# Control systems

hi everyone,
I have recently started studying abvout control engineering, but am not getting a grasp on the basic idea behind controls. All the textbooks say that the output should track the input ideally , but why is it so? i.e if i give a step input to a system, the response should ideally be an step. i mean, say you characterise a system by G(s), and give input X(s). the output is Y(s). say i want a some desired output , why cant after knowing G(S) give an appropriate input X(S) so as to produce the desired output.

also what are you doing by taking the laplace transform? is the laplace transform similar to taking logarithms and solving multi/div problems by simply adding/ sub the logarithms? are there any limitations of laplace?

A control system works by the Idea of closed-loop feedback. So your control system is supposed to take a command signal (your input) and the output is supposed to reach that command signal at steady state. The controller will look at the output of the system, and modify the input signal based on this output, which is your closed-loop feedback.

why cant after knowing G(S) give an appropriate input X(S) so as to produce the desired output.
This is essentially what you're doing when you design your controller, and your controller is what takes the desired output (the system's input X(S) also referred to as the command signal) and filters it to compensate for the plant to make the real output equal to your desired output.

You take the laplace transform to represent the system in the frequency domain. This is just a special application of transfer functions you've probably used in circuit analysis or signals and systems. It basically tells you how a system's output behaves with regard to it's input, and shows this in the frequency spectrum, and you will learn how a lot of control parameters involving stability, steady state error, and response time are related between time domain and frequency domain. The reason the laplace domain is so easy is because convolution can now be done by simple multiplication, so you design a compensator transfer function that will be in series with your plant in a simple control system, and basically by multiplying your compensation transfer function by the plant transfer function, you can then get the type of output you want from different types of command signals. Usually your plant transfer function is already known, or you need to model it, which can be just as involved as the actual controller design.

Also, limitations of the laplace transform is that it is linear, continuous, and time invariant. If you've had signals and systems or some kind of DSP, then you probably have learned much of the basic principles already, they just are carried over into detail for controls, so don't let the different terminology used confuse you, you probably already understand it. You will see controls is very similar to DSP, and your transfer function controller and plant transfer function blocks are actually just filters.

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I'm not sure if this applies to control systems, but in some of my classes we used laplace transforms to redraw a circuit in the frequency domain, and solving it seemed easier than solving differential equations, and then we inverse laplaced it to transform it back into the time domain to see the initial response as a function of time.

I'm not sure if this applies to control systems, but in some of my classes we used laplace transforms to redraw a circuit in the frequency domain, and solving it seemed easier than solving differential equations, and then we inverse laplaced it to transform it back into the time domain to see the initial response as a function of time.

Yes it does apply, and its basically the same reason to do it in controls, but also so that you can get a lot of information about your system and controller quickly, and it is very easy to analyze the frequency domain rather than using differential equations in the time domain. You do use diff eq a lot in controls though, especially in state-space methods.