Abstract
In this paper, the control of linear discrete-time Varying Single-Input Single-Output systems is tackled. By using flatness theory combined with a dead-beat observer, a two degree of freedom controller is designed with high performances in terms of trajectory tracking. The aim of this work is to avoid the choice of closed loop poles in linear discrete-time varying framework which build a very serious problem in system control. The effectiveness of this control law is highlighted by simulation results.
Highlights
The theory of linear time-invariant systems gives a wide range of design methods and solutions to control problems including all kinds of techniques such as state feedback controllers and observers, Kalman filters, H2 control and H∞ control
LTV (Linear Time Varying) systems are of a great interest because of the fact that time invariant nonlinear systems can be approximated by LTV systems around desired trajectories after there linearization
A fundamental part in the study of LTV systems is insured by the state transition matrix noted φ, which can be computed as the sum of the PeanoBaker series
Summary
The theory of linear time-invariant systems gives a wide range of design methods and solutions to control problems including all kinds of techniques such as state feedback controllers and observers, Kalman filters, H2 control and H∞ control. We find fuzzy control operating nonlinear systems to make nonlinear controllers via the use of heuristic information [3] Among these control design approaches, flatness-based control remains the most suitable method in trajectory tracking, in the rest of the paper, we are interested to this kind of controller in the LTV case. It is shown that flatness property considerably simplifies the 2DOF (Two Degree of Freedom) controllers design for continuous-time SISO (Single-Input Single-Output) systems for LTV framework [4], [5] In these works, the main feature of this flatness approach for 2DOF controllers design, using flatness-based control and dead-beat observer, is to avoid the choice of closed loop poles and no need to solve diophantine equation any more. We will develop the paper in a discretetime formulation, using the shift forward operator q and the delay operator q−1
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
