module2

# Module2 - clg echo on Dept of Electrical Computer Eng University of California Santa Barbara ECE 147 A Feedback Control Systems module2 PID control

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clg; echo on %--------------------------------------------------------- % % % University of California, Santa Barbara. % % ECE 147 A: Feedback Control Systems % % module2: PID control % % ------------------------------------------------- % % This module will show graphically the varying effects of % proportional (P), proportional-integral (PI), proportional- % derivative (PD) and proportional-integral-derivative (PID) % controllers on several typical systems. % The plants, we will discuss here are a motor with a voltage input % and a velocity output, the spring mas dashpot (SMD) system from % module 1, and a % third order Butterworth filter. The % controllers we will look at are of the form: % % C1(s) = Kp (proportional only) % % C2(s) = Kp + Ki/s (proportional and integral) % % C3(s) = Kp + Kd*s/(s/beta + 1) % (prop. and derviative) % % NOTE: The (s/beta + 1) term is added to the % derivative term to make it proper. % beta is chosen as a frequency well % above the bandwidth of the system so % that the effect of 1/(s/beta +) is % approximately equal to 1 in the frequency % range of interest. % % C4(s) = Kp + Ki/s + Kd*s/(s/beta + 1) % (prop., integ., deriv.) % pause % press any key to continue % % The plants we will use have the following form: % % P1(s) = A/(s+B) (voltage -> velocity) % % P2(s) = C/(S^2 + 2*z*wn*s + wn^2) % (force -> position) % % P3(s) = 1/((s + 1)(s^2 + 1.4142*s + 1)) % (Butterworth filter) % % % We will be graphing time response curves to illustrate % the effect of each gain on the closed loop time response.

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% Typically, PID controllers are tuned by control engineers % that understands which way to adjust specific gains in % order to achieve the desired response. For simple systems % there are some rules of thumb about tuning PID controllers % (look up Zeigler-Nichols rules for example). Often it is % a trial and error process with the control engineer % eventually getting a feel for the effect of the various gains. % In each case we will consider the standard unity gain negative % feedback setup: % % _________ __________ % y | | | | error ref. % <------o-----| plant |<-----| C(s) |<--------(+)<------ % | |_______| |________| ^ - % | | % |________________________________________| % The objective is to design C(s) so that the output, y, is equal % to the reference (this is the ideal - we will never get them % exactly equal). pause % press any key to continue. % For this control example, we must first build the models % of the plants and controllers. For the motor model, we % use values of A = 5 and B = 15. Thus, P1(s) = 5/(s+15). num = [0 5]; den = [1 15]; P1 = nd2sys(num,den); % The SMD model values are the same as in module 1; % C = 90, wn = 10, and z = .1. So, % P2(s) = 90/(s^2 + 2s + 100). num = [0 0 90];
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## This note was uploaded on 04/06/2010 for the course ECE 145 taught by Professor Rodwell during the Spring '07 term at UCSB.

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Module2 - clg echo on Dept of Electrical Computer Eng University of California Santa Barbara ECE 147 A Feedback Control Systems module2 PID control

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