This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: 6.241 Dynamic Systems and Control Lecture 8: Solutions of Statespace Models Readings: DDV, Chapters 10, 11, 12 (skip the parts on transform methods) Emilio Frazzoli Aeronautics and Astronautics Massachusetts Institute of Technology February 28, 2011 E. Frazzoli (MIT) Lecture 8: Solutions of Statespace Models Feb 28, 2011 1 / 19 Forced response and initialconditions response Assume we want to study the output of a system starting at time t , knowing the initial state x ( t ) = x , and the present and future input u ( t ), t ≥ t . Let us study the following two cases instead: Initialconditions response : x IC ( t ) = x , u IC ( t ) = 0 , t ≥ t , → y IC ; Forced response : x F ( t ) = 0 , u F ( t ) = u ( t ) , t ≥ t , → y F . Clearly, x = x IC + x F , and u = u IC + u F , hence y = y IC + y F , that is, we can always compute the output of a linear system by adding the output corresponding to zero input and the original initial conditions, and the output corresponding to a zero initial condition, and the original input. In other words, we can study separately the effects of nonzero inputs and of nonzero initial conditions. The “complete” case can be recovered from these two. E. Frazzoli (MIT) Lecture 8: Solutions of Statespace Models Feb 28, 2011 2 / 19 Initialconditions response (DT) Consider the case of zero input, i.e., u = 0; in this case, the statespace equations are written as the difference equations x [0] = x y [0] = C [0] x x [1] = A [0] x [0] y [1] = C [1] A [0] x [0] x [2] = A [1] A [0] x [0] y [2] = C [2] A [1] A [0] x [0] ... ......
View
Full
Document
This note was uploaded on 01/12/2012 for the course ECE 6.241j taught by Professor Prof.emiliofrazzoli during the Spring '11 term at MIT.
 Spring '11
 Prof.EmilioFrazzoli

Click to edit the document details