# Speed Control Of Dc Machine Engineering Essay

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Published: *Mon, 5 Dec 2016*

DC motors are electrical machines that consume dc electrical power and produce mechanical torque. DC motors are classified according to the connection of the field circuit with respect to the armature circuit. Traditionally dc motors were classified as shunt, series or separately excited. In additions it was common to see motors referred to as compound-wound. There is really no fundamental difference between shunt, series or separately excited dc motors, and the names simply reflect the way in which the field and armature circuits are interconnected.

The dc motor has two separate circuits. The smaller pair of terminals connect to the field windings which surround each pole and are normally in series, in the steady state all the input power to the field windings is dissipated as heat, none of it is connected to mechanical output power. The main terminals convey the current to the brushes which make the sliding contact to the armature winding on the rotor. The supply to the field is separate from that for the armature hence the description separately excited.

In shunt dc motors, the field circuit is connected in parallel with the armature circuit while DC series motors have the field circuit in series with the armature where both field and armature currents are identical. The brushes and commutators are troublesome for dc motors at very high speed whereas small dc motors say up to hundreds of watts output can run at perhaps 12000 rev/min but the majority of medium and large motors are usually designed for speeds below 3000 rev/min.

“Direct current (DC) motors have been widely used in many industrial applications such as electric vehicles, steel rolling mills, electric cranes, and robotic manipulators due to precise, wide, simple, and continuous control characteristics. The desired torque-speed characteristics could be achieved by the use of conventional proportional integral- derivative (PID) controllers.”[1]

Dc motors are mostly preferred because they are easy to use and control and not only this they even deliver High starting torque and their characteristic performance is also nearly linear. But when it comes to Speed control of dc motor the purpose of a motor speed controller is to take a signal representing the demanded speed, and to drive a motor at that speed. “The controller may or may not actually measure the speed of the motor. If it does, it is called a Feedback Speed Controller or Closed Loop Speed Controller, if not it is called an Open Loop Speed Controller. Feedback speed control is better, but more complicated.”[2]

## Speed Control of Separately excited Dc Motor

“In this method, shunt-field current is maintained constant from a separate source while the voltage applied to the armature is varied. Dc motors feature a speed, which is proportional to the counter emf. This is equal to the applied voltage minus the armature circuit IR drop. At rated current, the torque remains constant regardless of the dc motor speed (since the magnetic flux is constant) and, therefore, the dc motor has constant torque capability over its speed range.”[5a]

“The purpose of a motor speed controller is to take a signal representing the demanded speed, and to drive a motor at that speed. The controller may or may not actually measure the speed of the motor. If it does, it is called a Feedback Speed Controller or Closed Loop Speed Controller, if not it is called an Open Loop Speed Controller. Feedback speed control is better, but more complicated, and may not be required for a simple robot design.”[4]

The speed of a separately excited dc motor could be varied from zero to rated speed mainly by varying armature voltage in the constant torque region. Whereas in the constant power region, field flux should be reduced to achieve speed above the rated speed. “Control is obtained by weakening the shunt-field current of the dc motor to increase speed and to reduce output torque for a given armature current. Since the rating of a dc motor is determined by heating, the maximum permissible armature current is approximately constant over the speed range. This means that at rated current, the dc motor’s output torque varies inversely with speed, and the dc motor has constant-horsepower capability over its speed range.

Dc motors offer a solution, which is good for only obtaining speeds greater than the base speed. A momentary speed reduction below the dc motor’s base speed can be obtained by overexciting the field, but prolonged over excitation overheats the dc motor. Also, magnetic saturation in the dc motor permits only a small reduction in speed for a substantial increase in field voltage. If field control is to be used, and a large speed range is required, the base speed must be proportionately lower and the motor size must be larger. If speed range is much over 3:1, armature voltage control should be considered for at least part of the range. Very wide dynamic speed range can be obtained with armature voltage control. However, below about 60% of base speed, the motor should be de rated or used for only short periods.”[5b]The speed (N) of a DC motor is proportional to its armature voltage; the torque (T) is proportional to armature current, and the two quantities are independent, as illustrated in Figure below.

