The zeros zj of G(s) do not affect the system stability. However, they do affect the amplitudes of the mode functions in the system response and can block the transmission of certain input signals. In general, to assess the Impact of the zeros on the amplitude of the mode functions, …

Read More »## System Stability Analysis using MATLAB

Poles and Stability If pi is a pole of G(s), then the natural, or zero-input, the response of G(s) will consist of the mode functions epit if pi is distinct, and tq epit, q = 0, 1,. . ., r – 1, if pi has multiplicity r. Thus the natural …

Read More »## Zero State Response using Matlab

Response to a General Input In addition to computing and plotting the impulse and step responses of a system, MATLAB can be used to ﬁnd and display the response to general functions of time. This is done with the lsim command, which can be used in a variety of ways. …

Read More »## Step Response using Matlab Transfer Function

Step Response The Laplace transform of a system’s unit step response is the product of the system’s transfer function G(s), and 1/s, the transform of the unit step function. The poles of the resulting transform are the poles of G(s) and a pole at s = 0 (due to the …

Read More »## Impulse Response due to Repeated Poles using Matlab Transfer Function

Time Response Due to Repeated Poles Up to this point the discussion has been restricted to distinct poles. Either real or complex. For a repeated pole there will be more than one term in the time response, with the number of terms depending on the multiplicity of the pole. For …

Read More »## Impulse Response due to Real and Complex Poles using Matlab Transfer Function

Time Response due to Distinct Poles In addition to computing the time response of the output, we can use MATLAB to evaluate and display the time response due to an individual real pole or to a pair of complex poles. Recall that a real pole at s = p with …

Read More »## Impulse Response using Matlab Transfer Function

How to Obtain an Impulse Response Once a transform (or transfer function) G(s) has been deﬁned in MATLAB, operations can be performed to compute and display the corresponding time function g(t), known as the inverse Laplace transform. If the poles are known, G(s) can be written as a partial-fraction expansion …

Read More »## Transfer Function Calculation Matlab with Example

Transfer Functions Representation Consider a ﬁxed single-input/single-output linear system with input u(t) and output y(t) given by the differential equation $\begin{matrix} \overset{..}{\mathop{y}}\,+6\overset{.}{\mathop{y}}\,+5y=4\overset{.}{\mathop{u}}\,+3u & \cdots & (1) \\\end{matrix}$ Applying the Laplace transform to both sides of (1) with zero initial conditions, we obtain the transfer function of the system from the …

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