. drive.

In the induction motor, matters are less straightforward because we have no direct access to the rotor currents, which have to be induced from the stator side. Nevertheless, because the stator and rotor windings are tightly coupled via the air-gap field, it is possible to make more or less instantaneous changes to the induced currents in the rotor, by making instantaneous changes to the stator currents.

Any sudden change in the stator MMF pattern (resulting from a change in the stator currents) is immediately countered by an opposing rotor MMF set up by the additional rotor currents which suddenly spring up. All tightly coupled circuits behave in this way, the classic example being the transformer, in which any sudden change in say the secondary current is immediately accompanied by a corresponding change in the primary current. Organising these sudden step changes in the rotor currents represents both the essence and the challenge of the vector-control method.

We have already said that we have to make sudden step changes in the stator currents, and this is achieved by providing each phase with a fastacting closed-loop current controller. Fortunately, under transient conditions the effective inductance looking in at the stator is quite small (it is equal to the leakage inductance), so it is possible to obtain very rapid changes in the stator currents by applying high, short-duration impulsive voltages to the stator windings.

In this respect each stator current controller closely resembles the armature current controller used in the d.c. drive. When a step change in torque is required, the magnitude, frequency and phase of the three stator currents are changed (almost) instantaneously in such a way that the frequency, magnitude and phase of the rotor current wave jump suddenly from one steady state to another.

This change is done without altering the amplitude or position of the resultant rotor flux linkage relative to the rotor, i.e. without altering the stored energy significantly. General expression for torque is

T = kBIr cosɸr

The flux density term (B) in the equation therefore remains the same while the terms Ir and ɸr change instantaneously to their new steady-state values, corresponding to the new steady-state slip and torque.

We can picture what happens by asking what we would see if we were able to observe the stator MMF wave at the instant that a step increase in torque was demanded.

For the sake of simplicity, we will assume that the rotor speed remains constant, in which case we would find that:

(a) the stator MMF wave suddenly increases its amplitude;

(b) it suddenly accelerates to a new synchronous speed;

(c) it jumps forward to retain its correct relative phase with respect to the rotor flux and current waves.

Thereafter the stator MMF retains its new amplitude, and rotates at its new speed. The rotor experiences a sudden increase in its current and torque, the new current being maintained by the new (higher) stator currents and slip frequency.

We should note that both before and after the sudden changes, the motor operates in the normal fashion, as discussed earlier. The ‘vector control’ is merely the means by which we are able to make a sudden stepwise transition from one steady state operating condition to another, and it has no effect whatsoever once we have reached the steady state.

The unique feature of the vector drive which differentiates it from the ordinary or scalar drive (in which only the magnitude and frequency of the stator MMF wave changes when more torque is required) is that by making the right sudden change to the instantaneous position of the stator MMF wave, the transition from one steady state to the other is achieved instantaneously, without the variables hunting around before settling to their new values.

In particular, the vector approach allows us to overcome the long electrical time-constant of the rotor cage, which is responsible for the inherently sluggish transient response of the induction motor. It should also be pointed out that, in practice, the speed of the rotor will not remain constant when the torque changes (as assumed in the discussion above) so that, in order to keep track of the exact position of the rotor flux wave, it will be necessary to have a rotor position feedback signal.

Because the induction motor is a multi-variable non-linear system, an elaborate mathematical model of the motor is required, and implementation of the complex control algorithms calls for a large number of fast computations to be continually carried out so that the right instantaneous voltages are applied to each stator winding. This has only recently been made possible by using sophisticated and powerful signal processing in the drive control.

No industry standard approach to vector control has yet emerged, but systems fall into two broad categories, depending on whether or not they employ feedback from a shaft-mounted encoder to track the instantaneous position of the rotor. Those that do are known as ‘direct’ methods, whereas those which rely entirely on a mathematical model of the motor are known as ‘indirect’ methods. Both systems use current feedback as an integral part of each stator current controllers, so at least two stator current sensors are required.

Direct systems are inherently more robust and less sensitive to changes in machine parameters, but call for a nonstandard (i.e. more expensive) motor and encoder. The dynamic performance of direct vector drives is now so good that they are found in demanding roles that were previously the exclusive preserve of the d.c. drive, such as reversing drives and positioning applications.

The achievement of such outstandingly impressive performance from a motor whose inherent transient behaviour is poor represents a major milestone in the already impressive history of the induction motor.

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