Solve Cascade System: Find z(t) from x(t)=u(t)

  • Thread starter EvLer
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In summary, the student is trying to find the output signal of a 2-stage linear system by using the Laplace transform.
  • #1
EvLer
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Not even sure how to title this thread. I am saying honestly: we did not cover this in class but he gave us this in homework!
Two identical linear systems are connected in cascade. When the input signal to the first stage is x(t) the output signal from the first stage is y(t), the output of the second stage is z(t). If an input signal, tu(t) is applied to a single stage, the output signal of that stage is : [tex] (e^{-2t}-1)u(t)[/tex] find z(t) if x(t) = u(t).

u(t) is a step function, u(t) = 1 if t >=0, and 0 otherwise;

what i was thinking of doing is converting the e...-expression to frequency domain and also the tu(t) and then seeing how input is modified to get the output and apply the same thing to u(t) which is the input into cascaded system, but TA said that there's multiplication involved in s-domain. I am sort of clueless...
If someone could explain or direct to a source, that would be very much appreciated, 'coz my book does not these examples and i don't even know what to seach for on Google! :cry:
maybe i am not making a connection to something...the latest we covered was circuit analysis in frequency domain doing nodal analysis.
 
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  • #3
sorry, should have given more detail: i understand laplace transform.
What i don't understand is how to make use of the given info that input is one function and output signal is a different function and what to do in s-domain (laplace "world") to apply that to u(t) which is the input signal to the 2-stage linear system.
 
  • #4
EDIT: deleted my previous garbage...
EDIT: hold on...have another idea...would this work?:
[tex]H(s) = \frac{L(output)}{L(input)}[/tex]

then when i find this factor i will have to multiply my given L(input) by it in s-domain and take L-1 to get the time-domain signal...
would that work?
 
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1. What is a cascade system?

A cascade system is a control system that consists of multiple interconnected subsystems, in which the output of one subsystem serves as the input for the next subsystem. This allows for more complex control and greater flexibility in achieving the desired output.

2. How do you solve a cascade system?

To solve a cascade system, you must first determine the transfer functions for each subsystem. Then, using the principle of superposition, you can combine the transfer functions to find the overall transfer function for the entire system. Finally, you can use this overall transfer function to find the output of the system given an input.

3. What is z(t) and x(t) in a cascade system?

In a cascade system, z(t) represents the output of the system and x(t) represents the input. These variables can be any physical quantity, such as voltage, current, or position, depending on the specific system being analyzed.

4. What is u(t) in a cascade system?

U(t) is the input signal or control signal in a cascade system. It can be a steady-state signal or a time-varying signal that is used to control the output of the system. In most cases, u(t) is the input to the first subsystem in the cascade system.

5. Can a cascade system be used in real-world applications?

Yes, cascade systems are commonly used in real-world applications, particularly in control systems. They are often used in industries such as manufacturing, robotics, and aerospace to control complex systems and achieve desired outputs.

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