MM326 SYSTEM DYNAMICSHomework 1

Prepared by Nurdan Bilgin and Hamza Kamışlı

FORMAT, RULES AND GRADING:

Format:

1. Homeworks should be written using a computer except graphs, and it must be written in English

2. Extra cover page is necessary, Your Instructor’s name will be written in the top of the page. Your name, surname and student ID will be written in the middle of the page.

Rules:

1. Team work is a good thing. But the copy is not good. Team work, should not exceed beyond to discuss the solutions. We do not expect it would be something like this. but, if it does, this type of homework will be excluded from evaluation.

2. Your homework will be submitted to on time. Late submitted won’t be accepted.3. All sources, except your lecture notes, should be properly referenced.4. You should indicate all necessary explanations and details clearly in your solutions.5. You should submit your homework personally to Automatic control lab. on 24 April until

17:00 in exchange for signing. 6. Your homework must be stapled , don’t use clear file.

Grading:

1. Percentage of the homeworks are %15.

QUESTIONS:

Question 1:

We can clasify one-port pure elements as below.

Figure 1. clasification one-port pure elementConstruct the same diagram for translational-mechanical, rotational-mechanical, fluid, thermal and electrical systems. For example , velocity is a A-type active element for mechanical systems…

Question 2: (From System Dynamics:An Introduction, Rowell and Wormley,1997 Problems 4.6 page 114) For each systems show in Fig. 2, establish the sign convention and draw a linear graph

Figure 2: Rotational systems

One-Port Pure Elements

Active

A-type T-type

Passive

DissipatorD-type

Storage

Capacitive(A-type)

Inductive(T-type)

Question 3.

(Exam Question 2012)

a) Find all active and passive element of the system and show across variables.

b) Obtain the differential equations of the system in terms of room temperatures.

Figure 3: A thermal system

Question 4. (Adapted From System Dynamics:An Introduction, Rowell and Wormley,1997 Example 4.4 page 105) A water storage system consisting of a large reservoir, three control valves, and two tanks is illustrated in Fig. 4. The system is fed by rainfall. Draw a system linear graph and write necessary equations.

Figure 4: A fluid system

Question 5.

(Exam Question 2002) Draw the oriented linear graph of the system given below and write out the basic equations which describe the system behavior completely. Reduce the equations to find the system equation in terms of the displacement of the mass M.

Figure 5: A mechanical system