Question

Operation Research

Discuss the application of the Routh-Hurwitz stability criterion in control system analysis. What are its main limitations?I6 marke1

What is a transfer function? Discuss its main characteristics.

Consider the armature-controlled DC motor shown in Figure 2.1. The electrical system is represented by an armature circuit, in which ua is the applied armature voltage, ia the armature current, Ra the armature resistance, La the armature inductance and eb is the back electromotive force generated in the armature. The mechanical part is represented by a rotational system, in whichJ is the moment of inertia due to the rotor and the load, B the viscous rotational damping associated with the load, 0 is the angular position, Tm is the torque produced by the motor and TI, is the load torque.

The system is modelled by the following differential and algebraic equations

\begin{aligned} R_{a} i_{\alpha}(l)+L_{a} \frac{\mathrm{d} i_{a}(t)}{\mathrm{d} t}+e_{b}(t) &=v_{a}(t) \\ J \frac{\mathrm{d}^{2} \theta(t)}{\mathrm{d} t^{2}}+B \frac{\mathrm{d} \theta(t)}{\mathrm{d} t} &=\tau_{m}(t)-\tau_{L}(t) \\ e_{b}(t) &=K_{L} \omega(t) \\ \tau_{n}(t) &=K_{T} i_{a}(t) \end{aligned}

where KE is the back electromotive force constant of the motor, Kr is the torque constant of the motor, and w is the angular velocity.

Obtain a state-space representation of the armature-controlled DC motor if the state variables are the armature current and the angular velocity, the inputs to the system are the armature voltage and the load torque, and the only output is the angular velocity. Clearly identify matrices A, B, C and D.

[Hint: The derivative of angular position is angular velocity and the derivative of angular velocity is angular acceleration].  Verified     ### Question 40776  Operation Research

Consider the following list of activities and predecessors.
a)Draw the network diagram. Write down the LP to determine the completion time. Write down the activities on the critical path.
b)Suppose that by hiring additional workers, the duration of each activity can be reduced. The costs per day of reducing the duration of the activities are given in the following table. Write down the LP to complete the project within 20 days with minimum cost.

### Question 40775  Operation Research

9.5-3. The next diagram depicts a system of aqueducts that originate at three rivers (nodes RI, R2, and R3) and terminate at a major city (node T), where the other nodes are junction points in the system.
Using units of thousands of acre feet, the tables below the diagram show the maximum amount of water that can be pumped through each aqueduct per day.
The city water manager wants to determine a flow plan that will maximize the flow of water to the city.

### Question 40774  Operation Research

Consider the following network:
Formulate an integer program to find the shortest path from node 1 to 5.

### Question 40773  Operation Research

The Childfair Company has three plants producing child push chairs that are to be shipped to four distribution centers. Plants1, 2, and 3 produce 12, 17, and 11 shipments per month, respectively.Each distribution center needs to receive 10 shipments per month. The distance from each plant to the respective distributing centers is given in the table below. The freight cost for each shipment is \$100 plus 50 cents per mile. How much should be shipped from each plant to each of the distribution centers to minimize the total shipping cost?
a) Construct the transportation tableau
b) Is this a balanced transportation model? If not, convert it into a balanced model
c) Write the LP formulation for this problem.
d) Solve it with Excel or Lingo, write down the optimal solution on your answer sheet(values of the decision variables and the objective function ). Include your software model and output files

### Question 40772  Operation Research

Question 1) Tom Cruise, Freddy Prinze Jr., Harrison Ford, and Matt Le Blanc are marooned on a desert island with Jennifer Aniston, Courtney Cox, Gwyneth Paltrow, and Julia Roberts. The"compatibility measures" in Table 2 indicate how much happiness each couple would experience if they spent all their time together. The happiness earned of time they spend together.a couple is proportional to the fraction
A)Formulate an LP whose solution will maximize the total happiness, considering x_ij as the fraction of time ih man spends with j™ woman.
b) Solve it with Lingo, did you find an integer solution? What do you think it means?

### Question 38838  Operation Research

How to evaluate the quality of an OR model?

### Question 38837  Operation Research

4. Give an example on possible application of OR modeling approaches in two of the following areas:
d. Construction industry
b. Machining process
C. Oil industry
a. Healthcare
e. Agriculture planning

### Question 38836  Operation Research

3. What are some possible sources of data needed to derive parameters of OR models?

### Question 38835  Operation Research

. In solving real world problems, when it is more appropriate to use mathematical modeling instead of qualitative methods? And why the Operations Research modeling approach could be more effective?

### Question 38834  Operation Research

What do we mean by an Operations Research (OR) model? And what are the various elements of such model?

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