 Hello and welcome to this lecture on Advanced Electric Drives. In the last lecture, we are discussing about the control of Swiss reluctance motor. We have seen that a Swiss reluctance motor is nothing but a motor in which the torque is produced by variation of reluctance. The stator has got concentric winding, the rotor has got slotted structure and as the rotor rotates, there is variation of inductance seen by each winding of the stator and hence this variation of inductance is helpful for the torque production. So, we were seeing the closed loop speed control of a Swiss reluctance motor. So, this is the block diagram of the closed loop speed control. We have the reference speed, this is a reference speed and we compare this with the actual speed by having a speed feedback and then we have the PI controller, the proportional integral controller which gives something similar to the torque and we know the torque is given by k into i square. So, if you want to find out the current, current should be the square root of torque. So, in other words we can say that i is equal to t by k the constant under root, t is the torque k is the constant. So, we have a square root block here, this is the square root block, this is the square root block here and this is the limiter. So, this is the limiter that limits the maximum value of torque that can be produced and this limiter is practically very important because whenever we have a PI controller, this controller has the two parts, one is the proportional part, other is the integral part. The error is integrated and also the proportional part gives a proportion of the error in the output. Now, if the error is a DC error the integral part sometimes will go on reach a very high value and practically the motor torque is always limited. The motor current is always limited, we cannot get infinite amount of torque from a current neither can we inject infinite current into a motor. So, the motor torque and current are limited by virtue of the rating of the motor. So, it is practical to limit the value of the PI controller output and that is achieved by a limiter and then we get something similar to the torque here and we have a square root function and we get the reference current that is i star and the reference current have to be injected into the windings of the stator. The stator has got many phases we have seen this current i star has to be injected into the windings of the stator and that is achieved by a closed loop current control. So, we sense the actual current of the Swiss reluctance motor or SRM this currents are sensed here and compared with the reference current i star and then the controller is properly designed to inject the current onto the SRM. Now, when we want to inject the current the currents have to be injected in proper phase angle and this phase angle is decided by the rotor position. So, the controller will also have an input of theta and theta is the rotor position and that is obtained by the integration of the speed. We integrate the speed and get the rotor angle and this i is injected into the SRM by means of a converter and the controller decides the switching angle depending upon the theta. And as we know that when we control the Swiss reluctance motor it can be operated at a very low speed in chop mode and then after the base speed it can operate with constant power. And then beyond some speed we can go for P omega square constant and these are the various modes of operation and the modes are decided based on the speed. The speed is also fed as an input to the controller to decide the mode of operation and we have a speed sensor here the speed sensor senses the speed and hence we have a closed loop speed control. Now, in this case the synchronous this Swiss reluctance motor has to come with a converter without the converter the motor cannot be operated. So, the converter should be able to inject current into the machine winding and also should be able to control the current. So, we were seeing the various topologies of this converters. Now, let us look again the topology of the converters. So, this is the converter topology for the Swiss reluctance motor. Now, in this case this is one of the windings of the stator and for every winding we will have this kind of configuration a transistor and a diode. If the transistor is switched on the current will flow like this through the transistor and through the winding. And what we have here if we say that this voltage is V with this positive and this negative. So, we can say that when the switch is on V is equal to V dc plus V dc when S is on and D is off. So, we are able to apply a positive voltage to the winding by switching on S S is a transistor switch. And when we switch on S naturally the diode will be reverse biased that the diode D will be reverse bias and this automatically remains in the off position. And then if you want to apply a negative voltage if you want to apply a negative voltage we switch off the switch S. So, what we do here is that V is equal to minus V dc when S is off and it means D is on. So, it means when we want to apply a negative voltage we switch off S and when we switch off S what happens this current will vanish. And when this current vanishes earlier this current was flowing in this direction this path is not there. So, this current will try to maintain its direction through an alternative path. So, the path is provided by the diode. So, the earlier path is not present because the switch is off and when the switch is off the phase being