Problem 2: (40 Points) In this problem, use as many appropriate eigenvalues as you need from the following lists; For th

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Problem 2 40 Points In This Problem Use As Many Appropriate Eigenvalues As You Need From The Following Lists For Th 1 (43.22 KiB) Viewed 25 times

Problem 2: (40 Points) In this problem, use as many appropriate eigenvalues as you need from the following lists; For the system with feedback: j =-1+j1 =-1-1 13 = -1 For the observer: 14 =-3+3j ly =-3-3j 13 =-3 An LTI SISO system has internal representation X = 4X+bu y=ck with; A = [2] b = [1] C = [1] For this system; a- Find using Lyapunov equation and one other method, the state feedback gain k so that the resulting system after feedback is stable. Is the resulting system capable of regulation? Prove your assertion. Is the resulting system capable of tracking a constant input other than zero? Prove your assertion. b- Design a full order observer for this system using Lyapunov equation. - Draw and interconnect the system and the observer of part (b) and use output of the observer with the feedback gain of part (a) to obtain a closed loop system. If you have not been able to do part (a) use a generic gain k. d- Does this system have a reduced order observer? If yes, express its equation and draw and interconnect the system and this observer and use output of the observer with the feedback gain of part (a) to obtain a closed loop system. If you have not been able to do part (a) use a generic gain k e Design a robust scheme so that constant disturbances would be rejected and parameter variations would not affect steady state system output. Га 27- 1 [d -67 Note: dl ad -bc-C -] a