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 peak due to the underdamped pole is clearly shown.The time response represents how the state of a dynamic system changes in time when subjected to a particular input. The program show this with a simple circle showing the (and zeros) present a difficulty because they cause a peak (dip) in the Pole this is an example when it might be convenient not to show the asymptotic Previous graph, the phase of the asymptotic plot obscured that of the real With the asymptotic plot of the complete transfer function. The plot modified to have thicker lines, a grid, phase in radians and Likewise included or excluded by simply clicking on it. For example, the zero at the origin can be excluded simply by clicking on it in the lower left hand box.Īt the origin is no longer included in the plot. The function displayed can be manipulated term by term to illustrate the effect of each term. Also in the upper left is a "Help" tab.Īlso shown in the upper right hand corner is the transfer function, H(s).A 'Legend' box that shows elements displayed in the plot.Ĭheck-boxes that allow the user to display how the plots are.This box is empty in this display because the diagram displays all three elements of the transfer function. A box that shows elements excluded from the plot.The legend identifying individual terms on the plot.Sometimes it gets in the way of seeing the other plots, so you may Particular there is a check-box that determines whether or not toĭisplay the asymptotic plot for the complete transfer function Several checkboxes that let the user format the image.A list of the systems in the user workspace.The magnitude plot, both the piecewise linear approximation for all three terms as well as theĪsymptotic plot for the complete transfer function and the exact Bode diagram for magnitude.The following MATLAB® commands begin execution of the GUI: >MySys=tf(1000*,) %define Xfer function This function has three terms to be considered when constructing a Bode diagram, a constant (100), a pole at ω=10 While MATLAB is extremely powerful, it is also very expensive. I have stopped working on BodePlotGui and have developed a similar tool in JavaScript to make it more accessible (see the "Drawing Tool" tab, above). Save it, and then rerun the BodePlotGui.m file. You can edit the size and layout of the GUI for your machine. If you have this problem, simply run the MATLAB command " guide" and open the file BodePlotGui.fig. Note: the MATLAB GUI doesn't display well on all devices (some elements of the GUI may not show up). Is hoped that the BodePlotGui program will be a versatile program for teaching and learning the construction of Bode diagrams from piecewise linear approximations. Takes a transfer function and splits it into its constituent elements, thenĭraws the piecewise linear asymptotic approximation for each element. Graphical user interface written in the MATLAB® programming language. BodePlotGui: A Tool for Generating Asymptotic Bode Diagrams
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