201305.pdf 43279KB May 08 2013 11:07:04 PM

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MECHATRONICSIN DESIGNFRESH IDEAS ON INTEGRATINGMECHANICAL SYSTEMS,ELECTRONICS, CONTROL SYSTEMS,AND SOFTWARE IN DESIGNM ASA LR IT ED EF EN SE SP R O CE SS IY SN GSoftwareT E M SA UT O M ODigital ControlSystemsMechanicalCADC ON ST IControlSystemsMechanicalSystemsU MV EE RPAE R O SmechatronicsControlElectronicsElectromechanicsR O D UP ASC TC EM E D IElectronicSystemsM AF AN UC ALC TU RX ER OGI NG RA PH YFrequency response:the gold standardEngineers predict real-world response and identify model parameters.By Kevin C Craig, PhDWhat do engineers “see” when they look at a real systemor conceive a new design? They will look pastthe hardware and visualize the flow of energy, whereit is stored, and where it is dissipated. They will identify thekinetic energy of moving fluids and solid masses; the potentialenergy of compressible fluids, elastic hoses and tanks, anddeformable solids; the energy stored in electric and magneticfields; and the energy lost through friction generating heat.But they will also “see” how the system might respond to realworldinputs by understanding the frequency response of thesystem and the frequency spectrum of the probable inputs.A real system often can be modeled, over some range ofmotion and time duration, as stable, linear, and time invariant.If the input to this system is a sine wave, the steady-stateoutput (after the transients have died out) is also a sine wavewith the same frequency, but with an amplitude and phaseangle that are both frequency dependent. Plots of the inputoutputamplitude ratio versus frequency and the phase angleversus frequency are called Bode plots.If the system being excited were nonlinear or time varying,the output might contain frequencies other than the inputfrequency, and the amplituderatio might be dependent onthe input magnitude. Anyreal-world device or processwill need to function properlyfor only a certain range of frequencies;outside this range,we don’t care what happens.When one has the frequencyresponsecurves for any system and is given a specific sinusoidalinput, it is easy to calculate the sinusoidal output.What is not obvious, but extremely important, is that thefrequency-response curves are really a complete descriptionof the system’s dynamic behavior and allow one to computethe response for any input, not just sine waves.Two hundred years ago, Jean Baptiste Fourier showed thatany periodic waveform that exists in nature can be generatedby adding up sine waves. By picking the amplitudes, frequencies,and phases of these sine waves, one can generate awaveform identical to the desired signal. A periodic function,q i(t), can be represented by an infinite series of terms calleda Fourier series. Figure 1 shows a square wave and a plot ofthe first few terms of the Fourier series. The more terms usedin the series, the better the fit.Using the principle of superposition for linear systems, wecan combine the frequency spectrum of a real-world signalwith the system’s frequency response and calculate the timeresponse. A dynamic signal analyzer is the device used toexperimentally determine a system’s frequency response.Many excellent application notes on its use are available.EDNq i(t)(a)−0.011.5−0.5+0.01Figure 1 A periodic function, q i(t), can be represented by an infiniteseries of terms called a Fourier series; shown are a squarewave (a) and a plot of the first few terms of the Fourier series (b).tAMPLITUDE(b)21.510.50−0.5−1−0.01 −0.006 −0.002 0.002 0.006 0.01−0.008 −0.004 0 0.004 0.008TIME (SEC)24 EDN | MAY 2013[ www.edn.com]
CST STUDIO SUITE 2013Make the Connection…CST STUDIO SUITE 2012Discover what happens…Find the simple way throughcomplex EM systemsComponents don’t exist in electromagnetic isolation. They influence their neighbors’performance. They are affected by the enclosure or structure around them.They are susceptible to outside influences. With System Assembly and Modeling,CST STUDIO SUITE helps optimize component and system performance.Get the big picture of what’s really going on. Ensure your product and componentsperform in the toughest of environments.www.cst.com/pcbChoose CST STUDIO SUITE –Complete Technology for 3D EM.CST – COMPUTER CST of America®, SIMULATION Inc. | To TECHNOLOGY request literature | www.cst.com (508) 665 4400 | info@cst.com| www.cst.com
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