Question

Preliminary (1.5 marks) 1) Figure 4 shows the block diagram for the resonant servomechanism control system. Through out this lab we will be applying proportional control to the system, i.e. C(s)- Kp Controller Fiter L(s) C(s) G(S) Figure 4: Block diagram of control system using proportional control. Equivalent forward Y(s) Figure 5: Block diagram reduced to an equivalent unity feedback system. Determine the equivalent forward transfer function Geg(s), for the equivalent unity feedback system shown in Figure 5, in terms of Kp, for the following cases: a) CASE 1 No filter: Use G(s)1, and the nominal model G(s)-Gnom (s) given by b) CASE 2-First order filter: Use Gf(s) , and the nominal model G(s) = Gnom(s) c) CASE 3-Complex model: Use the first order filter G,(s) = , and model 1 G(s) = equation (8) given by equation (8) Gi(s) given by equation (9) 8+8 2) Do a rough sketch of the root locus expected for each case above. For each, list the open-loop poles and zeros. While asymptotes and break-in/away points do not need to be calculated, use knowledge of asymptote angles to assist in drawing the expected shape of the root locus Hint Roots of (1.12725s2 +1.2s) are 0,-1.065 Roots of (0.298s4 + 0.9804-' + 419.481-+ 446.4s) are 0.-1.066.-1.112 ±J37.47 3) For an 9% overshoot, determine the damping ratio (assuming a valid second order approxima- tion). From the damping ratio, determine the required angle (in degrees) of the 9% overshoot line For all parts, show ALL working As detailed in the Appendix, the simpler 'nominal'model of the servomechanism was determined to be: Gnom ) L (s) T,n(s) nom(s) = = 1.12725s* +1.2s 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: 0.12s +372 Tm(s) 0.298s4 0.9804s3 + 419.481s +446.4s

Answer 1

LS 32) 2 446uS

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