questions are linked to each other. I am posting 1st question
answer too.
The answer of 1st question is below.
- There Is No Need To Solve 1st Question 2 3 4 5 Required These Questions Are Linked To Each Other I Am Posting 1st Ques 1 (73.03 KiB) Viewed 14 times
- There Is No Need To Solve 1st Question 2 3 4 5 Required These Questions Are Linked To Each Other I Am Posting 1st Ques 2 (222.85 KiB) Viewed 14 times
- 32 dx, at dx. 2 xy “ 1 - 2 - 1 6. 别名 36 部 dxy Xu y= [loon] 20 2
1. For the below system find state space representation from input force u to position output yı. Define this system in python using cn.ss() function from control library. Use states as x= : [X1 X2 X3 X4]* = [yı yı yz yz]". Find initial condition response of the system for x(0) = [1 0 3 0]" with input being equal to zero. m1 = m2 = 1kg, k = 1 N/m, b = 2 N· sec/m. Vi y2 = k mi m2 u 2. Find transfer function for the above system by using cn.ss2tf() function. Obtain pole-zero diagram. Plot the step response of the system. 3. Now assume we apply proportional controller to the system with unity feedback. Draw Root Locus plot by using cn.rlocus(). Can you place two poles at -0.2 + 1.5j by adjusting K value? Why? 4. Design a lead compensator to place two poles at -0.2 + 1.5j. Define compensated closed loop system as clsys in python. For this system plot pole zero diagram and compare it with the one in Q1. Define your new closed loop system manually by using cn.tf() to avoid numerical problems. Can we consider poles at -0.2 + 1.5j as dominant poles? Why? Plot step response of the compensated system. 5. Now assume we have sensors to measure all states of the system. Design state feedback controller to place closed loop poles at -5,-4, -0.2 + 1.5j, -0.2 – 1.5j. That is, find feedback gain vector k. Define your system in Q1 again with modified Anew = A – Bk. Plot pole zero diagram. Plot step response and compare it with Q4.