Dc Motor characteristics

## Operation of Single-Phase Half-controlled Bridge Rectifier

A fully-controlled rectifier circuit contains only controlled-rectifiers, whereas a semi-controlled rectifier circuit is made up of both controlled and uncontrolled rectifiers. Due to presence of diodes, free-wheeling operation takes place without allowing the bridge output voltage to become negative. In a semi-controlled rectifier, control is effected only for positve output voltage, and no control is possible when its output voltage tends to become negative since it is clamped at zero volt. Here the operation of a single-phase half-controlled rectifier is explained.[3]

## .

Half controlled Bridge rectifier

In this circuit, SCRs S1 and S3 conduct during a < wt < p. During p < wt < (p + a) , the device in conduction is diode D and the output of the bridge is clamped at zero. During (p + a) < wt < 2p , the devices in conduction are SCRs S2 and S4. Diode D would conduct during 0 < wt < a .

Here are some results taken with the simulation of single phase half-controlled bridge rectifier on firing angle of zero degree.

## Steady-State operation of Separately Excited Dc Motor

Steady state is such a form for Dc motor characteristics in which it indicates how the motor behaves when any transient effects have died away and conditions have once again become steady. Steady State characteristics are usually much easier to predict than transient characteristics. Under steady state conditions the armature current I is constant.

The equation below is the armature circuit voltage equation.

V = E + IR + L(dI/dt)

Where voltage V is the voltage applied to the armature terminals and E is the internally developed motional e.m.f . The resistance and inductance of the complete armature are represented by R and L.

Under motoring condition, the motional e.m.f E always opposes the applied voltage V, and for this reason it is known as back e.m.f . And for the current to be forced in to the motor V must be greater then E. The last bit of the above mentioned equation represents the inductive volt drop due to armature self inductance. This voltage is proportional to the rate of change of current. So under steady state this last term will be ZERO. So we can ignore that last term for steady state operations. Then under steady state conditions the above equations becomes,

V = E + IR

So,

I = (V-E)/R

In shunt dc motors, the field circuit is connected in parallel with the armature circuit. It has the following equivalent circuit:

Fig. 1. Equivalent Circuit of

DC Shunt Motor

Under steady state condition the time derivative is zero assuming that the motor is not saturated. Some important field and armature equations are as follows.

For field circuit,

The back e.m.f is given by :

The armature circuit

Now the torque and speed under the steady state condition can be found with the following formulas: The motor speed can be easily derived:

If Ra is a small value, or when the motor is lightly loaded, i.e. Ia is small,

That is if the field current is kept constant, the motor speed depends only on the supply voltage.

The developed torque is :

The required power is :

Experiment

In the dc motor the field windings is used to excite the field flux. And the armature current is supplied to the rotor via brush and commutator for the mechanical work. This Interaction of field flux and armature current in the rotor produces torque. When a separately excited motor is excited by a field current of if and an armature current of ia flows in the circuit, the motor develops a back e.m.f and a torque to balance the load torque at a particular speed. The if is independent of the ia .Each windings are supplied separately. Any change in the armature current has no effect on the field current. The if is normally much less than the ia.

The first thing is to wire up the circuit of separately excited dc motor with DMS2 data acquisition system as mentioned on the manual provided for experiments.

## Steady State Characteristics

After starting the DMS2 Data acquisition system software the users parameters were defined in the software manually which are Input power, Output power and Efficiency for which the values has to be recorder. After putting all the parameters the dc motor started with the load torque value of 0 Nm and then the values for the parameters which were introduced in the software were taken in an automated manner using the F2 button on the keyboard. And then gradually increases the values of load torque from 0 – 0.5 Nm with 50 steps with each step recording the values of parameters predefined in DMS2 Software.

