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What is the response of a system?
The response of a system (with all initial conditions equal to zero at t=0-, i.e., a zero state response) to the unit step input is called the unit step response. If the problem you are trying to solve also has initial conditions you need to include a zero input response in order to obtain the complete response.
What is the natural response of a system?
The natural response is what the circuit does including the initial conditions, but with the input suppressed. The total response is the sum of the forced response plus the natural response. These responses can be combined using the principle of superposition.
What is the steady state frequency response?
Steady state frequency response is a major design approach in control theory, and is normally used to obtain reasonable response to commands up to a chosen or obtainable bandwidth. It asks for zero error during the transient as well as steady state response phases.
How to find the zero state response of the transfer function?
Since multiplication in the Laplace domain is equivalent to convolution in the time domain, this means that we can find the zero state response by convolving the input function by the inverse Laplace Transform of the Transfer Function. In other words, if A discussion of the evaluation of the convolution is elsewhere.
How to write transient response from transfer function?
To demonstrate this we start from the transfer function, and then write the Laplace Domain form of the differential equation Set the input to zero, and then take the inverse Laplace Transform to find the original zero input form of the differential.
How to find the transfer function of a system?
For a dynamic system with an input u (t) and an output y (t), the transfer function H (s) is the ratio between the complex representation ( s variable) of the output Y (s) and input U (s). For a better understanding we are going to have a look at two example, two dynamic systems, for which we are going to find (determine) their transfer functions.
Is the response given by the transfer function identical?
The response given by the transfer function is identical with the response obtained by integrating the ordinary differential equation of the system. This gives confidence in the calculation method for the transfer function.