Dc Motors Speed Control Using Different Techniques and Its Application

HEAVY INDUSTRY TEXILA EDUCATION CITY, HITEC

PROJECT REPORT

Dc Motors Speed Control Using Different Techniques and its

Application

Submitted by Waqar Akram07-Hitec-EE-124

Submitted to Dr Ikram

SEPTEMBER 2010

[DC MOTORS SPEED CONTROL] [2010]

"In the name of Allah,

Most Gracious, Most

Compassionate"

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ACKNOWLEDGMENT

Great thanks to our teachers and all friends of university. We are very fortune to be able to complete this project.

Every effort has been made by every participant of the group collectively by using different resources to collect material for the project. In some instances we were unable to trace the things but our teachers and other students helped us a lot and we would appreciate any information that would enable us to do so.

In the end thanks again to our all friends and teachers for all their effort for our project is really appreciate able we were in experienced students but they all helped us so we were able to make such a project and we expect that in future INSHALLAH we will be able to make more bigger and logical projects if so kind and competent teachers will continue to help us we have high dreams.

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Contents

1. History and background.......................................................................................................................4

2. Principles of Operation........................................................................................................................5

3. CLASSIFICATION OF DC MOTORS...............................................................................................6

3.1 Series DC Motor.........................................................................................................................7

3.2 Shunt DC Motor..........................................................................................................................7

3.3 Compound DC Motor..................................................................................................................8

4. Types of DC Motor..............................................................................................................................8

4.1 Stepper DC Motors......................................................................................................................9

4.2 Brushed DC Motors...................................................................................................................10

4.3 Brushless DC Motors.................................................................................................................11

5. Difference between the types of Dc Motors.......................................................................................12

6. DC Motor Characteristics..................................................................................................................13

6.1 TORQUE...................................................................................................................................13

6.2 SPEED.......................................................................................................................................14

6.3 TORQUE/SPEED CURVES.....................................................................................................15

6.4 POWER/TORQUE and POWER/SPEED CURVES.................................................................17

6.5 Parameters to Control Speed......................................................................................................18

7. Techniques to Control Speed of DC Motors......................................................................................19

7.1 DC motor speed controller Using PIC Controller......................................................................20

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7.2 DC Motor PWM Speed Controller............................................................................................22

7.3 BLDC Motor Control utilizing Hall-effect sensors....................................................................24

7.4 Digital DC Motor Speed Control with PID Control...................................................................25

8. Application of DC Motors.................................................................................................................31

8.1 Application of Shunt-Wound Motors.........................................................................................32

8.2 Application of Series-Wound Motors........................................................................................33

8.3 Application of Compound-Wound Motors................................................................................34

9. Tables................................................................................................................................................35

9.1 Weekly Plan...............................................................................................................................35

9.2 Difference Table........................................................................................................................35

10. References.....................................................................................................................................36

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1. History and background

At the most basic level, electric motors exist to convert electrical energy into mechanical energy. This is done by way of two interacting magnetic fields -- one stationary, and another attached to a part that can move. A number of types of electric motors exist, but most BEAM bots use DC motors1 in some form or another. DC motors have the potential for very high torque capabilities (although this is generally a function of the physical size of the motor), are easy to miniaturize, and can be "throttled" via adjusting their supply voltage. DC motors are also not only the simplest, but the oldest electric motors.

The basic principles of electromagnetic induction were discovered in the early 1800's by Oersted, Gauss, and Faraday. By 1820, Hans Christian Oersted and Andre Marie Ampere had discovered that an electric current produces a magnetic field. The next 15 years saw a flurry of cross-Atlantic experimentation and innovation, leading finally to a simple DC rotary motor. A number of men were involved in the work, so proper credit for the first DC motor is really a function of just how broadly you choose to define the word "motor."

2. Principles of Operation

In any electric motor, operation is based on simple electromagnetism. A current-carrying conductor generates a magnetic field; when this is then placed in an external magnetic field, it will experience a force proportional to the current in the conductor, and to the strength of the external magnetic field. As you are well aware of from playing with magnets as a kid, opposite (North and South) polarities attract, while like polarities (North and North, South and South) repel. The internal configuration of a DC motor is designed to harness the magnetic interaction between a current-carrying conductor and an external magnetic field to generate rotational motion.

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Let's start by looking at a simple 2-pole DC electric motor (here red represents a magnet or winding with a "North" polarization, while green represents a magnet or winding with a "South" polarization).

