Total marks 30 1 draw a dynamic diagram for the system...

Total Marks: 30 1. Draw a dynamic diagram for the system $$ \begin{bmatrix} \dot{x}_1 \\ \dot{x}_2 \end{bmatrix} = \begin{bmatrix} 1 & 2 \\ -2 & 1 \end{bmatrix} \begin{bmatrix} x_1 \\ x_2 \end{bmatrix} + \begin{bmatrix} 0 & 1 \\ -1 & 0 \end{bmatrix} \begin{bmatrix} u_1 \\ u_2 \end{bmatrix} $$ with output $$ y = \begin{bmatrix} 0 & 1 \end{bmatrix} \begin{bmatrix} x_1 \\ x_2 \end{bmatrix} $$

Transcript

00:01 In this question, we need to represent the dynamic system, okay, which is described by the following set of coupled linear ordinary differential equation, okay.

00:12 So, this is given as x1 dot minus 2 x1 minus 4 times of x2 is equals to 5 times of u, where x1 dot represent derivative with respect to t.

00:25 Similarly, we have x1 dot minus x2 dot plus 4 times of x1 plus x2 is equals to 0 and then we have y is equals to x1 dot minus x2 dot.

00:39 Let us see how we are going to solve this.

00:42 So, this i will write in the form of a state equation, a state equation form if i write down, it comes out to be equals to, here i will write down x1 dot x2 dot and so on till xn dot and this we write equals to, let's say the entries are a11, a12 and here we have an1, so it goes on till ann and here it is ann, okay.

01:17 So, this matrix times the variable which are x1, x2 so on up till xn plus the other matrix, let's say its entries are b11 up till b1n and so on and here also bn1, b2 goes up to bnn, then we have another variable, set of variable let's say u1, u2 up till un, okay.

01:45 So, this is the state equation form.

01:48 So, from this i write x dot is equals to ax plus b times of u, correct.

01:55 Now, we already have been given y is equals to cx plus d times of u and y is a set of output signal expressed in column vector form.

02:06 So, this is nothing but set of the output signals.

02:15 So, the differential equation of order 2, hence i write down in the differential equation of order 2 is x1 dot is equals to minus 2x1 plus 4x2 plus 5u, just rewriting the given equation, i call this as 1...

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