Augmented Controllable Region of Unstable Second Order Systems With Impulsive Actions

2009 ◽  
Vol 131 (5) ◽  
Author(s):  
Wookjin Sung ◽  
Jiecai Luo ◽  
Kwanho You
Keyword(s):  
Optimal Control ◽  
Model Uncertainty ◽  
Second Order ◽  
Control Input ◽  
Impulsive Action ◽  
Mixed Control ◽  
Collaborative Control ◽  
Control Actions ◽  
Simulation Results ◽  
Second Order Systems

In this paper, we suggest how to enlarge the maximum controllable region for unstable linear systems with mixed control actions. Using the impulsive action as an alternating control input, it is shown how the collaborative control inputs (bang-bang and impulsive action) work to augment the controllable region of unstable second order systems. However, the weakness resides in the sensitivity to model uncertainty and the time-consuming work to construct the switch curves (bang-bang switch curve and impulse firing curve). We suggest an efficient way to approximate the switch curves. It overcomes the shortcomings from the use of original switch curves, which are constructed through time backward computation. Simulation results show how the approximate switch curves can be used to determine the optimal control values for an augmented maximum controllable region.

scholarly journals Finite-Time Trajectory Tracking of Second-Order Systems Using Acceleration Feedback Only

Automation ◽  
2021 ◽  
Vol 2 (4) ◽  
pp. 266-277
Author(s):  
Romain Delpoux ◽  
Thierry Floquet ◽  
Hebertt Sira-Ramírez
Keyword(s):  
Finite Time ◽  
Sliding Mode ◽  
Algebraic Approach ◽  
Second Order ◽  
Asymptotic State ◽  
Control Input ◽  
Positioning Systems ◽  
Acceleration Feedback ◽  
On Line ◽  
Second Order Systems

In this paper, an algebraic approach for the finite-time feedback control problem is provided for second-order systems where only the second-order derivative of the controlled variable is measured. In practice, it means that the acceleration is the only variable that can be used for feedback purposes. This problem appears in many mechanical systems such as positioning systems and force-position controllers in robotic systems and aerospace applications. Based on an algebraic approach, an on-line algebraic estimator is developed in order to estimate in finite time the unmeasured position and velocity variables. The obtained expressions depend solely on iterated integrals of the measured acceleration output and of the control input. The approach is shown to be robust to noisy measurements and it has the advantage to provide on-line finite-time (or non-asymptotic) state estimations. Based on these estimations, a quasi-homogeneous second-order sliding mode tracking control law including estimated position error integrals is designed illustrating the possibilities of finite-time acceleration feedback via algebraic state estimation.

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