lec8_print

lec8_print - Analysis of Linear System Dynamics Srinivas...

Info iconThis preview shows pages 1–6. Sign up to view the full content.

View Full Document Right Arrow Icon
Analysis of Linear System Dynamics Srinivas Palanki University of South Alabama Srinivas Palanki (USA) Analysis of Linear System Dynamics 1 / 16
Background image of page 1

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

View Full DocumentRight Arrow Icon
Dynamics of a Linear System Recap A linear dynamical system in deviation form is represented as dX dt = AX + BU X (0) = X 0 (1) where X = x - x s U = u - u s (2) Srinivas Palanki (USA) Analysis of Linear System Dynamics 2 / 16
Background image of page 2
Dynamics of a Linear System We saw in the previous lecture that the solution of the above differential equation is given by X ( t ) = e At . X (0) + e At . Z t 0 e - At BU ( t ) dt (3) It is clear from the above equation that X ( t ) is affected by: the initial conditions , X (0) the input vector , U ( t ) We study these effects separately Srinivas Palanki (USA) Analysis of Linear System Dynamics 3 / 16
Background image of page 3

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

View Full DocumentRight Arrow Icon
Unforced Dynamics Unforced Dynamics Consider the system represented by eq. (1) in the previous slide. Suppose that: U ( t ) = 0 (the inputs are at their steady state values u s ) X (0) 6 = 0 (the initial conditions are not at their steady state values) How does X ( t ) change with time? Do the system states go to their steady state values, x s ? If so, how long does this take? Srinivas Palanki (USA) Analysis of Linear System Dynamics 4 / 16
Background image of page 4
Unforced Dynamics Since X ( t ) = e At . X (0) + e At . Z
Background image of page 5

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

View Full DocumentRight Arrow Icon
Image of page 6
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 16

lec8_print - Analysis of Linear System Dynamics Srinivas...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online