WUSTL ESE 543 - ESE 543 Homework 8 PP RS and Obs (2 pages)

Previewing page 1 of 2 page document View the full content.
View Full Document

ESE 543 Homework 8 PP RS and Obs



Previewing page 1 of actual document.

View the full content.
View Full Document
View Full Document

ESE 543 Homework 8 PP RS and Obs

396 views


Pages:
2
School:
Washington University in St. Louis
Course:
Ese 543 - Control Systems Design by State Space Methods

Unformatted text preview:

11 12 2012 Due 2 weeks Homework 7 1 The linearized suspended ball is described by 0 1 0 x x u 1 0 1 a Use state feedback to stabilize the system producing closed loop eigenvalues at 1 1 2 b The ball position x1 can be measured using a photocell but the velocity x2 is more difficult to obtain Suppose therefore that y x1 Design a full order observer having poles at 4 and 5 and use the observer feedback to produce closed loop eigenvalues at 1 2 1 4 5 c repeat b using a first order observer with pole at 6 Give a block diagram showing the controller as a single transfer function 2 Consider 7 2 6 1 1 x 2 3 2 x 1 1 u 2 2 1 1 0 a What eigenvalues can be obtained using state feedback Now suppose 1 1 2 y x 1 1 11 b Describe the pole placement possibilities using an observer and observer feedback 3 Suppose the LTI system is subjected to an unmeasurable disturbance w x Ax Bu Ew y Cx Suppose an observer is constructed in the following manner x Ax Bu K y y y Cx a is the observer estimating the state i e does x t x t b Suppose w is an unknown constant Suggest how an observer can be used to estimate w as well as the state x Hint w 0 Append w to the state vector forming a new state z and estimate z w 4 Consider again the magnetically suspended ball Suppose m 0 02 kg c 8 10 5 mks units g 10 for numerical convenience a It is desired that the nonlinear ball system have an equilibrium position at X 1 0 02 Find the corresponding equilibrium current b Obtain a linearized state model based upon a c Suppose y x1 for the linearized model Use a reduced order observer and pole placement to meet the following specifications 11 12 2012 Due 2 weeks i Error settling time for the observer is less than 0 08 seconds e x x ii settling time for the closed loop system is less than 0 25 seconds and overshoot to an initial offset in position deviation x1 is less than 20 d Draw a block diagram of your design as implemented on the actual system Show the observer feedback as a SISO controller and indicate



View Full Document

Access the best Study Guides, Lecture Notes and Practice Exams

Loading Unlocking...
Login

Join to view ESE 543 Homework 8 PP RS and Obs and access 3M+ class-specific study document.

or
We will never post anything without your permission.
Don't have an account?
Sign Up

Join to view ESE 543 Homework 8 PP RS and Obs and access 3M+ class-specific study document.

or

By creating an account you agree to our Privacy Policy and Terms Of Use

Already a member?