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

Abstract

This paper deals with the direct solution of the pole placement problem for singleinput linear systems using proportionalderivative (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 closedloop 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 timeinvariant and timevarying linear systems are treated. The effectiveness of the proposed method is demonstrated by the simulation examples of both timeinvariant and timevarying systems.