 Okay, let's start our next topic that is on smart sensors concept Okay, so I'll tell you what what it is and I know how it is very useful for many different sensors and then like No, we'll talk a little bit more on compliant mechanisms It's a little bit of it analysis and anything like that for me catonic purpose Like no, there's kind of mechanisms that we would we have seen in the CD-ROM drives and things like that Okay, so let's begin with the concept here for the smart sensors Let me get a pointer, right? Okay, so So you need to think about like how we can make a sensor which can be smart in some sense in the sense like See it can self calibrate itself. Okay, or Maybe like, you know, it can have Range and resolution Tussle, usually there is a tussle between the range and resolution the sensors that can measure at a very large range That the resolution will be typically low Sensor that can measure at a smaller kind of a range there their resolution can be high Okay, so This tussle between resolution and range is always there like we cannot have something which is measuring very large kind of a quantity at very very very high resolution Give an example You have seen Same we say we talk of like a measurement of the weight Okay, so if you go to the If you want to way like no way a gold for example, you go to this goldsmith or Jewelry manufacturer and like you know, you give the jewelry to way He'll have the small little micro balance, which will give you very very accurate kind of a weight of the Jewelry that you are measuring Now If you talk of like no other extreme like no, there are these way bridges You might have seen in the in the What do you call? You're Some some kind of a you know There are these vendors who are like having these way bridges which can be the cars actually cars and trucks Wait, you know, they can measure So you'll find like the way you have these gas pumps or like the petrol pumps like that Is this way bridges will be there If you ask them like what is the accuracy of measurement of the weight it'll be in hundreds of If not, like no tens of kgs. Okay Mostly hundreds of kgs. They made like no tons of material there Okay, so there is a huge kind of a Difference in the resolution of measurement or like no the accuracy of measurement in In on one side like if you go for very small kind of a Sensor very small kind of a range like a gold measurement versus like in a car measurement Of course One sees a need whether there is a need for like such a high accuracy We don't need like no the car weight to be known to such a high accuracy But the point here is that like no the things which are made to work with a Larger range typically give you a lower resolution Okay, and if you now demand like no, though, I want both No little bit extend the range of measurement Okay, say for example micro balance can go up to maybe 800 grams kind of a weight that can measure But if you want to measure like no step to 500 grams Okay, by the with the same resolution or up to one kg with the same resolution How can we make it possible? Okay, that is a kind of a question here So think about it like you know what kind of a thing comes to your mind to do that Okay, so we'll talk and discuss a little bit more about this example what kind of ideas that can be incorporated to enhance like the range of So let's talk specifically about this weight measurement Okay, so how the weight measurement principle is done. Okay, think about that and we'll come to that in a minute So let's say you have to enhance the range of the sensor with this kind of a specific example of Way balance, okay, the way balance typically has a spring Okay, you put some weight this spring will deform and like it will go down and typically on the scale You'll see some weight measurement One of the ways of measuring weights, okay Other way you you may have this kind of a you know the balance that your Subchip vendors they use but I try to know we just focus about You know these kind of a system for weight measurement Okay So so the the markings here, okay are Typically say save one mm marks which which we can identify from one to other maybe one mm we can identify now if I want to wave very very small quantity or very very small kind of a resolution kind of a measurement, then I use a spring which is Little low kind of a flexibility Okay, a little low rigidity Okay, highly flexible spring so even for a small weight it's going to get deformed and I can see it's marking on the on the base scale here okay now if I get this spring to go smaller in the Stiffness or higher flexibility Then you see that like no from this point to this point if the pointer can move Say this point being a limit that spring gets kind of completely compressed here, and this is a starting point So if this is a range that you'll be able to measure is proportional to Like the stiffness times the displacement, okay, so that will be the range So this is our whole displacement that can be possible for the spring and then stiffness times that will be like a small range Because like no more the stiffness is very very small okay, if I Increase the stiffness then like you know the the the range can be increased But then what happens is still for a moment of 1mm like I'll have to See that like no larger weight needs to be put So that means like my resolution for this 1mm kind of a measurement is going to be Like no little lower for higher stiffnesses. Okay, so this is a point like you can you all see this point? So now We are not right now, you know what worried about like no, there is a friction that will also play some