Difference between revisions of "Talk:ECE 382/Spring 2009/Test 2"
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Failed to parse (: Invalid response ("Math extension cannot connect to Restbase.") from server "http://wikimedia.org/api/rest_v1/":): {\displaystyle \begin{align} G_{eq}&=\frac{T}{1-T}\\ T&=\frac{N_T}{D_T}\\ G_{eq}&=\frac{N_T}{D_T-N_T} \end{align}}
Failed to parse (: Invalid response ("Math extension cannot connect to Restbase.") from server "http://wikimedia.org/api/rest_v1/":): {\displaystyle \begin{align} T&=\frac{G_{eq}}{1+G_{eq}}\\ G_{eq}&=\frac{N_G}{D_G}\\ T&=\frac{N_G}{D_G+N_G} \end{align}}
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Post general questions or requests for clarification here. | Post general questions or requests for clarification here. | ||
* For the 2008 test, problem III, part d, is the reasoning in the answer key that the calculated value for <math>\omega_d</math> is too different from <math>\omega_n</math>, so the extra zero/pole have an effect? [[User:Nbb5|Nbb5]] 22:56, 24 March 2009 (EDT) | * For the 2008 test, problem III, part d, is the reasoning in the answer key that the calculated value for <math>\omega_d</math> is too different from <math>\omega_n</math>, so the extra zero/pole have an effect? [[User:Nbb5|Nbb5]] 22:56, 24 March 2009 (EDT) | ||
| − | * Should we know how to use the equation that solves the phase space matrix, <math>\frac{Y}{U}=C(sI-A)^{-1}B+D</math>? [[User:Nbb5|Nbb5]] 22:56, 24 March 2009 (EDT) | + | ** The extra zero at -1 is too close to the origin. The (s+1) on top means the actual function in time is the typical second order response plus one times the derivative of the second order response; that messes up the phase and so the peak time is likely way off.[[User:DukeEgr93|DukeEgr93]] 12:55, 25 March 2009 (EDT) |
| + | * Should we know how to use the equation that solves the phase space matrix, <math>\frac{Y}{U}=C(sI-A)^{-1}B+D\,\!</math>?[[User:Nbb5|Nbb5]] 22:56, 24 March 2009 (EDT) | ||
| + | ** Yes, in life, but it will not be on the test. [[User:DukeEgr93|DukeEgr93]] 12:55, 25 March 2009 (EDT) | ||
| + | * In a translational system, like in Problem III of 2005 Test I, how do you know how many storage elements there are? Also, how do you know what to label as state variables? [[User:Ceh23|Ceh23]] 11:31, 25 March 2009 (EDT) | ||
| + | ** You have to see how many independent variables are required to determine the energy of the system. For problem III, the storage elements are the masses and springs. For masses, the variable of interest is the velocity and for springs, the variable of interest is the position. Because the ends of the springs are independent, that gives two state variables. The velocities of the masses are also independent, yielding two more. You can pick *any* four variables in the system from which those energy storage variables may be calculated, but a good *first* set of state variables to consider would be the positions of spring ends and the velocities of masses. [[User:DukeEgr93|DukeEgr93]] 12:55, 25 March 2009 (EDT) | ||
| + | * How does the relationship between wn and wd affect the physical properties of the system [[User:Ceh23|Ceh23]] 11:34, 25 March 2009 (EDT)? | ||
| + | ** <math>\omega_d</math> is the ''actual'' frequency at which the response of the system will oscillate, while <math>\omega_n</math> would be the frequency at which the system oscillates if there were no damping. So, a comparison between the two for an underdamped system gives you an idea how much damping (typically, resistance in electrical systems and dampers in mechanical ones) exists. [[User:DukeEgr93|DukeEgr93]] 12:55, 25 March 2009 (EDT) | ||
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== Community Equations == | == Community Equations == | ||
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* Damping ratio for a second-order system? [[User:DukeEgr93|DukeEgr93]] 02:20, 23 March 2009 (EDT) | * Damping ratio for a second-order system? [[User:DukeEgr93|DukeEgr93]] 02:20, 23 March 2009 (EDT) | ||
** Will add [[User:DukeEgr93|DukeEgr93]] 22:41, 23 March 2009 (EDT) | ** Will add [[User:DukeEgr93|DukeEgr93]] 22:41, 23 March 2009 (EDT) | ||
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=== Responses === | === Responses === | ||
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| − | {{:ECE | + | {{:ECE 382/Spring 2009/Test 2/RSR}} |
Latest revision as of 00:42, 4 January 2013
Contents
General Questions
Post general questions or requests for clarification here.