inducted the current has to be maintained. So, this current sides an alternative path through the diode and the diode turns on. And when the diode turns on we can see that positive is applied to B and negative to A which means V becomes minus V dc. Now, this converter is can be used, but there is a problem the problem is this that this converter uses two power supplies. The power supplies one is this power supply that is V dc plus minus and the other one is plus minus V dc. And totally if you see the voltage is 2 V dc. So, out of 2 V dc we are only using V dc we are applying plus V dc and minus V dc. So, the first reason is that we need two power supplies and second reason is that the power supply is not fully utilized. In one mode we are only switching off S 1. So, the bottom power supply is not used the top power supply is used in the other mode we are switching off S bottom power supply is used the top power supply is not used. So, the utilization of this two power supplies is not 100 percent. So, we can go to a second topology in which we have a single power supply here that is plus V dc and we have the winding and the winding in this case we can say this is the voltage here plus minus. So, we have the transistor S 1 S 2 and the diodes D 1 and D 2. Now, what we do here we first turn on S 1 and S 2 S 1 and S 2 are on. So, if we turn on S 1 and S 2 what happens the current path is given like this is the path of the current. So, the current flows through the switches returns back to the source. So, as a result we can say that V is equal to plus V dc. So, we can we can write down V in this case. So, V is equal to plus V dc because this A is connected to the positive supply and B is connected to the negative supply and hence the voltage V is plus V dc. And when we turn off the switches let us go to the second situation S 1 and S 2 are off and D 1 and D 2 are on normally the diodes remain reverse biased. The diodes you can see that the cathode is connected to the positive and the anode is connected to the negative terminal. So, naturally the diodes will be reverse biased and specially when the switches are on S 1 and S 2 are on. So, D 1 is fully reverse biased it is off D 2 is fully reverse biased and that is also off. So, we can also say that when S 1 and S 2 are on D 1 and D 2 are off. In the second situation when S 1 and S 2 are off we are turning on the transistor switches by removing the base drive or the gate drive we are turning off the transistor switches what happens? The winding was earlier carrying some current and this current has to be maintained and the former path is broken the current will try to find out an alternative path and the alternative path is provided not through the switch, but through the diodes. So, this path is not there. So, this path is broken this path is also not there, but the windings current is still present and this current is flowing in this direction this is original current, but the switches are turned off this current will forcibly make the diodes on. So, the diodes will be on and the path of the current will be through the diodes D 1 and D 2 that is why we say that the diodes turn on here. So, D 1 and D 2 are on and as a result the current flows like this and fed back to the source. So, the current which is present in the inductor the inductor stored energy is fed back to the source through the diodes and hence we can say here that V is equal to minus V dc. So, this is the situation when the transistors are off and the diodes come into conduction. So, we are able to apply plus V dc and minus V dc in this case and when we are applying plus V dc and minus V dc we can control the rate of rise of current. Because we know that if we ignore the inductance we can write down a simple equation that V is equal to L di by dt. So, the rate of change of current is determined primarily for a constant inductance primarily by the applied voltage. So, by applying a positive voltage. So, we can say that di by dt is positive when V is positive and di by dt is negative when V is negative. So, we can in fact control the current and maintain the current in the winding when it is necessary. Now, we have seen actually that sometimes there are two windings for a phase. If there are two windings for a phase we can extend this to two winding structure also. So, if we have two windings for phase. So, we can have a structure like this we have the voltage here that is the dc supply voltage and we can have the transistor switch in this case and then we have two windings for phase this is one winding may be a the other winding may be a prime. So, per phase we have two windings and this two winding can be series connected. So, we have two transistors here something similar to the previous situation and also we have the diodes. So, these are the two transistors and the diodes are present like this this is one diode and we have other diode which is present like this. So, this is applied voltage V dc. So, we have the transistors and we have the diodes. Now, this is for one phase now we have seen a switch reluctance motor which has got four phases phase A phase B phase B and phase A phase D. Now, this is for a single phase phase A phase B will be something similar to this phase C will also be something similar to this. So, phase B will be connected to this exactly in the same way we can have phase B here we have B and B prime this is B and B prime these are the transistor switches and this is the diode here is a diode. Similarly, we have another diode here and same thing