Trouble understanding block diagrams


by cyph1e
Tags: block, diagrams, trouble
cyph1e
cyph1e is offline
#1
Sep12-07, 02:41 PM
P: 2
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.



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

Edit: corrected LaTeX code.
Phys.Org News Partner Science news on Phys.org
Going nuts? Turkey looks to pistachios to heat new eco-city
Space-tested fluid flow concept advances infectious disease diagnoses
SpaceX launches supplies to space station (Update)

Register to reply

Related Discussions
Understanding PV Diagrams - Work Introductory Physics Homework 1
Problem understanding circuit diagrams Introductory Physics Homework 3
Trouble understanding!! Calculus 3
Signal block diagrams Electrical Engineering 1
Having trouble understanding this. Classical Physics 7