- For the 2008 test, problem III, part d, is the reasoning in the answer key that the calculated value for \(\omega_d\) is too different from \(\omega_n\), so the extra zero/pole have an effect? Nbb5 22:56, 24 March 2009 (EDT)
- The extra zero at -1 is too close to the origin. The (s+1) on top means the actual function in time is the typical second order response plus one times the derivative of the second order response; that messes up the phase and so the peak time is likely way off.DukeEgr93 12:55, 25 March 2009 (EDT)
- Should we know how to use the equation that solves the phase space matrix, \(\frac{Y}{U}=C(sI-A)^{-1}B+D\,\!\)?Nbb5 22:56, 24 March 2009 (EDT)
- Yes, in life, but it will not be on the test. DukeEgr93 12:55, 25 March 2009 (EDT)
- In a translational system, like in Problem III of 2005 Test I, how do you know how many storage elements there are? Also, how do you know what to label as state variables? Ceh23 11:31, 25 March 2009 (EDT)
- You have to see how many independent variables are required to determine the energy of the system. For problem III, the storage elements are the masses and springs. For masses, the variable of interest is the velocity and for springs, the variable of interest is the position. Because the ends of the springs are independent, that gives two state variables. The velocities of the masses are also independent, yielding two more. You can pick *any* four variables in the system from which those energy storage variables may be calculated, but a good *first* set of state variables to consider would be the positions of spring ends and the velocities of masses. DukeEgr93 12:55, 25 March 2009 (EDT)
- How does the relationship between wn and wd affect the physical properties of the system Ceh23 11:34, 25 March 2009 (EDT)?
- \(\omega_d\) is the actual frequency at which the response of the system will oscillate, while \(\omega_n\) would be the frequency at which the system oscillates if there were no damping. So, a comparison between the two for an underdamped system gives you an idea how much damping (typically, resistance in electrical systems and dampers in mechanical ones) exists. DukeEgr93 12:55, 25 March 2009 (EDT)
Community Equations
Requests
Requests for equations should go here. Start your request with an asterisk and end it with your signature, which is four tildes. For example:
* Damping ratio for a second-order system (4.39, p. 171)? ~~~~
will show up, for Dr. G, as:
- Damping ratio for a second-order system? DukeEgr93 02:20, 23 March 2009 (EDT)
- Will add DukeEgr93 22:41, 23 March 2009 (EDT)
Responses
COMPLETE as of 13:12, 25 March 2009 (EDT)~ See Equation Sheet
Approved
Chapter 2
- Motor Equation (2.153)
Chapter 4
- 1st Order Rise Time (4.9, 159)
- 1st Order Settling Time (4.10, p. 159)
- 2nd Order Peak Time (4.34, p. 171)
- 2nd Order %OS (4.38, p. 171)
- 2nd Order Damping Ratio (4.39, p. 171)
- 2nd Order Settling time (4.42, p. 172)
- 2nd Order Damped Frequency (4.44, p. 173)
- 2nd Order Normalized Rise Time (footnote 5, p. 173)
Other
- Geq from T for unity feedback
- T from Geq for unity feedback
Denied / Not Needed
- Motor transfer function constants (2.162 & 2.163, p. 79) - will not need
- Transfer function from state space (3.73, p. 133) - will not need
- General 2nd order transfer function (4.22, p. 166) - need to memorize
- Mason's Rule (5.28, p. 240) - need to memorize that and what the terms mean.
- Formula for system type, static error constants, and steady state errors (Table 7.2, p. 336) - need to memorize
