1 00:00:01,560 --> 00:00:10,950 This session, we will discuss about the mathematical modeling of Wacol vehicle is nothing but the math 2 00:00:10,950 --> 00:00:12,810 having its weight. 3 00:00:13,850 --> 00:00:20,670 If we understand the physics, when we applied the force to this vehicle, because we call it the. 4 00:00:22,200 --> 00:00:26,340 Device, which will result in linear motion if we apply the force 5 00:00:28,830 --> 00:00:35,280 perpendicular to the vehicle, it will result in particular velocity. 6 00:00:35,310 --> 00:00:42,240 It will get you some speed and it will travel some distance at the interval of some time. 7 00:00:43,590 --> 00:00:51,090 So mathematical modelling is to represent the vehicle in the form of a mathematical equation so that 8 00:00:51,090 --> 00:00:52,080 we can get the. 9 00:00:53,360 --> 00:01:00,740 Relation between the input and output, their input data applied for this position, it tangentially 10 00:01:01,160 --> 00:01:07,550 to the will through the electric motor and output is speed, velocity and displacement. 11 00:01:11,210 --> 00:01:11,990 So if we. 12 00:01:14,000 --> 00:01:24,040 Represent this system as a bloc in the block diagram form, we can see the vehicle is can be represented 13 00:01:24,040 --> 00:01:33,040 as a mathematical equation such that input into force and resultant output will be speed, velocity 14 00:01:33,040 --> 00:01:34,360 and the distance Clarin. 15 00:01:35,880 --> 00:01:44,280 We consider this terrorist threat equation, that means one will look forward, will you, the one we 16 00:01:44,340 --> 00:01:50,970 your speed, velocity and distance if force is the constant, if we apply the continuous and constant 17 00:01:50,970 --> 00:01:54,540 force, it will result in final, steady state speed. 18 00:01:54,750 --> 00:02:01,780 That means after a certain time, not instantaneously, speed can rise up to final value. 19 00:02:02,190 --> 00:02:10,890 So if we are interested in one, will your speed when we have a velocity or the distance for the airplane 20 00:02:10,900 --> 00:02:13,990 for support, say, for example, speed? 21 00:02:14,430 --> 00:02:20,910 So if we are having the same mathematical equation, so if we applied the force of 10 Newton Meter, 22 00:02:21,180 --> 00:02:27,990 then we will be how we will to answer that for this much amount of force. 23 00:02:28,200 --> 00:02:33,680 The speed will be accordingly from the calculator, from the mathematical equation. 24 00:02:33,870 --> 00:02:42,210 It's called the steady state equation, but we want the dynamic modeling of the vehicle and your time 25 00:02:42,210 --> 00:02:43,250 is important. 26 00:02:43,260 --> 00:02:51,000 So whenever the time is in what it's called the dynamic modeling, because now what we want when we 27 00:02:51,000 --> 00:02:59,270 apply the force after applying the force of a certain amount of time, what will be the speed? 28 00:02:59,550 --> 00:03:07,240 This answer we want so it can be accomplished with the help of dynamic modeling after any vehicle. 29 00:03:08,070 --> 00:03:12,650 So we are interested in dynamic modeling where time is involved. 30 00:03:13,230 --> 00:03:15,930 So we will require the differential equation. 31 00:03:19,950 --> 00:03:28,560 So that we will have the clear eyed understanding of what will be the speed at a certain time and what 32 00:03:28,830 --> 00:03:36,270 the speed response, so we can also find that solution and the response time in terms of settling time 33 00:03:36,510 --> 00:03:41,520 and peak our shoot, that's all requiring controller design. 34 00:03:42,060 --> 00:03:50,070 So we will have the mathematical blup in this situation will represent the Wacol in the mathematical 35 00:03:50,070 --> 00:03:59,070 form when applied force will result in speed and will also have time in our equation. 