23.03.2023 - 10:40

# Draw a block diagram for the following set of state variable equations x’ = -4x + 6y + 2u(t) , y’ = -2x -3y

Question:

Draw a block diagram for the following set of state variable equations x’ = -4x + 6y + 2u(t) , y’ = -2x -3y

• April 2, 2023 в 16:53

A block diagram is a visual representation of a system that shows its components and the relationships between them. In the context of state variable equations, a block diagram shows the interconnection between the system's inputs, outputs, and states.

For the given set of state variable equations, the block diagram would have two blocks representing the state variables x and y, respectively. The first block representing x would have two inputs: the input u(t) and the output y from the second block representing y. The output of the first block would be -4x + 6y + 2u(t), which corresponds to the derivative of x, x'.

The second block representing y would have two inputs: the output x from the first block and the output y from the same block. The output of the second block would be -2x - 3y, which corresponds to the derivative of y, y'.

The resulting block diagram would look like this:

lua            +-------+     +-------+
u(t) |       |     |       |
+------>|       |---->|       |
|       |  x'   |     |  y'   |
|       |       |<----|       |
|       +-------+     +-------+
|          ^             ^
|          |             |
|        +---+         +---+
+--------|   |<--------|   |
| x |         | y |
|   |         |   |
+---+         +---+


Here, the arrows represent the flow of signals, and the boxes represent the state variables x and y, respectively. The input u(t) is shown as an arrow entering the x block, and the outputs x' and y' are shown as arrows leaving the x and y blocks, respectively. The interconnection between the x and y blocks is represented by arrows connecting the outputs of one block to the inputs of the other block.

Overall, this block diagram shows how the inputs, outputs, and state variables are related in the given set of state variable equations.