Abstract
This paper deals with the direct solution of the pole placement problem for single-input linear systems using state-derivative feedback. This pole placement problem is always solvable for any controllable systems if all eigenvalues of the original system are nonzero. Then any arbitrary closed-loop poles can be placed in order to achieve the desired system performance. The solving procedure results in a formula similar to the Ackermann formula. Its derivation is based on the transformation of a linear single-input system into Frobenius canonical form by a special coordinate transformation, then solving the pole placement problem by state derivative feedback. Finally the solution is extended also for single-input time-varying control systems. The simulation results are included to show the effectiveness of the proposed approach.
Highlights
An important problem in the theory and practice of control system design is the design of feedback controllers, which place the closed-loop poles of a linear system at desired locations
In designing control systems based on pole placement, it may be satisfactory in practice that the closed-loop system has all poles at a desired location
The solution is based on recent efficient techniques for solving the pole placement problem by state feedback for SISO and MIMO linear time-invariant and time-varying systems [8, 9, 10]
Summary
An important problem in the theory and practice of control system design is the design of feedback controllers, which place the closed-loop poles of a linear system at desired locations. In this paper the problem of pole placement by state derivative feedback for single-input linear systems, both time invariant and time varying, is generally formulated and solved. The solution is based on recent efficient techniques for solving the pole placement problem by state feedback for SISO and MIMO linear time-invariant and time-varying systems [8, 9, 10]. It uses the transformation of a linear system into Frobenius canonical form and results in different versions of Ackermann’s formula.
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