36 00:04:03,630 --> 00:04:08,820 So we are going to design dynamic modeling of the vehicle. 37 00:04:13,760 --> 00:04:20,810 The vehicle, the force is applied tangential to the wheel in this direction, so if the force is applied 38 00:04:20,810 --> 00:04:24,440 in one direction, then what are the opposing force? 39 00:04:24,830 --> 00:04:31,790 F is equal to M in to the first opposing force will depend upon its mass and acceleration. 40 00:04:32,210 --> 00:04:39,290 If we consider V as a velocity, an acceleration will be DV by the rate of change of relativity. 41 00:04:39,680 --> 00:04:45,980 So if we apply the if force is produced with the help of electric motor, this is tangential force. 42 00:04:47,140 --> 00:04:51,200 The will and the opposing force is the M AI. 43 00:04:51,470 --> 00:04:53,810 So we can write simple mathematical equation. 44 00:04:54,050 --> 00:05:01,610 F is equal to M A is the rate of change of velocity DB with respect. 45 00:05:02,510 --> 00:05:07,010 So there is time in our equation, velocity in our equation. 46 00:05:07,010 --> 00:05:09,880 That means speed and forces. 47 00:05:09,930 --> 00:05:12,140 There is no equation. 48 00:05:12,150 --> 00:05:17,720 So this is the simplest way to represent the vehicle in the dynamic equation. 49 00:05:18,740 --> 00:05:24,350 What other kinds of force that will opposed the applied force? 50 00:05:24,700 --> 00:05:32,510 So depending upon the velocity, the aerodynamic drag force will oppose the vehicle depending upon the 51 00:05:32,510 --> 00:05:38,540 shape of the vehicle and the environment condition that miss. 52 00:05:40,920 --> 00:05:49,700 And density and all, so F.P. is also opposing force, it's called their aerodynamic drag force, which 53 00:05:50,050 --> 00:05:51,350 produces the braking effect. 54 00:05:51,680 --> 00:05:56,480 As with the higher speed, the opposing force will be higher. 55 00:05:57,490 --> 00:06:07,510 So we can take pressure, Applied Force F is equal to M plus F, B, if we can is excerpting Inclan, 56 00:06:07,840 --> 00:06:15,570 then they additional force component of gravitational force will also be opposed to applied force. 57 00:06:16,420 --> 00:06:18,100 So let us understand. 58 00:06:20,260 --> 00:06:21,670 The mathematical equation. 59 00:06:23,650 --> 00:06:31,060 Considering the two will have the vehicle, front wheel and real will, so it will remain same for the 60 00:06:31,060 --> 00:06:32,860 two wheeler as well as four wheeler. 61 00:06:33,130 --> 00:06:42,080 Ideally, we can consider either forces applied to one wheel or we can cut the total supply to combiner. 62 00:06:43,450 --> 00:06:51,220 What will front, as well as if the four wheel drive are considering the case of electric back to will 63 00:06:51,220 --> 00:06:59,260 drive, then run or produce a tranquil platform for produce it would need to consider. 64 00:06:59,680 --> 00:07:10,000 Yet for the simplicity we consider only rear wheel drive and consider this force f x at is produced. 65 00:07:11,820 --> 00:07:20,570 The electric motor, and this is it will drive the vehicle, the incline angle with the horizontal surfaces, 66 00:07:20,580 --> 00:07:24,480 the with yet Yaris, the city of we. 67 00:07:24,750 --> 00:07:32,970 So if we can see if this is perpendicular line to the incline angle and vehicle is moving along with 68 00:07:32,970 --> 00:07:35,410 this that along with this angle. 69 00:07:35,910 --> 00:07:37,580 So this is 90 degrees. 70 00:07:38,130 --> 00:07:46,710 And if we do the 90 degree to the horizontal surface, then this angle will also become a bit that this 71 00:07:46,710 --> 00:07:49,350 is 90 degrees with this and this is 90 degrees. 72 00:07:50,690 --> 00:07:52,810 This angle will become better. 73 00:07:53,460 --> 00:07:54,540 So if we consider. 