Trouble understanding block diagrams

In summary, a block diagram is a visual representation of a system or process that uses blocks and arrows to show the flow of information. They are commonly used in engineering, science, and technology to simplify complex systems, troubleshoot and design new systems. Block diagrams are read from left to right and top to bottom, with inputs on the left and outputs on the right. The advantages of using block diagrams include easier identification and understanding of components and their relationships, as well as the ability to spot errors and areas for improvement. However, they also have limitations such as oversimplifying systems, not accurately representing physical layouts, and not being suitable for all types of systems.
  • #1
cyph1e
2
0
Hello everyone!

I'm currently reading Signals, Systems and Transforms by Charles L Phillips, John Parr and Eve Riskin, and I can't really get a grip of how to read a specific block diagram.

The second-order differential equation

[tex]a_2 \frac{d^2y(t)}{dt^2}+a_1 \frac{dy(t)}{dt}+a_0 y(t)=b_2 \frac{d^2x(t)}{dt^2}+b_1 \frac{dx(t)}{dt}+b_0 x(t)[/tex]

is given. They integrate each side twice which yields

[tex]a_2y(t)+a_1y_{(-1)}(t)+a_0y_{(-2)}(t)=b_2x(t)+b_1x_{(-1)}(t)+b_0x_{(-2)}(t)[/tex]

where the notation [itex]y_{(k-n)}(t)[/itex] indicates the nth integral of the kth derivative of [itex]y(t)[/itex].

They present two types of block diagrams called "Direct Form I" and "Direct Form II", and I don't know if that is standard for these types of realizations. I understand "Direct Form I" perfectly well, but I'm really having some trouble understanding the second form as I can't really seem to follow the arrows, get a grip of where to start and derive an equation etc.

Here is the realization of the above equation using "Direct Form II", I'd be very glad if someone could walk me through how to read it.

http://www.photo-host.org/img/719732diagram.gif [Broken]

(The bottom diagram is a simplification of the top diagram with two integrators eliminated.)

Edit: corrected LaTeX code.
 
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  • #2



Hello there! As a scientist who has worked with block diagrams extensively, I understand how they can be confusing at first. Let me try to explain how to read the "Direct Form II" block diagram in the context of the given second-order differential equation.

First, let's understand the overall structure of the block diagram. The two integrators on the left represent the two integrals of the second derivative of y(t), while the two integrators on the right represent the two integrals of the second derivative of x(t). The arrows indicate the flow of information, with the input x(t) feeding into the first integrator on the right and the output y(t) being the final result on the left.

Now, let's focus on the individual blocks and their functions. The integrators essentially perform the integration operation on the input signal, with the output being the integral of the input. The summing junctions, represented by the circles with a plus sign, add the signals coming into them. The coefficients a0, a1, a2, b0, b1, and b2 are multiplied with the respective signals before being added at the summing junctions.

To read the diagram, start from the input x(t) and follow the arrows. The signal passes through the first integrator, then goes through the summing junction where it is multiplied by b0 and added to the integral of the second derivative of y(t). This sum is then multiplied by b1 and added to the integral of the first derivative of y(t). Finally, this sum is multiplied by b2 and added to the integral of y(t), giving us the output y(t).

I hope this explanation helps in understanding the "Direct Form II" block diagram. Keep in mind that there may be slight variations in notation and structure for different realizations, but the basic principles remain the same. Let me know if you have any further questions and I'll be happy to assist. Best of luck with your studies!
 

What is a block diagram?

A block diagram is a visual representation of a system or process using blocks to represent components and arrows to show the flow of information or signals between them.

Why are block diagrams used?

Block diagrams are commonly used in engineering, science, and technology to simplify complex systems and make them easier to understand. They can also be used for troubleshooting and designing new systems.

How do you read a block diagram?

Block diagrams are read from left to right and from top to bottom. The inputs are shown on the left and the outputs on the right. The flow of information or signals is shown by the direction of the arrows.

What are the advantages of using block diagrams?

Block diagrams allow for a visual representation of a system, making it easier to identify and understand the components and their relationships. They also make it easier to spot errors and identify areas for improvement.

What are the limitations of block diagrams?

Block diagrams can oversimplify a system and may not accurately represent the complexity of real-world systems. They also do not show the exact physical layout of components. Additionally, block diagrams may not be suitable for all types of systems, such as those with non-linear relationships.

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