Every DC motor has six basic parts -- axle, rotor (a.k.a., armature), stator, commutator, field magnet(s), and brushes. In most common DC motors (and all that Beamers will see), the external magnetic field is produced by high-strength permanent magnets1. The stator is the stationary part of the motor -- this includes the motor casing, as well as two or more permanent magnet pole pieces. The rotor (together with the axle and attached commutator) rotates with respect to the stator. The rotor consists of windings (generally on a core), the windings being electrically connected to the commutator. The above diagram shows a common motor layout -- with the rotor inside the stator (field) magnets.

The geometry of the brushes, commutator contacts, and rotor windings are such that when power is applied, the polarities of the energized winding and the stator magnet(s) are misaligned, and the rotor will rotate until it is almost aligned with the stator's field magnets. As the rotor reaches alignment, the brushes move to the next commutator contacts, and energize the next winding. Given our example two-pole motor, the rotation reverses the direction of current through the rotor winding, leading to a "flip" of the rotor's magnetic field, driving it to continue rotating.

In real life, though, DC motors will always have more than two poles (three is a very common number). In particular, this avoids "dead spots" in the commutator. You can imagine how with our example two-pole motor, if the rotor is exactly at the middle of its rotation (perfectly aligned with the field magnets), it will get "stuck" there. Meanwhile, with a two-pole motor, there is a moment where the commutator shorts out the power supply (i.e., both brushes touch both commutator contacts simultaneously). This would be bad for the power supply, waste energy, and damage motor components as well. Yet another disadvantage of such a simple motor is that it would exhibit a high amount of

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torque "ripple" (the amount of torque it could produce is cyclic with the position of the rotor).

You'll notice a few things from this -- namely, one pole is fully energized at a time (but two others are "partially" energized). As each brush transitions from one commutator contact to the next, one coil's field will rapidly collapse, as the next coil's field will rapidly charge up (this occurs within a few microsecond). We'll see more about the effects of this later, but in the meantime you can see that this is a direct result of the coil windings' series wiring:

3. CLASSIFICATION OF DC MOTORS

There are three basic types of dc motors: (1) Series motors, (2) shunt motors, and (3) compound motors. They differ largely in the method in which their field and armature coils are connected.

3.1 Series DC Motor

In the series motor, the field windings, consisting of a relatively few turns of heavy wire, are connected in series with the armature winding. The same current flowing through the field winding also flows through the armature winding. Any increase in current, therefore, strengthens the magnetism of both the field and the armature.

Because of the low resistance in the windings, the series motor is able to draw a large current in starting. This starting current, in passing through both the field and armature windings, produces a high starting torque, which is the series motor's principal advantage.

The speed of a series motor is dependent upon the load. Any change in load is accompanied by a substantial change in speed. A series motor will run at high speed when it has a light load and at low speed with a heavy load. If the load is removed entirely, the motor may operate at such a high speed that the armature will fly apart. If high starting torque is needed under heavy load conditions, series motors have many applications. Series motors are often used in aircraft as engine starters and for raising and lowering landing gears, cowl flaps, and wing flaps.

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3.2 Shunt DC Motor

In the shunt motor the field winding is connected in parallel or in shunt with the armature winding. The resistance in the field winding is high. Since the field winding is connected directly across the power supply, the current through the field is constant. The field current does not vary with motor speed, as in the series motor and, therefore, the torque of the shunt motor will vary only with the current through the armature. The torque developed at starting is less than that developed by a series motor of equal size.

The speed of the shunt motor varies very little with changes in load. When all load is removed, it assumes a speed slightly higher than the loaded speed. This motor is particularly suitable for use when constant speed is desired and when high starting torque is not needed.

3.3 Compound DC Motor

The compound motor is a combination of the series and shunt motors. There are two windings in the field: a shunt winding and a series winding. The shunt winding is composed of many turns of fine wire and is connected in parallel with the armature winding. The series winding consists of a few turns of large wire and is connected in series with the armature winding. The starting torque is higher than in the shunt motor but lower than in the series motor. Variation of speed with load is less than in a series wound motor but greater than in a shunt motor. The compound motor is used whenever the combined characteristics of the series and shunt motors are desired.

Like the compound generator, the compound motor has both series and shunt field windings. The series winding may either aid the shunt wind (cumulative compound) or oppose the shunt winding (differential compound).

The starting and load characteristics of the cumulative compound motor are somewhere between those of the series and those of the shunt motor.

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Because of the series field, the cumulative compound motor has a higher starting torque than a shunt motor. Cumulative compound motors are used in driving machines which are subject to sudden changes in load. They are also used where a high starting torque is desired, but a series motor cannot be used easily.

In the differential compound motor, an increase in load creates an increase in current and a decrease in total flux in this type of motor. These two tend to offset each other and the result is a practically constant speed. However, since an increase in load tends to decrease the field strength, the speed characteristic becomes unstable. Rarely is this type of motor used in aircraft systems.