74 00:07:55,670 --> 00:08:01,190 This component, because we are applying force in this direction, so vehicle will move in this direction 75 00:08:01,190 --> 00:08:04,770 and we lost direction of velocity will be this direction. 76 00:08:05,270 --> 00:08:08,240 So this component will be. 77 00:08:11,080 --> 00:08:17,470 M.G. Sine Theta and this component from this photo. 78 00:08:17,680 --> 00:08:25,350 This is M.G. Course Beta, so M.G. signed beta and energy costs beta. 79 00:08:25,630 --> 00:08:32,970 So this opposing force to their platforms will be M.G. Costs Vita. 80 00:08:34,150 --> 00:08:38,520 Represent the drag force opposing the applying platform. 81 00:08:38,570 --> 00:08:39,870 It opens their platforms. 82 00:08:40,420 --> 00:08:44,550 And this is the third component is also the directional Wakka. 83 00:08:44,620 --> 00:08:47,580 This forces em into a debate. 84 00:08:47,710 --> 00:08:49,170 Did we exist? 85 00:08:49,190 --> 00:08:50,360 The relativity? 86 00:08:53,860 --> 00:09:02,470 They feel that they question the total force f x if both the force mudhole, having the electric motor 87 00:09:02,830 --> 00:09:12,190 then is equal to effects and plus F plus, we consider that the Yarraville that they add is equal to 88 00:09:12,190 --> 00:09:24,010 M, maybe less F less M.G. sine with this all three component of the Applied Force or for their love 89 00:09:24,430 --> 00:09:25,630 and the V. 90 00:09:28,350 --> 00:09:37,490 Now, F.P. is the aerodynamic force, and it is equal to proportional to the square of the velocity, 91 00:09:37,810 --> 00:09:46,740 so as well as it is high, the opposing force will be more the equation that from which f the amount 92 00:09:46,740 --> 00:09:48,470 of meat can be calculated. 93 00:09:48,630 --> 00:09:51,740 One silly is the constant InterOil. 94 00:09:51,750 --> 00:09:58,000 The constant is the constant in Tahrir Square in the sign of V X. 95 00:09:59,490 --> 00:10:02,070 Now you need to understand this. 96 00:10:02,070 --> 00:10:06,530 In many books the FDA is given X minus one by two. 97 00:10:07,080 --> 00:10:13,590 It is the regulation into rule that add density into. 98 00:10:15,030 --> 00:10:21,030 The frontal area of the vehicle and velocity square. 99 00:10:22,380 --> 00:10:23,100 Because. 100 00:10:25,100 --> 00:10:26,780 If you consider this false. 101 00:10:27,870 --> 00:10:35,670 To represent that it is negative force, which, compared to velocity and with the direction of velocity, 102 00:10:35,970 --> 00:10:37,200 is for this negative. 103 00:10:37,440 --> 00:10:42,240 Then also you need to change the SIGNIOR and you need to write the minus Everleigh. 104 00:10:42,510 --> 00:10:46,930 But it will create the confusion in understanding this equation to simplify this. 105 00:10:46,950 --> 00:10:54,320 It is better to write your Safdie the same design with plus because all three are opposing force. 106 00:10:54,900 --> 00:11:00,980 So we need to consider the velocity because velocity and the force can have the difference. 107 00:11:01,020 --> 00:11:07,260 And this velocity we consider is the positive and this sine will reflect it. 108 00:11:07,290 --> 00:11:07,680 Yes. 109 00:11:07,980 --> 00:11:16,320 Why we required this sign of the velocity because the FDA direction of body will depend upon the direction 110 00:11:16,320 --> 00:11:18,390 of velocity, velocity, change. 111 00:11:18,390 --> 00:11:25,820 If vehicle is moving in the right direction, then this force will be changed that direction. 112 00:11:25,830 --> 00:11:34,020 So this will be always, always opposing to the direction of well, of the vehicle so that if we use 113 00:11:34,020 --> 00:11:37,710 only square, then the sine will never come here. 114 00:11:37,710 --> 00:11:40,350 And it always remains the positive. 115 00:11:40,860 --> 00:11:41,130 Right. 