Project 2
650:401 Mechanical Control Systems
Due: November 9, 2007
This project is a continuation from Project 1.
4. Use k1 = 1, b1 = 1, k2 = 1, b2 = 1, m1 = 1, m2 = 1, find the impulse and step response of y2(t) due to one input at a time. Use Matlab for this part. (4 pts)
5. (a) Formulate U1(s) = (Kp + s*Kd)*(R(s) - Y2(s)); Using Mason's rule find A4 and B4 which satisfy Y2(s) = A4*R(s) + B4*U2(s). (3 pts)
(b) Formulate U1(s) = (Kp+ s*Kd + Ki/s)*(R(s) - Y2(s)); Using Mason's rule find A5 and B5 which satisfy Y2(s) = A5*R(s) + B5*U2(s). (3 pts)
6. Take the model from 5a of a Proportional, Derivative controller. Choose Kd= 1 and then using Routh-Hurwitz, find the value of Kp when the roots of the denominator polynomial become unstable. (2 pts.)
What are the values of the roots at this transition? (1 pts.)
7. Still using the model from 5a, choose Kp= 2, Kd= 1. Use the final value theorem and find the steady state value of y2(t) for: (a) r(t) = step function, and for
(b) u2(t) = step function. (1 pt.)
8. Draw the step response till steady state occurs for each of the above cases in 7a and 7b. Use Matlab for this part. (2 pts.)
9. Take the model from 5b of a Proportional, Derivative, Integral controller. Choose Kp= 2, Kd= 1 and then using Routh-Hurwitz, find the value of Ki when the roots of the denominator polynomial become unstable. (2 pts.)
What are the values of the roots at this transition? (1 pts.)
10. Still using the model from 5b, choose Kp= 2, Kd= 1, Ki= 2.5. Use the final value theorem and find the steady state value of y2(t) for: (a) r(t) = step function, and for
(b) u2(t) = step function. (1 pt.)
Draw the step response till steady state occurs for each of the above cases in 7a and 7b. Use Matlab for this part. (2 pts.)
The work for this project should be done in Matlab and Maple. The solutions should have comments on the steps taken. The submission should have analysis, results and comments and is limited to 15 typed written pages. Presentation of the project should be formal and points will be deducted for poor presentation.