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%% Numeric Values of Frequency-Domain Characteristics of SISO Model % This example shows how to obtain numeric values of several frequency-domain % characteristics of a SISO dynamic system model, including the peak gain, % dc gain, system bandwidth, and the frequencies at which the system gain % crosses a specified frequency. %% % Create a transfer function model and plot its frequency response. H = tf([10,21],[1,1.4,26]); bodeplot(H) %% % Plotting the frequency response gives a rough idea of the frequency-domain % characteristics of the system. |H| includes a pronounced resonant peak, % and rolls off at 20 dB/decade at high frequency. It is often desirable % to obtain specific numeric values for such characteristics. %% % Calculate the peak gain and the frequency of the resonance. [gpeak,fpeak] = getPeakGain(H); gpeak_dB = mag2db(gpeak) %% % |getPeakGain| returns both the peak location |fpeak| and the peak gain % |gpeak| in absolute units. Using |mag2db| to convert |gpeak| to decibels % shows that the gain peaks at almost 18 dB. %% % Find the band within which the system gain exceeds 0 dB, or 1 in absolute % units. wc = getGainCrossover(H,1) %% % |getGainCrossover| returns a vector of frequencies at which the system % response crosses the specified gain. The resulting |wc| vector shows that % the system gain exceeds 0 dB between about 1.3 and 12.2 rad/s. %% % Find the dc gain of |H|. % % The Bode response plot shows that the gain of |H| tends toward a finite % value as the frequency approaches zero. The |dcgain| command finds this % value in absolute units. k = dcgain(H); %% % Find the frequency at which the response of |H| rolls off to –10 dB relative % to its dc value. fb = bandwidth(H,-10); %% % |bandwidth| returns the first frequency at which the system response drops % below the dc gain by the specified value in dB.