will be for phase C and D. So, here what we do in this case that the transistors are switched in pair. Now, this is we can call this to be T A transistor A and transistor A prime this is T B and B prime this is let us say we can call this to be D A and D A prime this is D B and D B prime and so on. So, we turn on let us say if we talk about phase A now if we concentrate on phase A when we want to apply positive voltage we turn on S A and S B. So, when or the or T A and T A prime so in this case what we have here is that if you turn on T A and T A prime the current through the winding will be flowing in the following fashion this is the current through A and A prime. And what is the voltage here if we say that this is terminal 1 and 1 prime we can say that V 1 and 1 prime is equal to plus V dc when T A and T A prime are on and D A and D A prime are off. Naturally when the transistors are on diodes will be off similarly if you want to apply a negative voltage we switch off the transistors if you switch off the transistors the current will flow through the diode. So, V 1 1 prime will be minus V dc when T A and T A prime are off and the diodes D A and D A prime are on. Now, if T A and T A prime are turned off what happens now suppose we turn on this to transistors current path will not be through the transistors. So, we can we can remove this path of the current, but the current through the inductor or the phase winding are still present. So, the current through the phase winding will be there. So, this is the current through the phase winding, but this current does not flow through T A and T A prime it has to flow through some alternative path and alternative path is provided by the diode. So, what happens here is that this current will be coming through the diode like this and the diodes will be conducting. So, this current will be flowing like this through the diode and the current through the winding will be maintained. Of course, it will be decaying, but it is maintained for that time. So, as a result what we have in this case the negative voltage applied across the winding. So, if we see here 1, 1 is now connected to this diode is on. So, D A is on here. So, 1 is connected to negative power supply. So, if you say that this is the 1 terminal, this terminal is same as this terminal negative and if you see 1 prime, 1 prime is connected to the positive through D A prime. So, if we say this is 1 prime and the 1 prime is connected to the positive terminal and hence we have V 1, 1 prime is minus V dc. And thus this thing can happen for phase A also for phase B and phase C, phase D after some phase shift. And thus we are able to control the current in each winding of the switch reluctance motor. The switch reluctance motors are used for light weight application where we need high torque to weight ratio. The rotor inertia is very small and hence it is popular for those applications where we need high torque to weight ratio. Now, we will go for another new motor, different kind of motor which are very widely used for control application and also application in robotics. And that motor is stepper motor. Stepper motor is very popular for many applications where the power range is not very high, may be a few watts, maximum few tens of watts not more than that. And examples can be from printer to robotic arm and so on. So, the uniqueness of stepper motor is that in stepper motor we can do inherently position control without any close to feedback. It is basically control in an open low fashion without a close to position feedback and hence the motor control is very simple and this is applied in those application where we need a position control. So, let us see some typical stepper motor which is also based on the principle of variation of reluctance. So, our next discussion will be on the stepper motors. Now, I will show you stepper motor here. Now, this is the stepper motor it is a very small motor which operates may be on 12 volt. And these are the connection of the windings that are brought out of the motor. And if we open this motor this is the motor shaft which is free to rotate. Now, if we open out this motor we will see that this is the rotor and this is the stator. The rotor has got lot of resistance. So, corrugations in fact we can say the rotor has got the slots and teeth it is not a smooth rotor and that is how the torque is produced. And similarly, the stator also has got the windings concentric windings the stator also has got some corrugations the stator is also having slots and teeth. Now, this slot and teeth of the rotor and the slot and teeth of the stator help us obtain a torque. And the torque is primarily reluctance torque and also sometimes we can have permanent magnet to also get the permanent magnet torque. So, we will be discussing right now the principle of a variable reluctance stepper motor. So, as we can understand that the stepper motor are of various types one type of stepper motor is variable reluctance stepper motor. Now, here the torque is produced by variation of reluctance there is a tendency of the rotor to align along the minimum reluctance position. So, if we shift the stator MMF again the orientation of the MMF will change and the rotor is having slots and teeth and the teeth will try to align itself with the minimum reluctance position. Now, let us take an example we will have a simple example where the stator has got 4 poles and the rotor has got 2 poles. So, we will we will see an example of a stepper motor which is variable reluctance time it