Suez Canal university
Faculty of Engineering
Mechanical department
Basics of Automatic Control Sheet(1):Mathematical modeling
1. Drive the relationship between f(t), y(t) for the fo;;owing mechanical systems
2. Find the relation between x(t), y(t) in the following system
3. Assuming zero initial conditions, Write the governing differential equation for System,
then draw the block diagram representing the relation between:
• qi and qo
• qi and h
where
C=5
,
R=3
4. Assuming zero initial conditions, Write the governing differential equation for System,
then draw the block diagram representing the relation between:
• q and h1
• q and h2
• q and q2
• h1 and h2
where
C1 = 5
,
R1 = 3
C1 = 4
,
R1 = 1
5. Assuming zero initial conditions, Write the governing differential equation for System,
then draw the block diagram representing the relation between:
• x and f
where
k=5
,
fv = 3
,
m = 10
6. Assuming zero initial conditions, Write the governing differential equation for System,
then draw the block diagram representing the relation between:
• X1 and f
• X2 and f
• X1 and X2
7. Assuming zero initial conditions, Write the governing differential equation for System,
then draw the block diagram representing the relation between:
• Vt and Vc
• Vt and I
where L= 5 ,
R = 3 , C=0.25
8. Assuming zero initial conditions, Write the governing differential equation for System,
then draw the block diagram representing the relation between:
• Vt and i1
• Vt and i2
• i1 and i2
• Vt and Vc
• i2 and Vc
where R1 = 5 ,
R2 = 3 L = 4 ,
C = 0.5
9. For the following system find the Transfer function relating r(t), y(t)
10. Consider the system shown below represented armature-controlled dc servomotor
drives a load consisting of the moment
of inertia JL. The torque developed by
the motor is T. The moment of inertia
of the motor rotor is Jm. The angular
displacements of the motor rotor and
the load element are ϴm and ϴ,
respectively. The gear ratio is n =
ϴ/ϴm Obtain the transfer function ϴ (t)/Ei(t).
11.Assuming zero initial conditions, Write the governing differential equation for System,
then draw the block diagram representing the relation between:
12.
12. Shown a schematic diagram of an aircraft elevator control system. The input to the system is
the deflection angle ϴ of the control lever, and the output is the elevator angle φ. Assume that
angles ϴ and φ are relatively small. Show that for each angle ϴ of the control lever there is a
corresponding (steady-state) elevator angle φ.