role and all those kind of things Are going to be there. Okay So so we are not right now kind of like no bothered about those things. Okay, so The question is then how do you kind of make like no enhance this range of measurement even for a small resolution, I mean even for a high resolution kind of our small stiffness kind of a Scenario in in this particular case. Okay, so So let's talk about that now So so you appreciate this point that you know the sensitivity would decrease if we have a demand for high range or resolution will be low for higher range Okay, and vice versa So If you want to increase weight, then like no, I propose that okay, we put an actuator in the sensor Okay, suppose we put an actuator in the sensor. Okay So I I formed little like a small feedback system around this Sensor such that like no the actuator is now giving an additional force. Okay, so I measure these on the scale Could take its feedback To my actuator and then like no actuate the actuator such that this reading always points to zero So if I even if I put some weight there like Then like actuator will come in place. So so so look there's a sequence will happen like that Okay, I put a weight on the surface then this pointer is going to kind of like no go down That means there is some error that is produced part from away from the zero position And then that error is fed back to the actuator and actuator kind of give some force and brings it back to zero. Okay, and This way like no, you can always maintain like you know some small Some some like no zero as a balance. Okay, it's called null balance. Okay, so you null balance the system Always no matter how much is a bit. I'm putting I mean my system is always balanced and now Depending upon what is the strength of your actuator? You can get now the the higher forces possibility. Okay, so you can use a spring still like no lower stiffness But now the spring has no deformation at all because actuator is providing like no the force to balance the weight So that is a kind of a idea that is utilized here to enhance the range by using an actuator Okay One can think of like, you know, what kind of actuator how we can put it and all those kind of things We are not right now worried about okay, but making sure that you know that actuator also doesn't have somehow any kind of additional friction force anything like that. Okay, so So see can you see this idea? So with this idea one can kind of like no enhance the range of sensor and Keep the resolution same and you get some additional advantages just a moment any Nonlinearity is that are existing in the system. They won't bother you here Okay Sorry about my Mobile Okay, so no Nonlinearity in the system like no say for example a spring as you deform more and more it would have it might become nonlinear Okay, instead of like no the your scale is linear, but spring is behaving in some kind of a nonlinear fashion because of the large deformations Okay To compensate for that you would have like no this marking also put in some kind of a nonlinear way but Because we are doing this null balance with actuator here, we don't need to do that Okay, you see this is a big advantage that you you get Okay By by doing this so now one can think about okay a little bit more detail about This concept and say okay. Oh look if I'm doing this okay putting this actuator here How do I know what is actuator force I should apply? So that will come from some kind of a feedback control now and one can think about what kind of feedback control now You can put here. Okay, so you have studied some like no PD control You know PD PID kind of controls or a proportional control one can kind of employ that and say that okay. Oh look if I Apply the actual force proportional to the error Okay, with some kind of a gain constant when slowly like you know, it will go go back to making make the error zero Okay, so that is how I can determine the actuator force So so you you you you might have like no Some other kind of a ways you just proportional algorithm may or may not give you great kind of advantage or those kind of things can be discussed more but but the basic concept is is Essential to kind of capture here is that like no, I'll always maintain like null balance or zero kind of a reading on the scale and Okay, then the question is okay. Oh look, I'm maintaining zero there But how do I know how much is in my weight that I'm putting on the surface? Oh that can be there then calculated by just saying seeing like, you know How much is a extra actuator force that you need to apply to maintain that? balance, okay, so When I put something on the on the on the way balance, I'll Have to apply some actuator force which will happen through some kind of a feedback control strategy And finally once it is settled in the final position Whatever is a like no the value that bias value that I need to apply I'll I'll get to know from that value What is a bit that I put on the surface? Okay, that is how like no one can get The the actuator based on actual force like you know, what is your? Weight that is put on the surface Okay Now one can do some kind of a mathematics to do like you know that okay. The actual force is a proportional KP kind of a control we can do then how do you analyze this is cementing that one can do a lot of this kind of Mathematical jugglery beyond is to find out. Okay, what kind of proportional constant I should use or I do I need In addition some kind of a derivative also probably you'll need a derivative control also to kind of make sure Your system settles into the final position rather than oxidating