Arab Academy for Science & TechnologyCourse Title: Fundamental of ControlCourse Code: EE311Sheet #1La Place Transfrom

Time-DomainLaplace-Domain

f(t)F(s)

1: unit step

1- Find the Laplace transform of the following time functions:a) b) 2- Find the inverse Laplace Transform of the following S-domain functions:a) b) c) 3- Using Laplace Transform, find the solution of the following differential equation.

4-Solve the following differential equation.

6

Sheet #3Electrical Compensating Circuits1-Derive the transfer function for the RLC circuits shown in the figures below: EiEoEoEiEoEi

2- For the electrical networks shown in figure below, assuming zero initial conditions, obtain the transfer function EiEoEiEoEoEi

3-Using Crammers rule, the transfer function for the circuit given below:EoEi

4- Obtain the transfer function for the circuits shown in the figure below:EoEi

5- Derive for the RLC ladder network given in the figure below:EoEi

Sheet #4Electromechanical Modelling1- An electromechanical open loop control system is shown in Figure1. The generator when driven at constant speed, provides the field voltage for the motor. The motor has inertia Jm and bearing friction Bm. Obtain the transfer function and draw the block diagram for the system, The generator voltage can be assumed to be proportional to the field current.RfgLfgVfVgLgRgRfmLfmIgIamLN1N2JL,BLLoadGeneratorMotor

2- An AC-DC servo system is shown in Figure2. The motor inertia and friction are negligible, Draw the block diagram of the system indicating the transfer function of each block. Obtain the transfer function.RfgLfgVfVgLgRgRaLaIaEamLN1N2JL,BLLoadGeneratorMotorN2RcKdKa

3- A simple close loop positioning system is shown in Figure 3. The operational amplifier is ideal. Determine a control system block diagram for this closed loop system. What is the transfer function Zo

RmLmZi

JL,BLVi

Vo

Em

K

uz

Sheet #5Block Diagram Reduction1- Find the transfer function

G1YR

G1G2YR

G1H1YR-

G1H1G2YR-

G1G3G2H1YR-+

-R

G4G3G2G1

--

A

YDCBAR

C

B

H2

Y+R

G3G2G1

--

H1

R

+Y++G4G3G1

++-G5G2

++

Sheet #6Signal Flow Graph1- Use Mason Gain formula to determine the transfer function between R(s) and y(s) in figure below:H3

+-

R++YG2G1

--H1

H2

G3

2- Use mason signal flow technique to find C(s)/R(s) for the block diagram in figure below:G5

++G6R+G3G2G1

+C+++

G4

----H3

H2

H1

H4

3- Use masons gain rule to determine the transfer function between R(s) and Y(s) in figure shown below:H1

-++G4G2

Y+G6-H2G1R

-

-H3++G5G3

Sheet #7Time Response1- Measurements conducted on a servomechanism show the system response to be:

When subjected to a unit step input:a) Obtain the system closed-loop T.F.b) Determine the system undamped natural frequency and damping ratio.2- A unity feedback system is characterized by an open-loop T.F.,

Determine the gain K so that the system will have a damping ratio of 0.5 for this value of K determine the settling time, peak overshoot and time to peak overshoot for a unit-step input.3- For the system shown in figure below, find the range of K so that the system is stable. Also, find the value of K which gives a maximum overshoot Mp=5% for a unit strep input, then find the corresponding values of ts, tp and ess.-R

K/s-2s

C+

4- A unity feedback system has an open-loop T.F.

a) Calculate the position, velocity and acceleration error constantsb) Determine ess for a unit step, a unit-ramp and a unit parabolic input.5- For the process control system shown below, find the unit-step input response. Calculate Mp, Tr, Tp,Tss and ess. Sketch c(t).

C

8-R+

1.0

Sheet #8Routh-Hurwitz Stability Criterion1- For the control system shown in figure below, using Routh-Hurwitz criterion. Find the gain K which makes the system critically stable.

+-RY

2- Find the range of K which makes the system with the characteristic equation:

3- For the unity negative feedback system with forward loop T.F.

Find, using Routh criterion, the value of K for which the system has undamped oscillatory response.

4- A system has a forward loop T.F. of: G(s)=K/(s+1)(s2+4s+5), and a feedback loop T.F. of H(s)=4/(s+3). Using Routh stability criterion, find K which make the system critically stable. Calculate the frequency of the sustained oscillations.

5- A unity feedback control system has the following open-loop T.F.

And r(t)=5t.a) If K1=1.5sec-1, determine ess.b) It is desired that, for a ramp input, ess