‘A plant has the following open-loop state-space model: Control System Analysis And Design Assignment, UCD, Ireland

Question 3

The state-space model of a self guiding vehicle’s steering angle system is given in observer canonical form:

it is proposed to design a ful order observer for the plant.
(a) Using a Block Diagram Mustrate the structure of the Luenbeeger Observer
(b) What are the eigenvalues of the plant?
(c) What Issues shousd be considered when deciding the observer pole locations? Discuss sumable ‘observer pale locations for this system.
(d) Determine the observer gains such that the observer poles are both placed at -30.

Question 4
‘A plant has the following open-loop state-space model:

A State-Variable Feedback regulator has been designed for the plant with the State Variable Feedback gains Ki= 13 and K2= -2.
(a) Determine the closed loop system matrix for this regulator design.

(b) What are the closed-loop pole locations?

{c) What is the steady-state error in response to a unit-step input?

(d) Explain, with the aid of a block diagram, how you could eliminate the steady-state error from this system by adding integral action.

(e) Assuming the transient performance of the above SVF design to be satisfactory, discuss the location of the additional pole associated with the integrator.