Primer Deber de Control Automático

Primer tema

Two masses are connected by springs to a rotating lever, as is shown schematically in Figure

P2.10.

a) Write the necessary and sufficent set of equations describing this system, assuming

that the angle never changes by more tan a few degrees and the lever is massless.

b) Draw the Functional Diagram for the system.

c) Obtain the transfer function from Fs/x3

Segundo tema

A thermocouple circuit is used to measure the temperatura of a perfectly mixed liquid, as

shoen in Figure P8.7. The hot junction of the thermocouple has the form of a small sphere of

radius r1. The density of the hot junction material is t, and the specific heat is ct. The termal

capacitance of the thermocouple wire is negligible. The mesauring voltaje e21 is related to the

hot junction temperatura Tt by the equation e21=aTt.

a) Derive a mathematical model for this system relating e21 to TL

b) Sketch the Block Diagram

c) How long will it take for the mesauring signal e21 to reach aproximately 95% of the

steady-state value after a step change of the liquid temperature? The thermocouple

parameters are t = 7800kg/m3, ct = 0.4KJ/kgoC, and r1 = 0.2mm. The convective heat transfer between the liquid and the hot junction is hc = 150W/m2 oC

Tercer tema

Considere el sistema del tanque cónico de agua de la

Figura 361. El flujo a través de la válvula es turbulento

y se relaciona con la altura H mediante 𝑄 = 0.005√𝐻

en donde Q es el flujo medido en m3/seg y H está en

metros. Suponga que la altura es 2m en t = 0. ¿Cuál

será la altura en t = 60seg? (Sugerencia: Linealice el sistema)

Cuarto tema

Para el sistema mostrado en Figure P2.34:

a) Reduzca el sistema usando algebra de bloques hasta obtener un solo bloque que

represente todo el sistema.

b) Obtenga el diagrama de flujo de señal del sistema. c) Obtenga la función de transferencia aplicando la Regla de Mason.

Quinto Tema

Figure P2.22 shows two pendulums suspended from frictionless pivots and connected at their

midpoints by a spring. Assume that each pendulum can be represented by a mass M at the end

of a massless bar of length L. Also assume that the displacement is small and linear

approximation can be used for sin and cos. The spring located in the middle of the bars is

unstreched when 1 = 2. The input force is

represented by f(t), which influences the left-hand bar only.

a) Obtain the equations of motion,

and sketch a block diagram for

them.

b) Determine the transfer function

T(s) = 1(s)/F(s)

c) Sketch the location of poles and

zeros of T(s) on the s-plane.

Nota: Los alumnos que estén repitiendo el curso deberán simular los

problemas 1 al 3. Para el problema 1 deberán dar valores a los parámetros

y en el tercer problema deben simular el sistema no lineal y el linealizado.

Las simulaciones deben ser enviadas al e-mail:

fkuonqui@fiec.espol.edu.ec hasta el viernes 21/11/2014.