A new algorithm for pole assignment of single-input linear systems using state feedback

2005 ◽  
Vol 48 (3) ◽  
pp. 307 ◽  
Author(s):  
Jiang QIAN
Keyword(s):  
Linear Systems ◽  
State Feedback ◽  
Pole Assignment ◽  
Single Input

Pole Placement for Single-Input Linear System by Proportional-Derivative State Feedback

2014 ◽  
Vol 137 (4) ◽  
Author(s):  
Taha H. S. Abdelaziz
Keyword(s):  
Linear System ◽  
Linear Systems ◽  
Degrees Of Freedom ◽  
State Feedback ◽  
Pole Placement ◽  
Feedback Gain ◽  
Time Varying ◽  
Placement Problem ◽  
Single Input ◽  
Time Invariant

This paper deals with the direct solution of the pole placement problem for single-input linear systems using proportional-derivative (PD) state feedback. This problem is always solvable for any controllable system. The explicit parametric expressions for the feedback gain controllers are derived which describe the available degrees of freedom offered by PD state feedback. These freedoms are utilized to obtain closed-loop systems with small gains. Its derivation is based on the transformation of linear system into control canonical form by a special coordinate transformation. The solving procedure results into a formula similar to Ackermann’s one. In the present work, both time-invariant and time-varying linear systems are treated. The effectiveness of the proposed method is demonstrated by the simulation examples of both time-invariant and time-varying systems.

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