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By Jean-Pierre Elloy
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Extra resources for Classical and Modern Control with Worked Examples
Example text
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.
75. What then is the pulsa tion of resonance ? b) Trace KG(s) in the Black diagram. 75. Find again the value of the pulsation of resonance. c) With the gain Κη fixed at the preceding value, we subject the system to a unit step input r(t). What will be the final value of the error e(t) ? What is the overshoot of the step response ? What is the instant of the first overshoot ? 9, where K' is the static gain of the open loop transfer function. 15 db. On the graph opposite we can see that ω r is near to 1.
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. 3 HYDRAULIC STEERING EQUIPMENT The figure represents steering equipment for a rapid navigation unit. 7. The variation in the position x of the jack causes an oil flow q under pressure p which we shall assume to be constant. The combination of this flow q and of a flow q causes the movement (x ) of the slide of a valve.