Chapter 6 frequency response, bode plots, and resonance. The nyquist plot combines gain and phase into one plot in the complex plane. Plot the bode plot with matlab assume that you wanted to use matlab in order to obtain bode magnitude and phase plots for the. If a transfer function is given and we need to plot frequency response and magnitude response and the. A linear system has a transfer function of determine the poles and zeros of the transfer function plot the poles and zeros in the splane. Webb engr 202 a measured signal has the frequency spectrum shown here. The most classical example is that of a body with mass m to which a spring with a.
Whereas, yaxis represents the magnitude linear scale of open loop transfer function in the magnitude plot and the phase angle linear scale of the open loop transfer function in the phase plot. Transfer functions with multiple simple poles and zeroes suppose we have a transfer function with more than one pole or zero, or a combination of simple poles and zeroes. Classical control systems welcome to the gmu ece department. Few gotchas m and m are interpreted the same by spice. It is a standard format, so using that format facilitates communication between engineers. Clearly, the closedloop poles are locat ed at s 2 and s 5, and the system is not oscillatory. The bode plot for a linear, timeinvariant system with transfer function being the complex frequency in the laplace domain consists of a magnitude plot and a phase plot. The plot displays the magnitude in db and phase in degrees of the system response as a function of frequency. The unitstep response, however, ex hibits overshoot due to the presence of a zero at s 1. Assuming the larger signal component has an amplitude of 500 mv, and that both signal components are in phase, write a time domain expression for the. Design example using bode plot insight suppose you want to build a treble booster for an electric guitar. The magnitude of frequency response of an under damped second order system is 5 at 0 radsec and peaks to 10v3 at 5v2 radsec. Find materials for this course in the pages linked along the left. Craig the term for n 1 is called the fundamental or first harmonic and always has the same frequency as the repetition rate of the original periodic wave form 50 hz in this example.
Needing a crash course in transfer functions, bode plots. Phase in bode plots the transfer function hs is a phasor. We used further insight into opamps to realize that we could fix the. For the transfer function given, sketch the bode log magnitude diagram which shows how the log magnitude of the system is affected by changing input frequency. This work has been released into the public domain by its author, i, mik81. I, mik81 grants anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law. A system has a transfer function with no zeros, a single pole at s 6, and a dc gain of 9. This is done by calculating the vertical distance between the phase curve on the bode phase plot and the xaxis at the frequency where the bode magnitude plot 0 db. Several examples of the construction of bode plots are included in this file. Bode plots page 1 bode plots a bode plot is a standard format for plotting frequency response of lti systems. In both the plots, xaxis represents angular frequency logarithmic scale.
The bode plot of a transfer function gs is shown in the figure below. Gain cross over frequency and phase cross over frequency. It is based on the complex analysis result known as cauchys principle of argument. Rules for drawing bode diagrams swarthmore college. Bode plots by matlab here is an example of doing bode plots with matlab. I highly recommend it and you can pick up an international version on amazon for pretty cheap. It is drawn by plotting the complex gain giw for all frequencies w.
Expressing magnitudes in decibels actual magnitude magnitude in db 12 6db b d 10 b d 26 5 102 20 db 6 db 14 db 10 20db 103 3. That is, the plot is a curve in the plane parametrized by example 3. We say that, in a bode plot, there is a drop in gain of 20 db per decade whenever a pole is encountered. Identify break points and put in ascending order 6. Bode plots bode magnitude and phase plots topic wise questions in control systems from 1987 2003 1. The approximate bode magnitude plot of a minimum phase system is shown in figure. Control systems construction of bode plots tutorialspoint. This is something that is very useful when working with experimental data. This is also available as a word document or pdf the table assumes. We can usually read the phase margin directly from the bode plot as shown in the diagram above. After you download this file, you must unzip it to regenerate the. Poles, zeros, and bode plots in analyzing the frequency response of an amplifier, most of the work involves finding the amplifier voltage gain as a function of the complex frequency s. Review of bode plots decibels g db 20log 10 g table 8.
Bode plot, gain margin and phase margin plus diagram. The bode angle plot always starts off at 00 for a second order system, crosses at 90 and asymptotically approaches 1800. Solved problems on transfer functions, poleszeroesbode plots problem 1. Since i have not done much real life engineering work with bode plot, can someone please show me an example of a bode plot of a real system that actually provides some more interesting insights. Becoming familiar with this format is useful because. Chapter 6 frequency response, bode plots, and resonance 3. The table below summarizes what to do for each type of term in a bode plot. Lots of worked examples and theres a widely circulated solution manual for the end of chapter problems. The bode plot or the bode diagram consists of two plots. Bode plot of frequency response, or magnitude and phase.
Computer modeling of electronic circuits with ltspice. Nyquist stability criterion a stability test for time invariant linear systems can also be derived in the frequency domain. Computer modeling of electronic circuits with ltspice phys3360aep3630 lecture 2021. Obtain the phasor for each output component by multiplying the phasor for each input component by the corresponding transferfunction value. Convert the phasors for the output components into time functions of various frequencies. In some countries this may not be legally possible. A bode plot is a graph of the magnitude in db or phase of the transfer. This is the example i gave in point 1 above, where the straight line approximation. We discovered two problems that we needed to fix 5. Many common system behaviors produce simple shapes e. Transfer functions and bode plots transfer functions for sinusoidal time variations, the input voltage to a.
Department of mechanical engineering massachusetts institute of technology 2. Some useful matlab commands for control systems 65 kb. Bode plots for 2nd order systems mercer university. What does the frequency response of the lag compensator alonelook like. For a rational function hs we add the phases from the. So, we can draw the bode plot in semi log sheet using the rules mentioned earlier. This point is known as the gain crossover frequency. Pdf control systems problems in bode plot devasena a. Bode plots bode magnitude and phase plots topic wise. In this sdomain analysis, a capacitance c is replaced by an admittance sc, or equivalently an impedance 1sc, and an inductance l is replaced by an impedance sl. Consider a system whose closedloop transfer functmn is this is the same system considered in problem a68. I have three questions that have been troubling me for a long while. The asymptotic bode plot of a transfer function is as shown in figure. Needing a crash course in transfer functions, bode plots, and nyquist.
Example h s s a 10 pole at s 1 zero at s 100 1 100 20 db 0 db 40 db 1 hs 10 1. Lightly damped systems the lower the c, the sharper the peak on the magnitude plot and. Department of mechanical engineering massachusetts. The bode plot is an example of analysis in the frequency domain. From the bode plots, we can say whether the control system is stable, marginally stable or unstable based on the values of these parameters. Click on the transfer function in the table below to jump to that example.
1461 1377 221 880 144 152 1364 792 242 1339 1328 548 1432 280 1563 782 408 1599 314 1372 1521 1335 1392 1481 1392 1126 323 1445 346 1399 1394 947 500 1358 1269 122 945 36 390 279 881 883