{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# hw2_solution - ECE 486 Assignment 2 Issued January 27 Due...

This preview shows pages 1–2. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ECE 486 Assignment # 2 Issued: January 27 Due: February 3, 2011 Reading Assignment: Continue reading ... FPE , 5th or 6th ed., Chapters 1–3 (ignoring subsections marked “ N ”). See also Belanger , Chapters 1–3, and Brogan , Chapters 3 & 5, or Chen Chapters 1–3. Problems: 4. Consider the plant described by the state space model ˙ x = [ 1 3- 3 ] x + [ 1 ] u y = [1 α ] x We consider two cases: The parameter α takes the value 1 or- 1. Consider a “state feedback control” of the form u =- Kx + v =- K 1 x 1- K 2 x 2 + K 3 r , where r is a reference input. For each value of α , (i) Verify that d dt x 1 = x 2 , so that y = x 1 + α d dt x 1 . (ii) Find K such that the resulting closed loop system with input r and output y is BIBO stable, and the DC gain of the transfer function Y ( s ) /R ( s ) is unity. Include step response plots in your solution — This can only be done using Matlab! (iii) Compute the transfer function of your closed-loop system Y ( s ) /R ( s ), identify the closed-loop poles and zeros in a pole-zero plot, and discuss your findings. Solution : (i) From the state space model, we have ˙ x 1 = x 2 and y = x 1 + αx 2 = x 1 + α ˙ x 1 . (ii) First consider the open loop transfer function with α = 0. Since ˙ x 1 = x 2 we have, ¨ x 1 = 3 x 1- 3 ˙ x 1 + u = ⇒ X 1 U = 1 s 2 + 3 s- 3 . The open loop poles are located at- 3 ± √ 21 / 6 ≈ (4 . 1 ,- 5 . 1). The pole at 4.1 will cause instability. We wish to move the poles into the left-half plane: Open loop poles:...
View Full Document

{[ snackBarMessage ]}

### Page1 / 6

hw2_solution - ECE 486 Assignment 2 Issued January 27 Due...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online