This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: ME 132 Solutions # 8 1 Sensitivity Analysis It is pretty simple to analyze the block diagram and determine that y ( t ) = AC 1 + ABC AD u ( t ) We can now compute the sensitivities: S a = ∂y ∂A · A y = 1 1 + ABC AD S c = ∂y ∂C · C y = 1 AD 1 + ABC AD 2 Model Properties Many of you had difficulty with this problem, particularly part (c). (a) This model is memoryless, nonlinear, timeinvariant, causal. (b) This model is memoryless, nonlinear (because of the affine term b ), timeinvariant, causal. (c) This model is dynamic, linear, timevarying, noncausal. It is timevarying because of the following. If we apply the pulse input u a ( t ) = 1 for  t  ≤ 1, we get the output y a ( t ) = 1 for  t  ≤ 1. If we delay this input by one second and use u b ( t ) = 1 for 0 ≤ t ≤ 2 we do not get a one second delayed version of y a . You can verify that y b ( t ) = 1 for 2 ≤ t ≤ 0. Plot u a ,u b ,y a ,y b to better understand my solution. It is not causal because y ( 4) depends on u (4). This also shows the model is dynamic. (d) This model is dynamic, linear, timeinvariant, noncausal. 2 4 6 8 1042 2 4 Time (sec) (a) (b) (c) 3 Homogeneous Solutions (a) The system has only one pole which is at 1, and so the form of the homogeneous solution is...
View
Full
Document
This note was uploaded on 10/20/2010 for the course ME 132 taught by Professor Tomizuka during the Spring '08 term at Berkeley.
 Spring '08
 Tomizuka

Click to edit the document details