Reference no: EM132821673
The Four Basic Steps of Problem Solving George Polya published the book "How To Solve IC in 1945. Ile identified four basic principles of problem solving.
1. Understand the problem: What is the question being asked.? Can you state the problem in your own words.? Can you draw a circuit or diagram to help you understand the problem.?
2. Devise a plan: Which variables are important.? Can you identify basic principles that the variables must satisfy.? Draw a picture. Consider special cases, develop a clear notation. Is there more than one way to the answer.?
3. Implement the plan: solve the equations. A computing device, generally. will be used in this step. Do not obscure your work with pages of mind numbing and trivial algebraic steps. State the method, software and hardware used to arrive at the given answer.
4. Reflect on your work: Verify the correctness of yor answer, and, see if your approach can be used on other problems.
Question 1. Write the dynamic equations and find the transfer function for the circuit shown below
Question 2. The equations for heating a house are given in Section 2.4 in your textbook.
In a particular case, they can be written with time in hours as
C dTh/dt = Ku - (Th -To)/R,
where
C thermal capacity of the house in J/°C
Th temperature of the house in °C
To temperature outside the house in °C
K heat rating of the furnace, = 94,955,400 J/h
It thermal resistance in °C per J/h
u furnace switch, = 1 if the furnace is on and = 0 if the furnace is off
It is measured that, with the outside temperature at 0 °C and the house at 16 °C, the furnace raises the temperature 1 °C in six minutes. With the furnace off, the house temperature falls 1 °C in 40 min. What are the values of C and R for the house?
3. Find the transfer function Y/R for the block diagram shown below
4. Consider the system shown below with PI control
(a) Determine the transfer function from It to Y.
(b) Determine the transfer function from W to Y.
(c) Under what conditions on (Kp, Kr) is the closed-loop system stable?
(d) What are the system types and error constants with respect to refer-ence input and with respect to disturbance rejection?
5. Use Routh's criterion to find the range of K for which the system below is stable, and use the root locus to confirm your calculations.