116 00:11:41,640 --> 00:11:47,870 So we require the sign-off velocity also so we can have the same function. 117 00:11:48,150 --> 00:11:57,270 It will give only the sign that it's either minus one or plus one, depending upon the sign of the velocity. 118 00:11:57,280 --> 00:12:01,110 It can be accomplished by the different simulation tool also. 119 00:12:01,320 --> 00:12:03,830 But this is only the sign of velocity. 120 00:12:03,840 --> 00:12:06,570 If it is positive, it will be plus one. 121 00:12:08,250 --> 00:12:14,940 That means multiplying by one and if it is in the other direction, then it will be multiplied minus 122 00:12:15,090 --> 00:12:19,590 one so that we will have the sign of that. 123 00:12:19,590 --> 00:12:24,480 They depend upon the relative else because of Square, it will always remain. 124 00:12:25,290 --> 00:12:28,350 So this is why we are having the same function. 125 00:12:28,350 --> 00:12:32,910 Same velocity is used in the equation. 126 00:12:34,590 --> 00:12:36,360 Now to build the simulation. 127 00:12:36,720 --> 00:12:47,180 We can simplify this equation in this form and we today we may need the equal to F into F add that is 128 00:12:47,580 --> 00:12:54,780 force produce and the Yarraville to the motor minus F minus the same B. 129 00:12:58,470 --> 00:13:02,760 So we will also discuss about the Matlab simulation. 130 00:13:02,760 --> 00:13:04,470 With the help of Matlab simulation. 131 00:13:04,710 --> 00:13:10,140 We will build this model when we can discuss Imada. 132 00:13:10,830 --> 00:13:19,800 During that simulation, we will discuss about the different values and components of the rule and but 133 00:13:19,800 --> 00:13:24,210 let's observe the parameters. 134 00:13:24,210 --> 00:13:31,190 And Mr Marcinkiewicz is the horizontal distance of the stage from front axis in meter. 135 00:13:31,710 --> 00:13:38,400 That means from the center of the country to the C.G., this is the center. 136 00:13:38,770 --> 00:13:43,220 The the the area will be currently in our equation. 137 00:13:43,320 --> 00:13:52,710 This parameters are not required at the height of CGA from the ground, but it is required in designing 138 00:13:52,950 --> 00:13:54,210 and analysis. 139 00:13:54,490 --> 00:13:56,490 Analyze the performance of the vehicle. 140 00:13:56,700 --> 00:13:57,780 We will see that later. 141 00:13:58,250 --> 00:14:01,260 A different area in Meter Square. 142 00:14:01,680 --> 00:14:05,760 So we will discuss this, a city and role in the simulation. 143 00:14:05,760 --> 00:14:12,510 When we do the simulation and we see the typical value of a role for the different case. 144 00:14:13,200 --> 00:14:14,280 Frontalot in meters. 145 00:14:14,310 --> 00:14:15,960 Kwanten is the decoction. 146 00:14:16,560 --> 00:14:20,220 We access the longitudinal relativity of a vehicle in Metropol. 147 00:14:20,220 --> 00:14:27,030 Second row is the mass density ahead in Kaiji parameter to FDA. 148 00:14:27,030 --> 00:14:34,620 As we discussed the aerodynamic drag force and this is the Farishta Applied Force and the Rundquist 149 00:14:34,620 --> 00:14:37,880 and therefore is the applied force at the table. 150 00:14:38,370 --> 00:14:46,410 And Adeste, that Eleazar will say if we want to transport the thought and calculate it into force multiplier 151 00:14:46,410 --> 00:14:47,670 by various. 152 00:14:49,470 --> 00:14:57,630 So ultimately this simple mathematical equation F is equal to maybe by DETI plus F.T. Plus M designed 153 00:14:57,870 --> 00:15:05,430 to represent the vehicle in the dynamic. 154 00:15:06,230 --> 00:15:12,270 So the dynamic equation Boutet presenta any vehicle. 155 00:15:14,100 --> 00:15:18,930 This force can be generated by changing our motor or by any way. 156 00:15:19,320 --> 00:15:25,110 But the mathematical equation, dynamic equation of a vehicle will remain c.