By Jean-Pierre Elloy
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Additional info for Classical and Modern Control with Worked Examples
S^* Concentration ΓΝ *' S ^S C I CnviMnn- 1 ·. conductivity tn-inu\ ((MM) fy„ Ic control (0-701/) fresh water m%cro-pump pump The concentration timeter output of the mixture by a continuous is, shown in the diagram then, electric v . flow d satur. water 1f column c —^ conductim, concentration 1 : V-, a 0^10 volts) v* > measure ment LINEAR SERVOMECHANISMS The transfer function of the whole unit 61 has been established in the form : Vc(s) _ Vd(s) in which k = 1 kg (1 - xqs) (1 + jqs) (1 + T2qs) (1 + T £s) (Volt/Volt) τ - 20 seconds, T = 60 seconds, T = 10 seconds q - Q /Q* Q being the nominal flow of fresh The system is made to follow v , by the error v and independent - v of the frequency a) Using the Routh test, stability a set point amplified of the closed v by controlling by a gain amplifier of the signal applied the input adjustable to it.
A) The open loop transfer function of the servo system is therefore : As (1 - 20 as) (1 + 20 qs) (1 + 60 qs) (1 + 10 s) KG(s) = The characteristic equation of the closed loop system is written (1+Aq) + (80q+lO-20Aq2)s + (1200q2+800q)s2 + 12000 q 2 s 3 = O Construction of the Routh table : 2 12000 q 8 0 q + 1 0 - 2 0 Aq 1200q2 + 800 q 1 + A q a 1+Aq with a = 1 2 1 + 8 (960q2 + 640q + 80 - A(240q3 + 280q2)) The system will be stable if a l l the elements in the f i r s t column are positive, therefore if A < a > O, i .
1s s(l + 2s) a) Trace the asymptotic approximations of the curves of gain and phase of KG(s) in the Bode diagram. h) Deduce from it an approximation of the transfer curve in the Black diagram. 3 ? In order to determine this value accurately3 we shall construct the useful part of the correct transfer curve in the Black diagram. What are the pulsation of resonance and the pass hand at - 3 dh ? * * * * * * a) See figure on following page. 3 and 1 rd/s (see figure on following p a g e ) . 53 rd/s 34 a) CLASSICAL AND MODERN CONTROL WITH WORKED EXAMPLES φ /KG deg r e e s 01 /l+0.