4. Types of DC Motor

DC Motors differ from AC Motors, as they are powered by a direct current of Electricity, as opposed to an Alternating current. There are three main types of Direct Current motor, each with different features and characteristics. These are:

Stepper DC Motors Brushless DC Motors Brushed DC Motors

Although the main principal of these motors is the same (the stepper DC motor does differ however), they each have different uses and different operation methods.

In a strict sense, the Brushed and Brushless motor types (which are by far the most common of the DC motors) are not strictly completely DC dependant. Their operation depends on the fact that they contain a Commutator, which converts the DC supply that they are given into AC.

DC motors are generally used for more precision and power than AC motors, as they tend to me more controllable.

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4.1 Stepper DC Motors

Stepper DC Motors are brushless, synchronous electric motors which rely on electromagnets to rotate the internal shaft. A typical stepples electric motor will have an iron toothed cog connected around the internal rotating shaft. Around this shaft are four toothed electromagnets, positioned at equal intervals around the cog.

When switched on, one of these toothed magnets (No. 2) will attract the center cog towards its teeth, until they are perfectly aligned. However, due to the way stepper motors are designed, the next magnet (No. 2) will be slightly offset to the teeth of the center cog. This means that when the first magnet switches off and the second magnet takes over, the cog will partially rotate so that its teeth align with those of the second magnet. The same thing happens for the next magnet (No. 3), and finally the last (No. 4). So when all four magnets have completed a cycle of partially rotating the center cog, the cog is now displaced by a distance of ONE tooth. And so on and so forth, so quickly that the center cog rotates.

Computer controlled stepper motors are now the most widely used form of positioning motor. They have applications in CD and Floppy drives, printers, scanners, toys, automated facilities, and even satellites. They are extremely controllable due to their operation, and can often be controlled to the nearest fraction of a millimeter. However, they are not high power motors, and do require an external controller to operate.

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4.2 Brushed DC Motors

Brushed DC Motors are the classic DC motors, which include a split ring commutator, and can be powered by any kind of DC battery. These motors are often considered to be limited, due to the need that brushes will always be in contact with the commutator ring, hence creating friction. Brushes also scratch the surface of the ring, which eventually will lead to replacement of the brushes and ring.

Although the brushes in these motors were originally made from copper wire (now obsolete), they are now made from carbon, which is a longer-lasting material, gives less friction, and is cheaper.

The advantages of Brushed DC motors are that their initial cost is extremely low, and that they have an extremely simple speed control system (Dynamo). However, it is the brushless DC motor which is recommended by most.

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http://www.dcmotorguide.com/BrushlessDCMotors/1106

http://www.dcmotorguide.com/BrushlessDCMotors/1106

http://www.dcmotorguide.com/Commutators/1117



4.3 Brushless DC Motors

Brushless DC motors are extremely desirably as they completely eliminate the need for brushes. This increases their life, survival without maintenance, power output and efficiency dramatically.

Their basic working principle is to facilitate an external commutator, which will reverse the direction of the current depending on the position of the rotor.

As there are no brushes, maintenance levels are lowered dramatically, and as there is no friction caused by brushes, the efficiency of a brushless motor is typically between 85 and 90 percent (a brushed motor's efficiency is usually about 75 to 80 %). This makes them ideal for heavy duty use, and cost efficiency in the long term. They also run much cooler than AC and brushed motors, which greatly increases the life of the motors in context.

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http://www.fracmo.com/english/motors/brushless_motors.htm


5. Difference between the types of Dc Motors

Difference between the types on basis of a. Starting Torqueb. Starting Currentc. Efficiencyd. Speed Regulation

Speed regulation is generally defined as the percentage speed change resulting from a specified percentage load change. If you look at the torque vs speed characteristic curves for the three motor types, you will see that the shunt motor has a relatively flat curve and thus provides the best speed regulation. The series motor has a very high speed when lightly loaded with the speed

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dropping rapidly as load is applied. That illustrates a very poor speed regulation. The slope of the curve for a compound motor is between the other two.

The current that can be tolerated by the power source and the comutator will limit the available starting torque. Since the series motor has the highest torque for a given starting current, it has the highest starting torque. The shunt motor has the lowest starting torque and the compound motor is intermediate.

The starting current is normally limited by inserting a series resistor or electronically reducing the voltage during starting. However, since the series motor offers the lowest starting current at a given torque, it can be said to have the lowest starting current. The shunt motor has the highest starting current and the compound motor is intermediate.

The armature and rotational losses for the three types of motors would be similar. The series field losses are higher than the losses for the shunt field. Since compound motors have a shunt field and a series filed, their losses are the highest. That makes the shunt motor the most efficient, the compound motor the least efficient and the series motor intermediate.

