Embedded Systems November 2000 Vol13_12

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SPECTRA e To tune a PI+ control, you need to choose the value of the low pass filter on the command input before tuning the integral. After that's done, its tuning is similar to the PI controller. be done, you wi ll probably need to reduce the proponiona l or de riva- tive gains. PID+ for your system. This will probably be less than 30%. A PI controller will always generate some overshoot. You do not have to retune the pro- portional gain after nming the inte- gral gain . Zone-based tuning is a popular and workable technique for separating out the control elements for tuning. For a discussion in greater detail than I am able to present here, consul t George Ellis's Control System Design Guide. At th is point we will neglect any changes in gai n regarding the plant (or motor). These are usually due to tem- perature or current and should be antic- ipated in the design of the system. Such changes, if they are large enough, can be compensated for with a technique known as gain scheduling. Thi requires changing the proportional gain on the fly. Its implementation depends on the controLler you are using. PI+ A control technique called PI+ helps reduce overshoot by putting a low pass filter in series with the command sig- nal. This tech inique allows the inte- gral gain to be set to a highe r value. It al o reduces the bandwidth of the command response by limiting the rate of change in the command signal. To nme a PI+ conu·ol, you need to choose the value of the low pass filter on th e command input before tun ing the integral. After that's clone, its tun- ing is similar to the PI conu·oll er. Obviously, s tting the turn-over fre- quency (3dB point) for this filte•· as high as possible will provide the great- est response and stiffness to the system. Differential The additi on of a differential gain can in crease sys tem respo nsiveness significan tl y, do ublin g it in some cases. It also introduces a phase lead of 90 degrees. A typi ca l di gital impleme ntatio n is: D =e[n] -e[n - l] II d/ This formula communicates one of the more significant problems of introducing derivative gain . As you can see, it represents a diffe rence between error samples. At higher fre- quencies that diffe rence can be large. The phase lead it contributes can improve low frequency response, but too high a gain can result in instabili ty at high frequencies. Noise can a lso cause a problem for de rivative terms, because the derivative amplifies it. Fo r that rea- son, a filte r following the de rivative is often a good idea. Take care, howev- er, not to set the turn-over frequency too low. If you do, you will lose the benefit of the derivative. Tuning the PID controller PID is also a two-zone control. To tune it, set the integral and derivative gain to zero and adjust the propor- tional gain . Allow for some overshoot, say 10%. Expect this overshoot to be ha ndled when yo u introduce the derivative gain . Next, raise the derivative gain until the overshoot is gone. Finally, increase the integral gain un til you have an overshoot acceptable to your system (maybe 10% to 15%). Probl ems h e re will pro bably come from no ise. If the no ise can- no t be eliminated at th e so urce, conside r raising th e resolution of the feedback sensor. If this cannot 24 NOVEMBER 2000 Embedded Systems Programming A PID+ controller is basically th e PID con troller from the las t section with the addition of a low pass filte• · on the command input. The tuning is the same as for the PlD controller, except that you need to choose the value of th e low pass filte r for th e command input before tuning the integral gain. PD A PD controller is the PID with the integral gain set to zero. Tune as with the PID controller; the problems will be th e ame. I hope these tips provide some help in this complex area. Of course, PID is not the only way to control mo ti on, as PvVM is not the only way to sou•·ce power to th e plant. These topics hold plen ty of material for future columns. Next month, we' ll examine some ways to use a digital signal processor to perform the fun ctions of resolve rs and sinusoidal converte rs for high- resolution encode rs. Don Morgan is smior engineer at Ultm Stereo Labs and a consultant with 25 years experience in signal processing, embedded systems, hardware, and soft- ware. Morgan recently cornfJleted a book about numeriral methods, featuTing multi-rate signal fnocessing and wavelets, called Numerical Methods for DSP Systems in C. He is also the author of Practical DSP Modelin g, Techniques, and Programming in C, jJublished by j ohn Wiley & Sons, (tnd umerical Methods for Embedded Systems from M&T Dan's e-mail addTess is dgm@baykitty.corn. Resources Ellis, George. Control System Design Guide. London: Academic Press, 2000. esp

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