is a stator and we have the rotor the stator as I have said has got 4 poles. So, let us draw the 4 poles of the stator. So, the 4 poles are equally spaced. So, this is one pole the second pole, third pole and the fourth pole and we can complete the intermediate parts this is a cross sectional view of the stator and this is the stator core we can complete the stator core structure and the stator carries windings and the windings are for every pole in every pole we have a winding and the windings are placed as follows. This is winding in may be phase A and we have phase B winding here and we have phase C winding here and we have phase D winding here. And these windings can be brought out of this this we can call as phase A this is a phase B this is phase C and this is phase D and this windings are brought out. So, we can bring out this winding of phase B here and phase C winding is also brought out here and phase D winding is also brought out here. So, we have the terminals which are brought out and these are the 4 phases of the stepper motor and the windings are also connected in a neutral point. So, we also have a neutral point which is available to us the neutral point is this. So, this neutral point is connected with this this is also connected with this this neutral point is connected with this and this neutral point is also brought out. So, this is the neutral point and usually this point is connected to the negative of the power supply that is a local ground and each phase is connected to a switch a transistor switch. So, here we have a transistor switch in phase A we have a switch in phase B we have a switch in phase C and we have a switch in phase D and these is connected to a battery. So, we can have a battery here this is a battery the source is also grounded. So, the return path here and the return path is this path. So, we can call this to be switch A this to be switch B this to be switch C and this to be switch D and what about the rotor the rotor is also a silent pole structure rotor also has got slots and teeth. Now, here we will consider a 2 pole rotor having only 2 teeth. So, in this case we have we have the rotor in which we have only 2 teeth one is like this or 2 poles and other one is like this. So, the rotor has got only 2 pole for simplicity of understanding we have shown this as 2 pole. So, the rotor is here. So, we have the stator in this case and this is the rotor and the motor is controlled by switching the various phases. Now, what we do here we switch in the sequence of A B C and D. So, the sequence of switching is A B C and D the sequence of switching of switching we can have 2 types of control the first one is a full step control. So, for full step control full step we go on switching A then B followed by C then D then again A and so on. So, what happens when you switch a particular phase only 1 phase is turn on at a time suppose we turn on phase A. So, this phase is turn on. So, when we turn on this particular phase this phase is energized and hence we have we have a flux coming out of this. So, this rotor will try to align itself along this particular phase and when phase A is switched off and B is switched on it means we are turning off phase A. So, this is not on right now. So, what we do here we now turn on phase B now when we turn on phase B the MMF or the flux of the stator shifts from A to B. So, it shifts from A to B. So, this is basically the MMF position. Now, to have this smooth transfer of MMF every phase is connected with a freewheeling diode. So, what we have here each one is connected to a freewheeling diode. So, in phase A we connect a freewheeling diode here phase B we also connect a freewheeling diode phase C we also connect a freewheeling diode and phase D we also connect a freewheeling diode. And when we turn off S A and turn on S B now we are turning on S B and we have already turned off S A. Now, the current in every winding will take some time to die out. So, if the transistor is switched off the current will prevail through the respective freewheeling diode. So, for some time A and B will both carry some current. So, the MMF from phase A to phase B will shift gradually although quickly the process will be gradual process from phase A the current is decreasing and phase B current is increasing. So, the MMF will change gradually from phase A to phase B and the rotor will try to follow the MMF. So, when phase A is switched off and then phase B is switched on the rotor moves in anticlockwise direction. The rotation in this case will be anticlockwise the rotation will be in anticlockwise direction. Now, what is the step angle? The step angle is angle between two subsequent switching we have switched off S A and now we have turned on S B. Now, between this the rotor has moved by 90 degree. So, from phase A to phase B if you see this the step size in this case is 90 degree. So, the step size is equal to 90 degree and that is called the full step operation. By full step we mean the step will be full the full step size is 90 degree. Now, what about the direction of rotation? Can it be reversed? Yes the direction of rotation can be reversed if we change the sequence of switching. Instead of switching A, B, C, D and A and so on if we switch A, D, C, B, A, D and so on the directional rotation will be changed from anticlockwise to clockwise. So, for the clockwise rotation for clockwise rotation what we have to do here the sequence of switching will be from A to D. It means when we turn on S A the rotor is aligned along phase A and then