6. DC Motor Characteristics

6.1 TORQUE

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6.2 SPEEDMotors are devices that convert electrical energy into mechanical energy. The D.C. motors

that we have been dealing with here convert electrical energy into rotational energy. That rotational energy is then used to lift things, propel things, turn things, etc... When we supply the specified voltage to a motor, it rotates the output shaft at some speed. This rotational speed or

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angular velocity, is typically measured in radians/second {rad/s}, revolutions/second {rps}, or revolutions/minute {rpm}.

6.3 TORQUE/SPEED CURVESIn order to effectively design with D.C. motors, it is necessary to understand their

characteristic curves. For every motor, there is a specific Torque/Speed curve and Power curve.

The graph above shows a torque/speed curve of a typical D.C. motor. Note that torque is inversely proportioal to the speed of the output shaft. In other words, there is a tradeoff between how much torque a motor delivers, and how fast the output shaft spins. Motor characteristics are frequently given as two points on this graph:

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The stall torque, , represents the point on the graph at which the torque is a maximum, but the shaft is not rotating.

The no load speed, , is the maximum output speed of the motor (when no torque is applied to the output shaft).

The curve is then approximated by connecting these two points with a line, whose equation can be written in terms of torque or angular velocity as equations 3) and 4):

The linear model of a D.C. motor torque/speed curve is a very good approximation. The torque/speed curves shown below are actual curves for the green maxon motor (pictured at right) used by students in 2.007. One is a plot of empirical data, and the other was plotted mechanically using a device developed at MIT. Note that the characteristic torque/speed curve for this motor is quite linear. This is generally true as long as the curve represents the direct output of the motor, or a simple gear reduced output. If the specifications are given as two points, it is safe to assume a linear curve.

Recall that earlier we defined power as the product of torque and angular velocity. This corresponds to the area of a rectangle under the torque/speed curve with one corner at the origin

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and another corner at a point on the curve (see figures below). Due to the linear inverse relationship between torque and speed, the maximum power occurs at the point where = ½

, and = ½ .

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6.4 POWER/TORQUE and POWER/SPEED CURVES

By substituting equations 3. and 4. (torque and speed, section 2.1) into equation 2. (power, section 1.3), we see that the power curves for a D.C. motor with respect to both speed and torque are quadratics, as shown in equations 5. and 6.

From these equations, we again find that maximum output power occurs at = ½ , and =

½ respectively.

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http://lancet.mit.edu/motors/motors3.html#sect1.3

http://lancet.mit.edu/motors/motors3.html#sect2.1


6.5 Parameters to Control Speed

Increase in flux decreases the speed but increases the torque. If torque is decreased by decreasing the field current, the following sequences are found:

1. Back EMF drops instantly, the speed remaining constant because of the inertia of heavy armature.

2. Due to decrease of EMF armature current I is increased because of I = (V − E)/R.3. A small decrease of flux is more than counterbalanced by a large increase of I which

means net increase of torque.4. If torque increases the speed also increases.

If applied voltage is kept constant, motor speed has inverse relation with flux.

where:

N = revolutions per minute (RPM) ,i.e. motor speed K = proportional constant R = resistance of armature (ohms) V = electromotive force (volts) I = current (amperes) Φ = flux (webers)

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http://en.wikipedia.org/wiki/Weber_(unit)

http://en.wikipedia.org/wiki/Ampere

http://en.wikipedia.org/wiki/Volt

http://en.wikipedia.org/wiki/Ohm

http://en.wikipedia.org/wiki/Counter-electromotive_force


7. Techniques to Control Speed of DC Motors

7.1 DC motor speed controller Using PIC Controller

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Circuit

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Pattern

Wiring side photograph

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7.2 DC Motor PWM Speed ControllerDC motor speed controls (as used in cordless drills and the like) are most commonly a

relatively low frequency PWM, and while higher frequencies can be used, there is really not much point. While the switching speed is almost invariably within the audible range, the motor noise is louder than the switching noise at all but the lowest speed setting.

There is no reason that the frequency needs to be fixed (the inbuilt ones aren't), and that makes the controller marginally simpler to build. As shown below, the controller featured uses one readily available (and cheap) CMOS hex Schmitt trigger IC and a few passive components. The MOSFET can be salvaged from the drill if you choose to cannibalise one for the motor, and you may be able to rescue the diode as well - if you can find it!

The unit described is designed for 12V motors, but higher (or lower) voltages can be used. If the voltage is less than around 9V, you may need an auxiliary supply for the oscillator or it may not have enough voltage swing to drive the MOSFET gate properly. The oscillator voltage must not exceed 15V, or the CMOS IC will be destroyed. I suggest that the supply for the oscillator/ gate driver section should be between 10V and 14V. I have tried the controller with a couple of different sized motors - one from the drill, and another (much smaller) robotics motor. It worked perfectly with both, giving a smooth speed change and starting the motor at even the lowest speed setting.