From no-load to full load the speed falls linearly as a consequent the back e.m.f falls linearly too. The power losses in the armature resistance are I2R. The power converted from electrical to mechanical is given by VI. The power required to overcome friction and iron losses can be found under no-load conditions and get deducted from the loaded condition when the losses are not taken into account. Two important observation follow from these calculations. Firstly the speed drop with load is very small. This is very desirable for most applications. Since all we have to do to maintain almost constant speed is to set the appropriate armature voltage and keep it constant. Secondly a delicate balance between V and E is revealed. The current is in fact proportional to the difference between V and E . so that quite small changes in either E or V give rise to disproportionately large changes in the current. Hence to avoid excessive current difference between E and V must be limited. The no-load speeds are directly proportional to the applied voltage, while the slope of each curve is the same, being determined by the armature resistance. The smaller the resistance the less the speed falls with load.

## Motor Armature Voltage & Current in Steady State Operation

Steady state is such a form for Dc motor characteristics in which it indicates how the motor behaves when any transient effects have died away and conditions have once again become steady. Steady State characteristics are usually much easier to predict than transient characteristics. Under steady state conditions the armature current I is constant.

The second part of the experiment consists of using the DMS2 system as a digital storage oscilloscope. In this experiment the instantaneous waveforms are recorded at load torque values of 0.1, 0.3 and 0.4 Nm. As we increases the value of load torque it causes the motor speed to decreases gradually.

Results

## Steady-state characteristics

## Waveforms of motor armature voltage and current in steady-state operation

## 0.1 Nm

## 0.3 Nm

## 0.4 Nm

## Discussion

For a DC motor, the speed (RPM) is proportional to the applied voltage. The current that the motor will take from the supply is proportional to the load. A motor with no load will take very little current, a motor which is loaded and doing some work will take more current. The load on the motor appears as a torque on the output shaft, the more load, the more torque. So to trying and summaries: After Setting the motor speed by setting the supply voltage, as we increase the load (torque) on the motor, the current taken from the supply will increase. The motor will also slow down a bit as an increment in the load torque. We have seen that if the load torque on the shaft of motor increases, the speed falls and the armature current automatically increases until equilibrium of torque is reached and the speed gain becomes steady. If the armature voltage is at its maximum value, and we increase the mechanical load until the current reaches its rated value, we are clearly at full- load i.e. we are operating at the full speed and full torque.

Clearly if we increase the load on the shaft still more, the current will exceed the safe value, and the motor will began to overheat. But the question which this prompts is if it were not for the problem of overheating, could the motor deliver more and more output, or is there a limit?

We can see straightaway that there will be a maximum point by looking at the torque-speed curve. The mechanical output power is the product of torque and speed and we see that the power will be zero when either the load torque is zero or the speed is zero. And it is easy to show that the peak mechanical power occurs when the speed is half of the no-load speed. But familiarization with the dc motors brings the concept of high maintenance cost and large size of the motors as compared to induction motors. And dc machines are not suitable for high speed operations due to the commutator and brushes and they are also not suitable for the clean or explosive environments.

## Conclusions

A shunt or separately excited dc motor has a torque-speed characteristic whose speed drops linearly with increasing load torque. Its speed can be controlled by changing its field current, its armature voltage or its armature resistance. The graph obtained from the resulting values between torque-armature voltage shows that the relationship between the torque and armature voltage is almost linear as the armature voltage increases it brings a linear change in torque also. Whereas the speed decreases as the torque increase in a steady manner. Efficiency of the motor increases rapidly and then decrease in a rapid manner as we increase the value of torque. The results show that when the machine is running at the rated conditions, the steady-state values are in good agreement.

It has been observed that under maximum power conditions the overall efficiency is only nearly 50% because an equal power is burned off as heat in the armature resistance. And only very small motors can ever be operated continuously in this condition.

## Introduction

It is not only supremely elegant as an electromechanical energy converter, but is also by far the most important, with something like one third of all the electricity generated being converted back to mechanical energy in induction motors. Like the d.c motor, the induction motor develops torque by the interaction of axial currents on the rotor and a radial magnetic field produced by the stator. But whereas in the dc motor the current has to be fed in to the rotor by means of brushes and a commutator, the torque producing current in the rotor of the induction motor are induced by electromagnetic action, hence the name induction motor. The stator winding not only therefore procuring the magnetic field but also supplies the energy that is converted to mechanical output. The absence of any sliding mechanical contacts and the consequent saving in terms of maintenance is a major advantage of the induction motor over its d.c rival.

