Be Ol 8 Gnom S 1 1 12725s2 1 2s 8 Tm S A However In Some Cases E G When Evaluating The Effect Of Shaft Reson 1 (479.77 KiB) Viewed 25 times
be: OL(8) Gnom(s) 1 1.12725s2 + 1.2s (8 ) Tm(s) a However, in some cases (e.g. when evaluating the effect of shaft resonance), a more accurate model of the drive system which includes the effect of non-ideal motor-load coupling, is required. Again using mechanical principles, a more accurate model (Model 1) of the servomechanism was determined to be: G1(s) 0 (8) Tm(s) 0.12s + 372 0.298s4 +0.980433 + 419.481s2 + 446.4s (9) Filters are often used to reduce the effects of noise in a system. In this laboratory, we will consider the k system without a filter (ie. Gf(s) = 1), and with a first order filter with (i.e., with Gf(s) sta). In the following experiments, we will: • Determine the value for gain Kp, using the root locus, to achieve the required transient response requirement. Initially, a simple nominal model will be used to represent the ser- vomechanism, and no filter. • A first order filter will be introduced to the system, and the design process using the root locus repeated. The effect of including a filter will be considered. • The model will be changed to the higher order Model 1 for the servomechanism, and the design process using the root locus will be repeated. The effect of using an approximation to a system verses more accurate model will be considered. Should you have time, (BONUS) • Gain Kp values will be tested within the RSVL environment. A comparison of Matlab simu- lated response to more realistic virtual lab responses will be considered.
Experiment 1: 2nd order model, no filter Consider a feedback control system with proportional control. Using the Nominal Model given in equation (8) for the above described servomechanism, determine the proportional gain Kp which will result in a response with 9% (0.1%) overshoot. To achieve this, complete the following steps: a) Write instructions to create the transfer functions representing the filter Gf(s), model G(s) = Gnom(s) (equation 8), and feedback transfer function (H(s) = 1). b) Write instructions to find the equivalent forward transfer function Geg(s), and the open-loop transfer function Geg(s).H(s). c) Plot the root locus of the system. d) Plot a close-up of the root locus with axes going from -1 to 0 on the real axis, and -2 to 2 on the imaginary axis. Do this in separate figure window. e) Overlay the 9% overshoot line on the close-up root locus. f) Allow interactive selection of the point where the root locus crosses the overshoot line. Retrieve and record the gain at that point, as well as all of the closed-loop poles for that gain. g) Generate the step response for the system with your determined gain for an 9% overshoot. 6 h) Retrieve and tabulate the characteristics of the actual response. Ensure the overshoot is within 0.1%. If the overshoot is not sufficiently accurate, improve the resolution of the root locus and recollect results. i) Use the root locus to determine the stability region of the system. j) Answer all questions in the worksheet for experiment 1, including column 2 of Table 1.
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