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Figure 1 - DC Motor Speed Controller

It might look complex, but it isn't. There are a number of inputs and outputs that are paralleled, and as shown, U1A is the entire oscillator. The output of this could be used to drive the MOSFET directly (ignoring the other circuits), but this output already has a fairly heavy load because of the feedback components. You could also reverse the polarity (just reverse D1 and D2), and all remaining circuits can be used to drive the output. Why did I do it this way? Because I wired it up without really thinking about the polarity, and since there were 5 Schmitt inverters left in the package I knew that I could invert it if needed with no need to de-solder what I had done already.

With the values shown, the on time is fixed by R1 at 146us, and the frequency for minimum speed is just over 560Hz. At maximum speed, the frequency is about 6.5kHz, with an off period of only 2.6us - limited by the fact the U1A will insist on oscillating, and the small residual resistance of VR1. You can increase the minimum on time by increasing R1 (some motors may need this to run), and the maximum speed can be limited by installing a resistor in series with VR1.

As noted above, the MOSFET can probably be salvaged from the drill along with its heatsink - my unit used a P45NF MOSFET, which appears to be a manufacturer's special part number. Otherwise, use an IRF540 or anything else that will do the job. One IRF540 will be sufficient for motors drawing up to around 20A - the MOSFET is rated at 33A, but some safety margin is always advisable. The diode may cause a problem, as it needs to be rated at around the same current as the motor at full load. You may get away with less, but you also may not. During tests,

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I was able to get the diode quite hot, depending on motor speed. I used a MUR1560 (15A/600V ultrafast) because I had them handy, although it might be overkill.

D1 and D2 need only be 1N4148 or similar. Do not use 1N400x diodes, as they are not fast enough and will cause problems with the oscillator. The 15V (1W) zener is used to protect the CMOS IC from excessive spike voltages. If you intend using the circuit shown from a supply voltage above 15V, then you will have to increase the value of R3. As shown, it's purpose is only to limit peak zener current from spikes, but increasing it will allow the circuit to operate from higher voltages.

There is no real reason that the circuit couldn't be scaled up to handle very powerful motors, but for such applications, a feedback system would probably be expected to maintain the set speed regardless of load. Needless to say that is not available in the above circuit, and for many tasks (such as coil winder or motorised axis on a milling machine) it is not always a good idea - it's nice to be able to stop the motor by hand in an emergency without it trying to tear your arm off

The diode is critical for motor speed control. It allows the back EMF from the motor (which occurs when the MOSFET switches off) to be put to good use - in this case it is re-applied to the motor, so is not wasted generating a high voltage pulse that may damage the motor's insulation. Without the diode, speed control is poor, low speed torque is minimal, and the motor will probably refuse to even start at less than 50% duty cycle.

7.3 BLDC Motor Control utilizing Hall-effect sensors

This element demonstrates how to use a PSoC® to control a 3-phase Brushless Direct Current (BLDC) motor utilizing Hall-effect sensors.

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Block Diagram

7.4 Digital DC Motor Speed Control with PID Control

Continuous to Discrete ConversionPID Controller

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http://www.engin.umich.edu/group/ctm/examples/motor/digital.html#PID

http://www.engin.umich.edu/group/ctm/examples/motor/digital.html#Con2Dis


We will consider the digital control version of DC motor speed problem. A digital DC motor model can be obtained from conversion of the analog model, as we will describe. The controller for this example will be designed by a PID method.

From the Modeling: a DC Motor, the open-loop transfer function for DC motor's speed was derived as:

Where:

*electrical resistance (R) = 1 ohm

*electrical inductance (L) = 0.5 H

*electromotive force constant (Ke=Kt) = 0.01 Nm/Amp

*moment of inertia of the rotor (J) = 0.01 kg*m^2/s^2

*damping ratio of the mechanical system (b) = 0.1 Nms

*input (V): Source Voltage

*output (theta dot): Rotating speed

*The rotor and shaft are assumed to be rigid

The design requirements for 1 rad/sec step input are

Settling time: Less than 2 seconds Overshoot: Less than 5% Steady-state error: Less than 1%

Continuous to Discrete ConversionThe first step in designing a discrete control system is to convert the continuous transfer function to a discrete transfer function. Matlab command c2dm will do this for you. The c2dm command requires the following four arguments: the numerator polynomial (num), the denominator polynomial (den), the sampling time (Ts) and the type of hold circuit. In this example, the hold we will use is the zero-order hold ('zoh').