we turn off phase A S A and turn on S D. So, the MMF will be shifting from A to D and hence the rotor will be rotating in a clockwise direction. So, in this case A D, C, B and again A. Now, this is again the full step operation, but the rotation will be in the clockwise direction. So, we have already seen full step. Is there any scope of reducing the step size? Because if the step size is more the machine will be switching in jerks. There will be lot of jerk while changing from one to the other. The MMF is shifting in step which may not be desirable and this can be reduced if the step size can be reduced. So, here we have facility for micro stepping in which we switch on phase A then phase A and B then phase B then phase B and C and so on. Now, let us see how we can reduce the step size. The step size can be reduced by micro stepping in which the two phases are excited at the same time. So, the sequence of the switching for micro stepping will be as follows. So, for micro stepping we will first start with the anticlockwise rotation. So, what we do here? We excite or energize phase A then energize A and B together and then B then B and C then C then C and D then D then D and A then A and so on. Now, if we do that the MMF will have a intermediate step. Now, when we excite A and then A B MMF was originally in A it was somewhere here and then we are exciting both A and B. If we are exciting both A and B phase S A and S B are closed simultaneously. So, these two switches are closed simultaneously. So, in that case what we have here this MMF is here this MMF is here and the resultant of these two will be somewhere here. So, this resultant MMF will subtend 45 degree with the phase A axis and the rotor will rotate by 45 degree. So, here the step size will be half of the full step and it is 45 degree. So, the step size here will be 45. Now, similarly we can have anticlockwise this is anticlockwise rotation similarly we can have clockwise rotation also. In clockwise rotation we change the sequence in a different fashion. So, for clockwise rotation we will go for the following sequence we will start with A and then A plus D. So, we are basically shifting in the opposite direction right now we are not exciting A and B now. So, what we are trying to do here we are trying to excite A and D simultaneously. So, when we excite A and D simultaneously the resultant MMF will be somewhere here and hence the rotate will rotate in the clockwise direction. So, the sequence of switching will be A A plus D and then D D plus C then C C plus B then B B plus A then A and then B B plus B plus B plus B plus B plus B plus and so on. So, this will give us the rotation in the clockwise direction with the step size of 45 degrees. Now, this stepper motor is called 4 phase 4 by 2 pole variable reluctance stepper motor. So, we can write the name here this is called 4 phase because this has got 4 different phases A B C and D. So, we call this to be 4 phase 4 by 2 pole variable reluctance stepper motor. So, if we want to suppose we need to have a reduce step size. So, the step size need to be reduced we can go for different configuration we will now see a configuration where the stator has got 8 poles and the rotor has got 6 poles there the step size is reduced and we will see how it is reduced by going for higher number of stator pole and rotor pole. So, we will be discussing about a 4 phase we have 4 different phases here 4 phase 8 by 6 pole variable reluctance type. Now, let us see how this motor looks like again we will be taking a transverse section and trying to see the orientation of the stator and the rotor with respect to each other the stator has got 8 poles. So, we will draw this once again the stator is a cylindrical structure the rotor is also a cylindrical structure and we have the stator core the stator core here and the stator has got 8 different poles. So, we have 8 pole structure this is one pole this is second pole, the third pole, the fourth pole, fifth pole, the sixth pole, the seventh pole and the eighth pole. So, these are the stator poles. So, we can complete this pole structure of the stator and what about the rotor it is the rotor has got only 6 poles. So, the rotor poles will be as follows this is basically 60 degree shifted. So, 6 means 360 by 6 the distance between 2 poles will be 360 by 6 that is 60 degrees. So, this is 60 degree here and then 60 plus 60 will be 120 it will be something like this. So, we have the rotor poles which will be in the following fashion. So, this is the rotor structure now we can name the rotor poles also. So, we can call this to be 1, 2, 3, 4, 5 and 6 this is pole 1, pole 2, pole 3, pole 4, pole 5 and pole 6. So, we can complete the rotor complete structure here the rotor structure the stator boundary the stator core and the stator poles carry windings. So, we have windings in the stator and the windings are concentric winding each pole is having its own winding. So, we can have the windings for let us say this pole and these are the windings here this pole we can call it to be phase A and the diametrically opposite will be A prime. So, each phase has got 2 windings A and A prime. So, this is A prime which may be series connected similarly we have phase B here and this is B prime and so on. So, we have phase C here and this is C prime and we have phase D here and this will be D prime. So, this all this will be carrying winding. So, this will be carrying some winding D will also be carrying some winding same as D prime. So, A and A prime could be series