Since is a complex number, we can plot both its magnitude and phase (the Bode Plot) or its position in the complex plane (the Nyquist Diagram). If is the open-loop transfer function of a system and is the frequency vector, we then plot versus. (varying between zero or "DC" to infinity) and compute the value of the plant transfer function at those frequencies. The frequency response of a system can be found from its transfer function in the following way: create a vector of frequencies These magnitude and phase differences are a function of the frequency and comprise the frequency response of the system. Then the steady-state output will also be sinusoidal at the same frequency, but, in general, with different magnitude and LTI systems have the extremely important property that if the input to the system is sinusoidal, Of the governing differential equations, respectively.Īll the examples presented in this tutorial are modeled by linear constant coefficient differential equations and are thus These correspond to the homogenous (free or zero input) and the particular solutions The time response of a linear dynamic system consists of the sum of the transient response which depends on the initial conditions and the steady-state response which depends on the system input. MATLAB provides many useful resources for calculating time responses for many types of inputs, as we shall see in the following Nonlinear systems or those subject to complicated inputs, this integration must be carried out numerically. For some simple systems, a closed-form analytical solution may be available. Since the models we haveĭerived consist of differential equations, some integration must be performed in order to determine the time response of the The time response represents how the state of a dynamic system changes in time when subjected to a particular input.
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