in the in the in the study state Okay Typically like no that friction will be there in these kind of practical systems So even if you don't put the derivative control in place like no There'll be a natural damping that will happen because of the friction in the system and like no your system will finally settle down Okay, it's not going to continue oscillating forever Okay So You can kind of think of this mathematical model to represent like you know this dynamics of a system and then like you know Formulate like your control strategy and validate how your error behavior happens and things like that. Okay, so Maybe you can try this exercise yourself and then like no look at some of these Developments that are given in this slide. Okay so so For any kind of a system will come to this in more in the detail when I when we start modeling different different kinds of systems But typically for modeling any systems they says you have understood this system, you know, actually there is some some mass That will happen for this You know the station that the dead weight of the stage itself and then there is a stiffness and then some kind of a You know the damping you can consider here and then this becomes like a simple spring mass damper system and for which like no, you know very well known equation which is You know the force that I'm applying on the system will be mass times acceleration plus c times x dot and plus k times X will be will be there in addition. Okay so So so So this f that we talked here like, you know This f is is a force of actuator. Okay, that has to balance like Finally like no some kind of a dynamics of a system. Okay, I'm sorry, okay so The the the steady state value of the force. Okay, we'll we'll give you the final reading. Okay, so Expression, you know, so these are the two expressions for the force one is like no based on the dynamics of the system and other expression is what you would Develop as a control strategy. Okay based on the feedback So these the previous expression that you saw here was we are considering that okay We'll apply the actuator force to be equal to this amount. Okay. That was our feedback in some sense for the for the system So when x t is null balance or zero then like no you'll get this as a feedback expression for the for the force and then like no, this is a This is a system dynamics. I think these are there's a term corresponding to the spring missing here k times x also will be coming as an additional term here, but And then then like no, we'll apply like no some proportional control kp times No x as as this force. Okay. That's how that's how the things things are going to happen Okay So right now the friction in the system is needed So so when you do analysis of how this control would work or like no How this control will will take care of or settle in the system into then like no You need to substitute this value of force from like as you are proposing as a control here in the expression of dynamics And then do the analysis and then like no, you'll be able to find out the the Details of how this force is going to how this Proportional feedback that you are proposing is going to affect your system or affect your state of x of the system Or you can like no convert the state x into the error Dynamics and like no study like no what will happen to the error? How will it go to zero? Will it go to be zero instantaneously or to oscillate how I can kind of have like no the settling time of that Oscillations control all those kind of things one can talk about in in lot more details Okay, so we'll come to some some more kind of analysis of such kind as we as we progress Okay, you have done something already But now we'll see from a little bit more practical perspective when the friction and other In terms are there or if you want to model the motor also like the actuator also in the in the system in some some way Okay, how do you kind of take care of some of these things that will be seen here? Okay, so By the way to balance these if we use a screw kind of a system to drive Actuator means like no motor and a screw type kind of a system then since it is not back drivable that will not work here Okay, so anything which is having a friction a lot of lot amount of friction will will not work for for such kind of a thing So we will need to employ here a non contact linear actuator Which will kind of drive the system to kind of make things in zero So you need to be aware about this like we say we have seen okay Linear motion means like no we'll put some kind of a rack and pinion or like no this Screw kind of actuator if you start putting that it will for certainly balance like no this through null balance But now the kind of force that I need to apply is the system is locked in this place Actually you any place you you take the system will be locked So even if you now say okay if it is at zero and I play some more weight on the system since it is not back drivable I am not going to get any deformation up here So this crew kind of actuators will not work here unless they are like no very smooth back back drivability is there Okay, so typically screwed it screw act pictures will not have a back drivability So here we need to have a non friction non contact kind of a Linear actuators to do drive the system. Okay, then things are going to work here much better Okay, so You can think about and like no see whether you yourself are able to kind of do this You know error analysis here with one control expression or some other kind of a control expression And like no we can talk about that in more details later. Okay