Download Continuous-Time Signals - Linear Dynamic Systems and Signals - Exam and more Exams Electronic Circuits Analysis in PDF only on Docsity! Sample Exam 6: Chapters 6, 8, and 12 #1a) Convolve graphically continuous-time signals Ä Å[ÆÇ ÈpÉIÊ-ËLÌ and ÄÍÆ.Ç/ÌjÎÂÏÍÆÇ"Ì . #1b) Using the sliding tape method find the discrete-time convolution ÐÑÒUÓ ÔÕ±Ð Í ÒEÓ3Ô , where Ð Ñ ÒEÓLÔÖØ×ÙÙÙÚ ÙÙÙÛ É ÓÜÖ%ÝÞ ÓÜÖ Þß ÓÜÖ ßÞ ÓÜÖAàÝ áIâ/ãäåæèç§é@äMê ÐÍÒEÓLÔÖØ×ÙÙÙ Ú ÙÙÙÛ Þ ÓÜÖ Þß ÓÜÖ ßÈ Þ ÓÜÖAàÈÉ ÓÜÖ%ËÝ áIâ"ãäKå"ægçé@ä #2A) Consider the continuous-time linear system represented in the state space form byëLìí Ñ Æ.Ç/Ììí ÍÆ.Ç/Ìî Ö ë Ý ÉÈ Þ È ß î ë í Ñ ÆÇ"Ìí ÍÆÇ"ÌIî Î ë Ý É)î ÐMÆ.Ç/Ì ê ë í Ñ ÆÝLïÌí ÍÆÝ3ïÌî Ö ë ÞÝjîð ÆÇ"ÌÖ°Ò ß ÝjÔ ë í Ñ ÆÇ"Ìí Í ÆÇ/Ì î a) Find the system transition matrix ñ\ÆòÌ , and obtain ñPÆÇ"Ì using the Laplace inverse transform. b) Find the system transfer function. c) Find the system state response for ÐqÆÇ"Ì\Ö³óaÆÇ"Ì and the given initial conditions. d) Find the system output response ( ð ÆÇ/Ì ) due to ÐqÆÇ"Ì#Öõô ï Å/ö÷ Æ.Ç/Ì and the given initial conditions. #2B) Consider the discrete-time linear system represented in the state space form byë í Ñ ÒUÓvÎAÉ·Ôí ÍÒUÓtÎAÉ·Ô î Ö ë Ý ÉÈ Ñø Èúùø î ë í Ñ ÒEÓLÔí ÍÒEÓ3Ô î Î ë ßÝ î ÐÒ-ÓLÔ ê ë í Ñ ÒUÝÔí ÍÒUÝÔ î Ö ë ÉÞ îð Ò-ÓLÔFÖ°ÒEÝ Þ Ô ë í Ñ ÒUÓLÔí Í ÒUÓLÔ î a) Find the system transition matrix ñ\Æû3Ì . Obtain ñxÒEÓ3Ô via the ü -transform b) Find the system transfer function. c) Find the system output response ( ð ÒEÓ3Ô ) due to ÐjÒEÓLÔMÖ7ý"È Ñþ(ÿ ÷ Ò-ÓLÔ and the given initial conditions. d) Given the system represented byð ÒEÓÎÂËÔÎ ð Ò-ÓiÎmàIÔÈ ð ÒEÓÎ ß ÔÈ ð ÒEÓtÎ Þ ÔÎ Þ ð ÒUÓiÎGÉKÔÈ Þ ð Ò-ÓLÔMÖ%ÐjÒEÓÎ ß Ô(Îmà(ÐjÒEÓLÔ Find the system state space form. #3) The system open-loop system transfer function is given by Æ@òÌ#Ö òÆògÎGÉÌ"Æò\Î Þ Ì"Æò\Î0Ë3Ì Assuming the unity feedback system and the system asymptotic stability for some values of the static gain , find the steady state step, ramp, and parabolic errors in terms of . Hint: Some common pairs:÷ Æ.Ç/Ì Éò ê ô ï ö ÷ ÆÇ"Ì ÉògÎ ê Ç@ô ï ö ÷ ÆÇ"Ì ÉÆògÎ Ì Í ê ÷ Ò-ÓLÔ ûûÈ ê Ó ÷ Ò-ÓLÔ LûÆ@ûÈ Ì Í 6 Docsity.com
