DSC HW 2: Assigned 6/18/11, Due 6/25/12 - SOLUTION Page 1

NOTE: For all of these problems, it is good practice to list the key constitutive relationsassumed for the physical elements in the system under study.

Problems 1-4: The four problems studied in HW #1.

Figure 1: Four systems from HW #1

Solution: A brief guide to solving these problems:

R.G. Longoria, Summer 2012 ME n344, UT-Austin

DSC HW 2: Assigned 6/18/11, Due 6/25/12 - SOLUTION Page 2

Problems 5-8: Repeat steps above for the 4 problems on Quiz #1.

Solution: Here is a brief guide to solving these problems:

R.G. Longoria, Summer 2012 ME n344, UT-Austin

DSC HW 2: Assigned 6/18/11, Due 6/25/12 - SOLUTION Page 3

Problem 9: Solution:

R.G. Longoria, Summer 2012 ME n344, UT-Austin

DSC HW 2: Assigned 6/18/11, Due 6/25/12 - SOLUTION Page 4

Problem 10: The permanent-magnet dc (PMDC) motor/load system was studied in classand equations were derived from inspection of the schematic. Develop a bond graph of thePMDC motor/load system, referring to Figure 3 below. For the motor, assume the motortorque is related to the armature current by Tm = rmim, where rm is the motor (gyrator)constant. , Apply causality to the bond graph and show that the state variables are λm (fluxlinkage of motor inductor, Lm) and rotor momentum, hm. Derive a state equation for eachone of these state variables assuming all elements have linear constitutive relations.

Figure 2: PMDC motor with load

Solution:

R.G. Longoria, Summer 2012 ME n344, UT-Austin

DSC HW 2: Assigned 6/18/11, Due 6/25/12 - SOLUTION Page 5

Problem 11: The two systems in Figure 4 were discussed in class as analogous mechanical-electrical systems. A handout was provided showing how to derive the equations usinga classical approach. Complete the following: (a) confirm these are analogous systems bydeveloping a bond graph for each system. (b) Apply causality, and identify the state variablesfor each system. (c) Assuming all linear constitutive relations for the elements, derive thestate space equations for each system.

Figure 3: Analogous mechanical-electrical systems

Solution:

R.G. Longoria, Summer 2012 ME n344, UT-Austin