1 00:00:00,530 --> 00:00:01,310 ‫Welcome back. 2 00:00:01,910 --> 00:00:05,130 ‫So let's see how we can solve this exercise. 3 00:00:05,840 --> 00:00:15,080 ‫You want to put these equations that you have here, the simplified ones where you assumed that you're 4 00:00:15,080 --> 00:00:15,500 ‫fired. 5 00:00:15,500 --> 00:00:19,300 ‫Three triangles in the transfer matrix are zeroes. 6 00:00:19,880 --> 00:00:21,530 ‫So you take these equations. 7 00:00:22,570 --> 00:00:30,490 ‫And you want to put them in this form and it doesn't mean that you have an LPI system here, your matrixes 8 00:00:30,490 --> 00:00:32,320 ‫might end up being like this. 9 00:00:33,250 --> 00:00:36,250 ‫Let's first think about the state vector X. 10 00:00:37,030 --> 00:00:40,820 ‫The state vector contains all the states that the system has. 11 00:00:41,320 --> 00:00:48,820 ‫So what are the states in this simplified states based equation's version? 12 00:00:49,600 --> 00:00:53,260 ‫Well, you have five double dot equals something. 13 00:00:53,680 --> 00:00:57,910 ‫You have theta double that equals something and then you have citable. 14 00:00:57,910 --> 00:00:59,380 ‫That equals something. 15 00:01:00,300 --> 00:01:10,620 ‫And so from here, you can see that your fishable dot depends on Seeta dot and side that and also the 16 00:01:10,620 --> 00:01:21,270 ‫Omega, then your Theta double that depends on you find out and that and Omega and then PSI double. 17 00:01:21,270 --> 00:01:22,860 ‫That depends on that. 18 00:01:22,860 --> 00:01:23,880 ‫And see to that. 19 00:01:24,660 --> 00:01:29,310 ‫And of course, phi double dot, theta double dot and BPCI double that. 20 00:01:29,310 --> 00:01:34,090 ‫They also depend on you to Q3 and Q4 respectively. 21 00:01:35,040 --> 00:01:39,600 ‫Now you could count your Omega as a state as well. 22 00:01:40,080 --> 00:01:45,330 ‫However, in our case it's not necessary and you're going to see why. 23 00:01:46,200 --> 00:01:54,780 ‫The thing with states based equations is that remember your state's basic equations, they had your 24 00:01:54,780 --> 00:01:59,210 ‫states and then their first order derivatives. 25 00:02:00,060 --> 00:02:07,620 ‫So your first order derivatives are five double date, three to double that and double date and then 26 00:02:07,620 --> 00:02:11,910 ‫means that your states are Phi Dot, Theta dot. 27 00:02:12,150 --> 00:02:18,660 ‫And beside that, at this point, you don't have Omega Dot in your model. 28 00:02:19,500 --> 00:02:30,960 ‫However, remember that our output vector y must contain the variables Phi Theta and PSI right. 29 00:02:31,830 --> 00:02:41,610 ‫In order to compare them with fly our feet are Anasuya and in the previous course we learned then output's 30 00:02:41,610 --> 00:02:46,200 ‫in most cases are simply a set of selected states. 31 00:02:46,770 --> 00:02:52,740 ‫That means that also Phi Beta and PSI are your state's. 32 00:02:53,890 --> 00:03:03,820 ‫So your state vector looks like this, you have then you have fired that, then you have theta and theta 33 00:03:03,820 --> 00:03:07,750 ‫that, and then you have BPCI and then you have outside that. 34 00:03:07,990 --> 00:03:09,720 ‫And of course, it's a common vector. 35 00:03:10,660 --> 00:03:13,780 ‫It's a six by one vector. 36 00:03:14,740 --> 00:03:23,060 ‫And out of these six states that you have here, you choose three of them, you choose Phi Theta and 37 00:03:23,060 --> 00:03:26,480 ‫BPCI, you choose them as your outputs. 38 00:03:27,610 --> 00:03:34,580 ‫So right away, you know how this equation here looks like this is your output vector. 39 00:03:34,960 --> 00:03:41,470 ‫This is this Y and then this is your state vector. 40 00:03:42,280 --> 00:03:45,520 ‫Then this, of course, would be your C matrix. 41 00:03:46,640 --> 00:03:52,930 ‫This would be your control input vector and then, of course, this one would be your The Matrix. 42 00:03:53,900 --> 00:03:59,060 ‫And so in order to get this output vector here, your C matrix must be like this. 43 00:04:00,250 --> 00:04:11,110 ‫These ones here that you have in the C Matrix, they will extract your Phi Theta and PSI and of course 44 00:04:11,110 --> 00:04:12,710 ‫you don't need anything from here. 45 00:04:12,730 --> 00:04:15,350 ‫So this entire term here will be zero. 46 00:04:16,390 --> 00:04:19,560 ‫So you can just cancel it out altogether.