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Extra resources for Aircraft Performance & Design
In the term T = A/GK T is called the ‘time constant’ and has units of time (check units: m2 / m3 /s /m = s or in 2 / in 3 / sec /in = sec). e. at high frequencies) the response xo /xi tends to 1/TD which looks like an integrator. • Similarly when things are changing slowly the term TD becomes very small relative to unity hence the closed loop response xo /xi tends to 1. 6 Calculating Frequency Response Frequency response is expressed as the ratio between the output vector and the input vector as a function of j .
2K Let us check the units in each unit convention. e. a second-order system associated with an electronic circuit, a chemical reaction, a hydraulic or pneumatic pressure oscillation can all be expressed in the standard form. This is an interesting aspect of feedback control systems in that it all boils down to a series of transfer functions that can be studied in control systems terminology and independent of any speciﬁc engineering discipline. Here are some observations we can make regarding second-order system response.
Analysis and/or testing can focus on a speciﬁc number of frequencies in the range of interest. For (mostly) linear systems sinusoidal inputs generate (mostly) sinusoidal outputs with attenuation (or magniﬁcation) and a time delay (also referred to as a phase shift or phase lag expressed in degrees). 6. Typically, we observe that at frequencies below a certain value, the output follows the command closely with little attenuation or phase shift. 7). Frequency response is expressed as the ratio between the output amplitude and the input amplitude plotted against frequency together with a plot of phase lag against frequency.
Aircraft Performance & Design by Anderson