System Control Query - Find y(t) from Y(s)

Thread starter DrMath
Start date Nov 7, 2009
Tags

Control System

In summary, the System Control Query is a mathematical tool used in control systems engineering to find the output response, y(t), of a system from its input response, Y(s), in the Laplace domain. This is done by using the inverse Laplace transform and the partial fraction expansion method. To use the System Control Query, the transfer function of the system and the input signal must be known. However, it may not be suitable for complex or higher-order systems.

Nov 7, 2009

DrMath

Dear PF Friends,

Given the system to be controlled.
I'm stuck in finding the inverse laplace (to find y(t) from Y(S)) - any advice?

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Nov 17, 2009

matematikawan

Must forgive me if it not correct. I'm trying

[tex]Y(s)=\frac{1}{s} ( \frac{k}{s(s+1)+k}) = \frac{1}{s} ( \frac{k}{(s+1/2)^2+ (k-1/4)})[/tex]

Invert
[tex]y(t)=\frac{k}{\sqrt{k-1/4}} \int_0^t e^{-t/2} \sin{(\sqrt{k-1/4})t } dt[/tex]

1. What is the purpose of using the System Control Query for finding y(t) from Y(s)?

The System Control Query is a mathematical tool used in control systems engineering to find the output response, y(t), of a system from its input response, Y(s), in the Laplace domain. This allows for the analysis and design of control systems to be done in the frequency domain, making it easier to analyze and improve system performance.

2. How is the System Control Query used to find y(t) from Y(s)?

The System Control Query uses the inverse Laplace transform to convert the input response, Y(s), from the Laplace domain to the time domain, giving the output response, y(t). This is done using the partial fraction expansion method to decompose the transfer function into simpler terms that can be easily converted using standard Laplace transform tables.

3. What information is needed to use the System Control Query for finding y(t) from Y(s)?

In order to use the System Control Query, the transfer function of the system must be known. This can be obtained through system identification techniques or by modeling the system's dynamics using physical laws and principles. Additionally, the input signal, u(t), must be known or can be assumed to be a standard signal such as a step, ramp, or sinusoid.

4. Are there any limitations of using the System Control Query for finding y(t) from Y(s)?

One limitation of using the System Control Query is that it assumes the system is linear and time-invariant. This means that the system's output response is directly proportional to the input response and does not change over time. Additionally, the method may become complicated for systems with complex transfer functions or multiple inputs and outputs.

5. Can the System Control Query be used for any type of control system?

Yes, the System Control Query can be used for any type of control system as long as the system dynamics can be modeled by a transfer function. This includes mechanical, electrical, and chemical systems. However, the method may be more suitable for systems with first- or second-order transfer functions rather than higher-order systems, as it may become more complex and time-consuming.