By Torsten Soderstrom, Petre Stoica
Presents uncomplicated innovations and effects with derivations for either rookies and specialists within the box. The textual content discusses the sensible concerns and illustrates the function of idea while utilizing platforms id. It contains difficulties, extra complicated fabric and calculations in appendices.
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Additional resources for System identification
The resulting traces are shown in Fig. 6. The traces are obtained assuming that the friction B is negligible compared with KP . 5 at a constant value. The proportional gain KP is varied, affecting the damping factor ξ (Eq. 38) and changing the closed-loop zero z1 = −KI /KP . Fig. 6. Step response of the closed-loop system in Fig. 2. The natural frequency ωn and the gain KI are kept constant (Eq. 38), while the gain KP assumes four different values, affecting the damping factor ξ and changing the value of the transfer function zero z1 = –KI /KP .
The complex image of the given load disturbance TL(t) can be obtained by the Laplace transform. It is assumed that TL(t) = 0 for t < 0. The complex image TL(s) can be expressed in terms of the numerator NL(s) and denominator DL(s): 38 2 Basic Structure of the Speed Controller TL (s ) = L [T (t )] = ND ((ss)) . L L L With TL(t > 0) = TL(∞) = 1, one obtains TL(s) = 1/s, with NL(s) = 1 and DL(s) = s + 0. In case of a ramp signal, TL(t) = t, NL(s) = 1 and DL(s) = s2 + 0·s + 0. The speed controller WSC (s) has to remove the impact of TL(t) on the steady-state value of the output ω (∞).
27, it is possible to observe the impact of the feedback gains on ξ and ωn. 27 can be rewritten by multiplying both the numerator and denominator by KI /J. The denominator assumes the form shown in Eq. 38. Within the same expression, it is evident that the integral gain KI determines the natural frequency ωn of the closed-loop poles, while the proportional gain KP can be used for tuning the damping factor ξ. 38) The effects of the damping factor ξ on the step response are investigated in Figs. 5.