connected B and B prime could be series connected and so on. Now, what we do here we in the same way excite first phase A then phase B then phase C and phase D. So, each phase now has got 2 windings. So, each phase will have windings like this phase A will have 2 windings and we can call this combined and phase A and A prime as phase A. Similarly, phase B will have 2 windings and they are series connected. So, this is B and B prime we call it as phase B phase C will have 2 windings here. So, we have C and C prime we call that to be C and D again will have 2 windings D and D prime we call that to be D. Now, what we do here we again excite phase A followed by phase B followed by phase C and then phase D and again A. So, the sequence of switching here in this case the sequence of switching is A B C D and again A and so on. Now, if we do that how does the rotor respond to the sequence of switching? Now, if A is switched on A is excited the MMF is along phase A. So, the MMF will be along phase A means it is something along this. So, this is the direction of the MMF and the rotor orient its pole along the stator MMF. So, this 1 and 4 1 is diametrical opposite to 4. So, 1 and 4 will be aligned along that MMF. So, it is stable position. So, the rotor will be held at that particular position. Now, when we switch of phase A and switch on phase B. So, we will be switching of phase A and then switching on phase B. So, phase B is this 1 this 1 is phase B and here we have also diametrical opposite which is here. So, if phase B is switched on what happens phase A is no longer excited. So, we can deenergize phase A this also is deenergized. So, we have energized phase B how does the rotor respond? The rotor rotates in such a direction. So, as to align its pole along the MMF. So, the rotor pole closest to this particular excited phase is basically is 6 and 3. So, 6 will be moving under phase B and 3 will be moving under B prime. So, what is that angle? That angle can be determined if we extend this and try to calculate this angle. This angle by which the rotor will move the stator pitch is 45 degree stator is actually having 8 poles stator pole pitch is 45. So, we can say that the stator pole pitch stator pole pitch is equal to 360 divided by 8 that is 45. What about the rotor pole pitch? The rotor pole pitch is 360 by 6 that is 60 degree. The rotor pole pitch is rotor pole pitch is equal to 360 by 6 is 60 degree. So, this angle the differential angle is basically 60 degree minus 45 degree. So, this angle is nothing but 15 degree is equal to 60 minus 45 that is why it is calculated. So, this from 1 to 60 degree from phase A to phase B of the stator is 45 degree. So, if you subtract 45 from 60 we get 15 degrees. So, this 15 degrees is the step by which the rotor will move. So, here we can say that the step size is 15 degree. So, in this case what we obtain here is that the step size is 15 degree and the rotor rotates in clockwise direction clockwise direction. So, the rotor is rotating in the clockwise direction 6 is coming under phase B 3 is coming under B prime. So, the rotation is clockwise. Now, suppose we would like to have anti clockwise rotation in that case we can go for the other sequence phase A then phase D and so on. So, for the anti clockwise rotation we can go for anti clockwise rotation the sequence of switching will be earlier we had A B C D and A. Now, you will have A D B C and so on. So, we have A B C B and then A and then D and so on. Now, in this case also we can have microstaping by microstaping we mean the 2 phases should be excited at the same time. So, that we have a reduced step size. So, in this case the microstaping can be done by exciting phase A then by exciting phase A and B like this. So, for the microstaping we can have the following sequence we will have A then A plus B then B then B plus C then C then C plus D then D then D plus A then A and so on. So, what happens in microstaping we are first energizing phase A rotor aligns along phase A we are energizing then both phase A and B. So, when we energize both phase A and B this is energized and also this is energized. Now, in this situation the rotor will try to occupy an intermediate position here the pole will not be aligned fully along the stator M M F. So, it will be occupying an intermediate position. So, here the intermediate position is 15 degrees by 2. So, in fact what happens here is this that this seeks tries to come within or below phase B. And one tries to go little away from phase A and this angle is 7.5 degrees. So, the step size in this case we have the step size here 15 degrees by 2 is 7.5 degrees. And this is for the same clockwise rotation for the anti clockwise we can have similarly the sequence of switching. So, this is for clockwise and what about for the anti clockwise rotation for the anti clockwise rotation we will do the following way that A then A plus D and then D and then D plus C then C then C plus B. So, the M M F will be changing from A to A and D then D to D and C and so on. And the rotation in that case will be anti clockwise. So in the next lecture we will be discussing more about this variable reluctance stepper motor. And we will see how this step size can be reduced. Actually if the step size is reduced we have an advantage that we can have finer steppings. The motion will be almost continuous and that is basically desirable in many applications. So, if we can reduce the step size we can have better application with stepper motor that we will be discussing in the next lecture.