Question

Problem 1 Consider two first order low-pass systems connected in parallel: -2u The objective is to determine a second order ODE describing the variable y by manipulating the differential equations (no transfer function techniques are allowed). Answer the following series of questions: 1. (2 points) Write the variable y in terms of i and 2 2. (6 points) Determine the relationship between y, j, and z1, z2 and u. Write your final expression in a matrix-vector format: ? 01 ?? 02 You need to determine the constants denoted by for y from Part 1 and then use the ODEs to eliminate the derivatives of xi and x2- Hn: differentiate the expression 3. (4 points) Invert the 2 x 2 matrix from Part 2 in order to determine expressions for and x2 in terms of y, y and u. 4. (8 points) Finally, determine a second order ODE for y and write it as follows:

Answer 1

Hello user,

t o A. o -2 M2 and 状2 CP.) n2 n2 4

-i 냐 2x) 왜2 I 2 M,J S+H o $+2 SHI 3 2 Sィ2. DQ2グ! 十一昂

2t 2.

Thank You