Feedback Control of Dynamic Systems Solutions Manual (6th by Gene F. Franklin, J. David Powell, Abbas Emami-Naeini

By Gene F. Franklin, J. David Powell, Abbas Emami-Naeini

Recommendations handbook for suggestions keep an eye on of Dynamic platforms (6th version) by means of Franklin. discovered it on the net someplace, seems to be lovely strong and every little thing appears to be like there.

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55. Assume that Eq. 74) describes ‡ow through the equal-sized holes at points A, B, or C. (a) With holes at A and C but none at B, write the equations of motion for this system in terms of h1 and h2 . Assume that h3 = 20 cm, h1 > 20 cm; and h2 < 20 cm. When h2 = 10 cm, the out‡ow is 200 g/min. (b) At h1 = 30 cm and h2 = 10 cm, compute a linearized model and the transfer function from pump ‡ow (in cubic centimeters per minute) to h2 . (c) Repeat parts (a) and (b) assuming hole A is closed and hole B is open.

DYNAMIC MODELS (a) Relation between torque constant and electric constant. Torque constant: 1 ounce 1 inch 0:2778 N = 1 Ampere 2:540 1A 10 2 m = 7:056 10 3 N m= A Electric constant: 1V 1 J=(A sec) = = 9:549 1000 RPM 1000 30 rad/ s 10 3 N m= A So, 1 oz in= A = = 7:056 10 3 V=1000 RPM 9:549 10 3 (0:739) V=1000 RPM (b) 25 V=1000 RPM = 25 1 oz in= A = 33:872 oz in= A 0:739 (c) 25 V=1000 RPM = 25 9:549 10 3 N m= A = 0:239 N m= A 19. The electromechanical system shown in Fig. 50 represents a simpli…ed model of a capacitor microphone.

18, and assuming the area of both tanks is A; the values given for the heights ensure that the water will ‡ow according to 1 1 WA = [ g (h1 h3 )] 2 R 1 1 WC = [ gh2 ] 2 R WA WC = Ah_ 2 Win WA = Ah_ 1 From the out‡ow information given, we can compute the ori…ce resistance, R; noting that for water, = 1 gram/cc and g = 981 cm/sec2 ' 1000 cm/sec2 : 1p 1p WC = 200 g= mn = gh2 = g 10 cm R p R p 1 g= cm3 1000 cm= s2 10 cm g 10 cm R = = 200 g= mn 200 g=60 s s 1 1 g cm2 s2 100 = 60 = 30 g 2 cm 2 3 2 2 200 cm s g (b) The nonlinear equations from above are h_ 1 = h_ 2 = 1 1 p g (h1 h3 ) + Win AR A 1 p 1 p g (h1 h3 ) gh2 AR AR The square root functions need to be linearized about the nominal heights.

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