To understand how an induction motor operates, we must first unravel the mysteries of the rotating magnetic field. The rotor will be effectively dragged along by the rotating field, but that it can never run quite as fast as the field. When it is needed to control the speed of the rotor it is best to control the speed of the field. The mechanism of the rotating field focus on the stator windings because they act as the source of flux. In this part the presence of rotor gets neglected just to make it easier to understand what governs the speed of rotation and the magnitude of the field, which are the two factors which mostly influence the motor behaviour. The interaction between the rotor and the stator well justifies the external characteristics of the motor. i.e. the variation of motor torque and stator current with speed.

Broadly speaking the motor designer shapes the stator and rotor teeth to encourage as much as possible of the flux produced by the stator to pass right down the rotor teeth, so that before completing its path back to the stator it is fully linked with the rotor conductors which are located in the rotor slots. This is tight magnetic coupling between stator and rotor windings is necessary for good running performance. And the field which provide the coupling is of course the main or air-gap filed. The vast majority of the flux produced by the stator is indeed main or mutual flux. But there is some flux which bypasses the rotor conductor, linking only with the stator winding, and known as storage leakage flux.

“We all know that the synchronous speed of the induction motor is given by Ns = 120f/P. So from this relation, it is evident that the synchronous speed and thus the speed of the induction motor can by varied by the supply frequency. This method has its own limitations. The motor speed can be reduced by reducing the frequency, if the induction motor happens to be the only load on the generators. Even then the range over which the speed can be varied is very less.”[6]

## V/f constant Principle

Because of advances in solid state power devices and microprocessors, variable speed AC Induction motors powered by switching power converters are becoming more and more popular. Switching power converters offer an easy way to regulate both the frequency and magnitude of the voltage and current applied to a motor. As a result much higher efficiency and performance can be achieved by these motor drives with less generated noises. The most common principle of this kind, is the constant V/Hz principle which requires that the magnitude and frequency of the voltage applied to the stator of a motor maintain a constant ratio. By doing this, the magnitude of the magnetic field in the stator is kept at an approximately constant level throughout the operating range. Thus, (maximum) constant torque producing capability is maintained. When transient response is critical, switching power converters also allow easy control of transient voltage and current applied to the motor to achieve faster dynamic response. The constant V/Hz principle is considered for this application. The energy that a switching power converter delivers to a motor is controlled by Pulse Width Modulated (PWM) signals applied to the gates of the power transistors. PWM signals are pulse trains with fixed frequency and magnitude and variable pulse width. There is one pulse of fixed magnitude in every PWM period. However, the width of the pulses changes from period to period according to a modulating signal. When a PWM signal is applied to the gate of a power transistor, it causes the turn on and turn off intervals of the transistor to change from one PWM period to another PWM period according to the same modulating signal. The frequency of a PWM signal must be much higher than that of the modulating signal, the fundamental frequency, such that the energy delivered to the motor and its load depends mostly on the modulating signal. Figure 1 shows two types of PWM signals, symmetric and asymmetric edge-aligned. The pulses of a symmetric PWM signal are always symmetric with respect to the center of each PWM period. The pulses of an asymmetric edge-aligned PWM signal always have the same side aligned with one end of each PWM period. Both types of PWM signals are used in this application.

Symmetric and Asymmetric PWM Signals

It has been shown that symmetric PWM signals generate less harmonics in the output current and voltage. Different PWM techniques, or ways of determining the modulating signal and the switch-on/switch-off instants from the modulating signal, exist. Popular examples are sinusoidal PWM, hysteresis PWM and the relatively new space vector PWM. These techniques are commonly used with three phase Voltage Source power inverters for the control of three-phase AC induction motors. The space vector PWM technique is employed in this application.