From the design requirement, let the sampling time, Ts equal to 0.12 seconds, which is 1/10 the time constant of a system with a settling time of 2 seconds. Let's create a new m-file and enter the following commands:

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http://www.engin.umich.edu/group/ctm/extras/mfile.html

http://www.engin.umich.edu/group/ctm/digital/digital.html#zoh

http://www.engin.umich.edu/group/ctm/digital/digital.html#conv

http://www.engin.umich.edu/group/ctm/examples/motor/motor.html


R=1;L=0.5;Kt=0.01;J=0.01;b=0.1;

num = Kt;den = [(J*L) (J*R)+(L*b) (R*b)+(Kt^2)];

Ts = 0.12;[numz,denz] = c2dm(num,den,Ts,'zoh')

Running this m-file should return the following:

numz =

0 0.0092 0.0057

denz =

1.0000 -1.0877 0.2369From these matrices, the discrete transfer function can be written as:

First, we would like to see what the closed-loop response of the system looks like without any control. If you see the numz matrices shown above, it has one extra zero in the front, we have to get rid of it before closing the loop with the Matlab cloop command. Add the following code into the end of your m-file:

numz = [numz(2) numz(3)];[numz_cl,denz_cl] = cloop(numz,denz);

After you have done this, let's see how the closed-loop step response looks like. The dstep command will generate the vector of discrete output signals and stairs command will connect these signals. Click here for more information. Add the following Matlab code at the end of previous m-file and rerun it.

[x1] = dstep(numz_cl,denz_cl,101);t=0:0.12:12;stairs(t,x1)xlabel('Time (seconds)')ylabel('Velocity (rad/s)')title('Stairstep Response:Original')

You should see the following plot:

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http://www.engin.umich.edu/group/ctm/extras/dstep.html


PID ControllerRecall that the continuous-time transfer function for a PID controller is:

There are several ways for mapping from the s-plane to z-plane. The most accurate one is . We cannot obtain PID transfer function in this way because the discrete-time transfer function would have more zeroes than poles, which is not realizable. Instead we are going to use the bilinear transformation shown as follows:

Thus we can derive the discrete PID controller with bilinear transformation mapping. For more detail derivation of discrete PID controller, see Discrete PID Controller. Equivalently, the c2dm command in Matlab will help you to convert the continuous-time PID compensator to discrete-time PID compensator by using the "tustin" method in this case. The "tustin" method will use bilinear approximation to convert to discrete time of the derivative. According to the PID Design Method for the DC Motor page, Kp = 100, Ki = 200 and Kd = 10 are satisfied the design requirement. We will use all of these gains in this example. Now add the following Matlab commands to your previous m-file and rerun it in Matlab window.

% Discrete PID controller with bilinear approximationKp = 100;

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http://www.engin.umich.edu/group/ctm/examples/motor/PID2.html

http://www.engin.umich.edu/group/ctm/examples/motor/PID2.html

http://www.engin.umich.edu/group/ctm/extras/PID_Bilinear.html


Ki = 200;Kd = 10;

[dencz,numcz]=c2dm([1 0],[Kd Kp Ki],Ts,'tustin');

Note that the numerator and denominator in c2dm were reversed above. The reason is that the PID transfer function is not proper. Matlab will not allow this. By switching the numerator and denominator the c2dm command can be fooled into giving the right answer. Let's see if the performance of the closed-loop response with the PID compensator satisfies the design requirements. Now add the following code to the end of your m-file and rerun it. You should get the following close-loop stairstep response.

numaz = conv(numz,numcz);denaz = conv(denz,dencz);[numaz_cl,denaz_cl] = cloop(numaz,denaz);

[x2] = dstep(numaz_cl,denaz_cl,101);t=0:0.12:12;stairs(t,x2)xlabel('Time (seconds)')ylabel('Velocity (rad/s)')title('Stairstep Response:with PID controller')

As you can see from the above plot, the closed-loop response of the system is unstable. Therefore there must be something wrong with compensated system. So we should take a look at root locus of the compensated system. Let's add the following Matlab command into the end of your m-file and rerun it.

rlocus(numaz,denaz)

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title('Root Locus of Compensated System')

From this root-locus plot, we see that the denominator of the PID controller has a pole at -1 in the z-plane. We know that if a pole of a system is outside the unit circle, the system will be unstable. This compensated system will always be unstable for any positive gain because there are an even number of poles and zeroes to the right of the pole at -1. Therefore that pole will always move to the left and outside the unit circle. The pole at -1 comes from the compensator, and we can change its location by changing the compensator design. We choose it to cancel the zero at -0.62. This will make the system stable for at least some gains. Furthermore we can choose an appropriate gain from the root locus plot to satisfy the design requirements using rlocfind.Enter the following Matlab code to your m-file.

