1 00:00:00,580 --> 00:00:01,400 ‫Welcome back. 2 00:00:02,160 --> 00:00:10,990 ‫So now you know how to go from your non-linear state based equations to your LPI form, and once you 3 00:00:11,140 --> 00:00:18,940 ‫have your Lopevi, A, B, C and D matrices, then you discreetness them exactly as it was done in the 4 00:00:18,940 --> 00:00:19,840 ‫previous course. 5 00:00:20,200 --> 00:00:30,250 ‫This with a equals the identity matrix plus continues a times sample time interval. 6 00:00:31,120 --> 00:00:41,500 ‫This could be equals continuous B times sample time interval and then discrete C equals continuous C 7 00:00:41,500 --> 00:00:45,790 ‫and discrete the equals continuous D. 8 00:00:46,600 --> 00:00:54,130 ‫And then what happens next has the exact same procedure, like in the previous course you have your 9 00:00:54,130 --> 00:00:56,750 ‫discrete equations in this form. 10 00:00:57,520 --> 00:01:02,310 ‫And so this is a screenshot from the autonomous vehicle course. 11 00:01:03,100 --> 00:01:08,530 ‫And just like in the previous course, this matrix, the D equals zero. 12 00:01:08,540 --> 00:01:12,000 ‫So this entire term here, it will become zero. 13 00:01:13,030 --> 00:01:26,050 ‫Also, from now on, we will call our A, B, C, D and matrices simply A, B, C and D, simply because 14 00:01:26,050 --> 00:01:28,270 ‫it's annoying to write the D all the time. 15 00:01:28,810 --> 00:01:36,820 ‫But when I say A, B, C and D, then now you know that they are discrete matrices, not continuous 16 00:01:36,820 --> 00:01:40,090 ‫matrices unless I specify otherwise. 17 00:01:40,840 --> 00:01:43,030 ‫Unlike in the previous course though. 18 00:01:43,570 --> 00:01:53,830 ‫Now your state vector is this one here with these six variables and your control input is now a vector, 19 00:01:54,070 --> 00:01:55,210 ‫not a scalar. 20 00:01:55,780 --> 00:02:01,230 ‫In the previous course, your control input was Delta K, right? 21 00:02:01,990 --> 00:02:06,340 ‫So that was your control input here, your steering wheel angle at K. 22 00:02:07,180 --> 00:02:16,270 ‫However, now you have three control inputs that the NPC needs to find you to subquery use three subquery 23 00:02:16,630 --> 00:02:23,920 ‫and U for some K and transposed in the autonomous vehicle case. 24 00:02:24,160 --> 00:02:35,980 ‫You had four states, you had Y that then BPCI beside that and then the inertial Y and then out of those 25 00:02:35,980 --> 00:02:43,150 ‫four states you had two outputs and of course one control input. 26 00:02:43,990 --> 00:02:49,720 ‫Therefore the A matrix, there was a four by four matrix. 27 00:02:50,380 --> 00:03:00,190 ‫It looked like this four by four, then your B matrix was four by one because you have four states and 28 00:03:00,190 --> 00:03:02,410 ‫then one control input. 29 00:03:02,980 --> 00:03:09,070 ‫Then the C matrix was two by four because you have two outputs in four states. 30 00:03:09,430 --> 00:03:15,630 ‫And then finally your matrix was a two by one zero matrix. 31 00:03:15,670 --> 00:03:16,210 ‫All right. 32 00:03:16,510 --> 00:03:20,890 ‫Because you have two outputs and one control input. 33 00:03:21,250 --> 00:03:28,120 ‫But since there is no contribution from that controller input, then this the matrix is a zero matrix. 34 00:03:28,480 --> 00:03:37,510 ‫But now in the other case, you have six states and six time derivatives of your states and three control 35 00:03:37,510 --> 00:03:41,310 ‫inputs and also three outputs. 36 00:03:41,860 --> 00:03:46,820 ‫So these ones here, they will be your outputs as well. 37 00:03:47,260 --> 00:03:56,600 ‫So now you're a matrix will be a six by six matrix because you have six states and then six time derivatives 38 00:03:56,620 --> 00:03:57,580 ‫of your states. 39 00:03:58,120 --> 00:04:07,390 ‫Then your B matrix is a six by three matrix because you have six time derivatives of your states and 40 00:04:07,690 --> 00:04:09,220 ‫three control inputs. 41 00:04:09,670 --> 00:04:17,440 ‫Then your C matrix is three by six because you have three outputs and six states. 42 00:04:18,040 --> 00:04:25,840 ‫And finally your matrix is a three by three zero matrix because you have three outputs and three control 43 00:04:25,840 --> 00:04:29,950 ‫inputs, but you have no contribution from your control inputs.