Assume the voltage applied to a three phase AC Induction motor is sinusoidal and neglect the voltage drop across the stator resistor. Then we have, at steady state,

from which it follows that if the ratio V/ f remains constant with the change of f , then A remains constant too and the torque is independent of the supply frequency. In actual implementation, the ratio between the magnitude and frequency of the stator voltage is usually based on the rated values of these variables, or motor ratings. However, when the frequency and hence also the voltage are low, the voltage drop across the stator resistance cannot be neglected and must be compensated. At frequencies higher than the rated value, the constant V/ f principle also have to be violated because, to avoid insulation break down, the stator voltage must not exceed its rated value. This principle is illustrated in Figure 2.

Voltage Versus Frequency under constant V/ f Principle

Since the stator flux is maintained constant, independent of the change in supply frequency, the torque developed depends on the slip speed only, which is shown in Figure 3. So by regulating the slip speed, the torque and speed of an AC Induction motor can be controlled with the constant V/Hz principle.

Torque Versus Slip speed of induction motor while constant stator flux

Both open and closed-loop control of the speed of an AC induction motor can be implemented based on the constant V/Hz principle. Open-loop speed control is used when accuracy in speed response is not a concern such as in HVAC (heating, ventilation and air conditioning), fan or blower applications. In this case, the supply frequency is determined based on the desired speed and the assumption that the motor will roughly follow its synchronous speed. The error in speed resulted from slip of the motor is considered acceptable. When accuracy in speed response is a concern, closed-loop speed control can be implemented with the constant V/Hz principle through regulation of slip speed, as illustrated in Figure 4, where a PI controller is employed to regulate the slip speed of the

motor to keep the motor speed at its set value.

## Operation of Three-Phase Voltage Source

The structure of a typical three-phase voltage source power inverter is shown in Figure 6. Va, Vb and Vc are the output voltages applied to the windings of a motor. Q1 through Q6 are the six power transistors that shape the output, which are controlled by a, a’, b, b’, c and c’. For AC Induction motor control, when an upper transistor is switched on, i.e., when a, b or c is 1,

the corresponding lower transistor is switched off, i.e., the corresponding a’, b’ or c’ is 0. The on and off states of the upper transistors Q1, Q3 and Q5, or equivalently, the state of a, b and c, are sufficient to evaluate the output voltage.

Three Phase Power inverter

As shown in Figure 6, there are eight possible combinations of on and off patterns for the three upper power transistors that feed the three phase power inverter. Notice that the on and off states of the lower power transistors are opposite to the upper ones and so are

completely determined once the states of the upper power transistors are known. The eight combinations and the derived output line-to-line and phase voltages in terms of DC supply

voltage Vdc, Space Vector PWM refers to a special switching sequence of the upper three power transistors of a three phase power inverter. It has been shown to generate less harmonic distortion in the output voltages and or currents applied to the phases of an AC motor and provides more efficient use of supply voltage in comparison with direct sinusoidal modulation technique.

## Steady-State operation on a Squirrel-Cage Three-Phase Induction Motor

The term squirrel-cage is actually a type of rotor used in induction motor. The rotor consist of a stack of steel laminations with evenly spaced slots punched around the circumference. As with the stator laminations, the surface is coated with an oxide layer, which act as an insulator, preventing unwanted eddy current from flowing in the iron. The cage rotor is by far the most common, each rotor slot contains a solid conductor bar and all the conductors are physically and electrically joined together at each end of the rotor by conducting end-rings. Cage rotors are usually cheaper to manufacture and are very robust and reliable.

The behaviour of Squirrel-cage induction motor when connected to a constant frequency supply. This is by far the most widely used and important mode of operation, the motor running directly connected to a constant voltage mains supply, 3-phase are the most important to dealt with in this case.

The rotor resistance and reactance influenced the shape of the torque-speed curve. For small values of slip, i.e. in the normal running region the lower we make the rotor resistance the steeper the slope of the torque-speed curve becomes. We can see that at the rated torque the full-load slip of the low resistance cage is much lower than that of the high-resistance cage. But the rotor efficiency is equal to (1-s), where s is the slip so, it is concluded that low resistance rotor not only gives better speed holding, but is also much more efficient. There is of course a limit to how low we can make the resistance, copper allow us to achieve the lower resistance than aluminium. The drawbacks with a low resistance rotor is the starting torque gets reduced and worse till the starting current increases. The lower starting torque may prove insufficient to accelerate the load, while increased starting current may lead to unacceptable volt drops in the supply. Whereas altering the rotor resistance has little or no effect on the value of peak torque.