dencz = conv([1 -1],[1.6 1]) numaz = conv(numz,numcz);denaz = conv(denz,dencz);

rlocus(numaz,denaz)title('Root Locus of Compensated System');[K,poles] = rlocfind(numaz,denaz)[numaz_cl,denaz_cl] = cloop(K*numaz,denaz);

[x3] = dstep(numaz_cl,denaz_cl,101);t=0:0.12:12;stairs(t,x3)xlabel('Time (seconds)')ylabel('Velocity (rad/s)')title('Stairstep Response:with PID controller')

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The new dencz will have a pole at -0.625 instead of -1, which almost cancels the zero of uncompensated system. In the Matlab window, you should see the command asking you to select the point on the root-locus plot. You should click on the plot as the following:

Then Matlab will return the appropriate gain and the corresponding compensated poles, and it will plot the closed-loop compensated response as follows.

The plot shows that the settling time is less than 2 seconds and the percent overshoot is around 3%. In addition, the steady state error is zero. Also, the gain, K, from root locus is 0.2425 which is reasonable. Therefore this response satisfies all of the design requirements.

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8. Application of DC Motors

DC Motors are argueably the most useful type of electrical motors, and with good reason, they are designed to be used with batteries, solar cells or similar cell based energy sources, and as a result are used in systems where you don't have to be tied to a wall. Furthermore, even in systems where they are tied to the wall, sometimes it can be more efficient and cost effective to run DC Motors even in certain situations. Motors generally though give the impression of a gas guzzling car.

Low Power DC Motors The lower power motors aren't really useful for things commonly associated with motors. Lifting and transportation applications require more power & torque for them to work. However, what they lack in power they make up in precision. Low power DC motors are particularly useful as speed changes from 0 to 1 are almost instantaneous. Therefore, they can be used successfully in digital systems.

A low speed, low power brushless DC motor can be found in most turntable devices, particularly precision turntable devices. Devices with such motors are things like personal computers (usually, with 3 motors in it, one for the hard drive, and one for the processor cooler), CD & DVD players.

Medium Power DC Motors Medium power DC Motors have a use too in systems. Generally they are connected to the mains, and use a rectifier to convert the AC current into a DC current to be used for the task in hand. As a result of this, they also need to be stepped down (voltage reduced) so that the current doesn't overpower the circuit and burn out the motor. This limits their usage to larger systems that require room for both a stepper and a rectifier. But they still serve a purpose, particularly in systems where size nor speed is an issue, just reliability.

High Power DC Motors Argueably the most common and useful motors are High Power DC Motors. These motors are generally used in open systems, and generally used in systems were torque and power, as well as drive are paramount. Examples of such systems include electric wheelchairs, electric scooters, Segways, hybrid cars, as well as in elevators.

Of course, with power comes great power usage, and whilst the most energy efficient form of motor, they can require a lot of energy to run. Part of the creative process of using them is to be efficient (drive systems in hybrid cars use the petrol motor's momentum to recharge a battery, which will be then used to power the DC motor), but generally the battery will need to be recharged or replaced at regular intervals. Even so, it's usually infrequently the

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battery needs replacing. Furthermore, any systems attached to the mains don't suffer from this problem.

8.1 Application of Shunt-Wound MotorsThis type of motor runs practically constant speed, regardless of the load. It is the type

generally used in commercial practice and is usually recommended where starting conditions are not usually severs. Speed of the shunt-wound motors may be regulated in two ways: first, by inserting resistance in series with the armature, thus decreasing speed: and second, by inserting resistance in the field circuit, the speed will vary with each change in load: in the latter, the speeds is practically constant for any setting of the controller. This latter is the most generally used for adjustable-speed service, as in the case of machine tools.

The shunt motor is probably the most common dc motor used in industry today. Components of the shunt motor are the armature, labeled A1 and A2, and the field, labeled F1 and F2. The coils in the shunt field are composed of many turns of small wire, resulting in low shunt field current and moderate armature current. This motor provides starting torque that varies with the load applied and good speed regulation by controlling the shunt field voltage. If the shunt motor loses it’s field it will accelerate slightly until CEMF rises to a value sufficient to shut off the torque producing current. In other words, the shunt motor will not destroy itself if it loses its field, but it won’t have the torque required to do the job it was designed for.

Some of the common uses of the shunt motor are machine shop lathes, and industry process lines where speed and tension control are critical.

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8.2 Application of Series-Wound Motors This type of motor speed varies automatically with the load, increasing as the load

decreases. Use of series motor is generally limited to case where a heavy power demand is necessary to bring the machine up to speed, as in the case of certain elevator and hoist installations, for steelcars, etc. Series-wound motors should never be used where the motor cab be started without load, since they will race to a dangerous degree.

Components of a series motor include the armature, labeled A1 and A2, and the field, S1 and S2. The same current is impressed upon the armature and the series field. The coils in the series field are made of a few turns of large gauge wire, to facilitate large current flow. This provides high starting torque, approximately 2 ¼ times the rated load torque. Series motor armatures are usually lap wound. Lap windings are good for high current, low voltage applications because they have additional parallel paths for current flow. Series motors have very poor speed control, running slowly with heavy loads and quickly with light loads. A series motor should never drive machines with a belt. If the belt breaks, the load would be removed and cause the motor to over speed and destroy itself in a matter of seconds.

Common uses of the series motor include crane hoists, where large heavy loads will be raised and lowered and bridge and trolley drives on large overhead cranes. The series motor provides

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the starting torque required for moving large loads. Traction motors used to drive trains are series motors that provide the required torque and horsepower to get massive amounts of weight moving

8.3 Application of Compound-Wound MotorsA combination of the shunt wound and series wound types combines the characteristics

of both. Characteristics may be varied by varying the combination of the two windings. These motors are generally used where severe starting conditions are met and constant speed is required at the same time

When comparing the advantages of the series and shunt motors, the series motor has greater torque capabilities while the shunt motor has more constant and controllable speed over various loads. These two desirable characteristics can be found in the same motor by placing both a series field and shunt field winding on the same pole. Thus, we have the compound motor.

The compound motor responds better to heavy load changes than a shunt motor because of the increased current through the series field coils. This boosts the field strength, providing added torque and speeds.

Common uses of the compound motor include elevators, air compressors, conveyors, presses and shears. Compound motors can be operated as shunt motors by disconnecting the series field. Many manufacturing process lines are designed this way. The reason being that, most off the shelf motors are compound motors, and the series field can always be connected later to provide additional torque, if needed.

Compound motors can be connected two ways, cumulatively and differentially. When connected cumulatively, the series field is connected to aid the shunt field, providing faster response than a straight shunt motor. When connected differentially, the series field opposes the shunt field.

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Differentially connected compound motors are sometimes referred to as “suicide motors,” because of their penchant for self destruction. If perhaps, the shunt field circuit were to suddenly open during loading, the series field would then assume control and the polarity of all fields would reverse. This results in the motor stopping, and then restarting in the opposite direction. It then operates as an unloaded series motor and will destroy itself. Differentially connected motors can also start in the opposite direction if the load is too heavy. Therefore, it is seldom used in industry

9. Tables

9.1 Weekly Plan

Week 1st Factory Visit, Project Discussion, Selection of Project

Week 2nd Types of motor, Study of DC Motor, DC Motor types, Difference between different types of motor

Week 3rd Speed of DC Motor, Changing Speed of DC Motor and Controlling it, Different Techniques for Speed Controlling

Week 4th Application of DC Motors, Different connections, Series Connection, Shunt Connection, Compound Connection

Week 5th Compilation of all the Data, Editing, Final Report, Formatting, Submission

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9.2 Difference Table

D.c. shunt motorLathes,fans,pumps disc and band saw drive requiring moderate

torques

D.c. series motorElectric traction, high speed tools

D.c. compound motor

Rolling mills and other loads requiring large momentary toques.

10. References

1. "What is an Actuator?", wiseGEEK. Conjecture Corp., 2010. Retrieved 2010-03-13.

2. Schoenherr, Steven E. (2001), "Loudspeaker History". Recording Technology History. Retrieved 2010-03-13.

3. Faraday, Michael (1844). Experimental Researches in Electricity. 2. See plate 4.

4. spark museum

5. http://www.traveltohungary.com/english/articles/article.php?id=135 a b Electricity and magnetism, translated from the French of Amédée Guillemin. Rev. and ed. by Silvanus P. Thompson. London, MacMillan, 1891

6. Nature 53. (printed in 1896) page: 516

7. a b http://www.mpoweruk.com/timeline.htm

8. http://www.fh-zwickau.de/mbk/kfz_ee/praesentationen/Elma-Gndl-Generator%20-%20Druckversion.pdf

9. http://www.uni-regensburg.de/Fakultaeten/phil_Fak_I/Philosophie/Wissenschaftsgeschichte/Termine/E-Maschinen-Lexikon/Chronologie.htm

10. http://www.mpoweruk.com/history.htm

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http://www.mpoweruk.com/history.htm


11. Gee, William (2004). "Sturgeon, William (1783–1850)". Oxford Dictionary of National Biography. Oxford, England: Oxford University Press. doi:10.1093/ref:odnb/26748.

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Dc Motors Speed Control Using Different Techniques and Its Application