The less attractive feature of induction machines is that it is never possible for all the power crossing the air-gap from the stator to be converted to mechanical output, because some is always lost as heat in the rotor circuit resistance. Infact it turns out that at slip s the total power P crossing the air-gap always divides so that a fraction sP is lost as heat, while the remainder(1-s)P is converted to useful mechanical output. Hence, when the motor is operating in the steady state the energy conversion efficiency of the motor is given by,

nr = Mechanical output power / Rated power input to Rotor

nr = (1-s)

this result is very important and shows us immediately why operating at small values of slip is desirable. With a slip of 5%(0.05) for example, 95% of the air-gap power is put to good use. But if the motor was running at half of the synchronous speed (s = 0.5) , 50% of the air-gap power would be wasted as heat in the rotor.

## Experiment

All the calculation made in the experiment were performed in an automated manner by means of computer driven DMS2 data acquisition system. The only process after setting up the whole circuit was to increase the value of load torque with the torque knob in approximately 50 steps in an ascending order.

After the increment of load torque, hitting upon the key F2 over the keyboard gives every time a new string of values in the table. Firstly the load-test has been performed on the squirrel-cage induction motor for the torque-speed curve over fixed values of frequencies and after that in the second experiment DMS2 has been used as a digital oscilloscope to measure the motor current and voltage in the steady state operation over different frequencies with constant load torque of 0.2 Nm and then at a frequency of 40Hz with load torque of 0.4 Nm and 0.6Nm.

The no-load test of an induction motor measures the rotational losses of the motor and provides information about its magnetization current. The motor is allowed to spin freely. The only load on the motor is the friction and the windage losses, so all Pconv in this motor is consumed by mechanical losses, and the slip of the motor is very small, possibly as small as 0.001 or less. With its very small slip the resistance corresponding to its power converted, R(1-s)/s, is much larger than the resistance corresponding to the rotor copper losses R, and much larger than the rotor reactance X.

In this motor at no-load conditions the input power measured by the meters must equal the losses in the motor. The rotor copper losses are negligible because the current I2 is extremely small because of large load resistance so they may be neglected. The stator copper losses are given by

Pcl = 3I2R

So the input power equals

Pin = Pcl + Pcore

Pin = 3I2R + Prot

Where Prot is the rotational losses of the motor.

Results

20 HZ

30 HZ

40HZ

50 HZ

75 HZ

100 HZ

## Waveforms of motor voltage and current in steady-state operation

## AT 0.2 Nm

20Hz

30Hz

40Hz

50Hz

75Hz

100Hz

## NOW AT 40HZ

0.4 Nm

0.6 Nm

## Conclusions

Having established earlier that at any given slip, the air-gap flux density is proportional to the applied voltage and the induced current in the rotor is proportional to the flux density. The torque, which depends on the product of the flux and the rotor current , therefore depends on the square of applied voltage. That’s why a comparatively modest fall in the voltage will result in a much larger reduction in torque capability, with adverse effects which may not be apparent to the unwary until too late.

Having explored the torque-speed curve in the graph of induction motor it has been found out that the torque-speed curve for the normal motoring region where the speed lies between zero and just below synchronous. If the synchronous speed increases more than the synchronous speed or become negative the torque also becomes negative. It is moreover concerned to the slip, rather than the speed. When the slip is positive the torque is positive and vice versa. The torque therefore always acts so as to urge the rotor to run at zero slip, i.e. at the synchronous speed. If the rotor is tempted to run faster than the field it will be slowed down, whilst if it is running below synchronous speed it will be urged to accelerate forwards. In particular, we note that for slips greater than 1,i.e. when motor is running backward in the opposite direction to the field the torque will remain positive so that if the rotor is unrestrained it will first slow down and then change direction and accelerate in the direction of field

## Discussion

While doing the load test on the squirrel-cage induction motor one most prominent thing which was

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