8 research outputs found
Reach Control on Simplices by Piecewise Affine Feedback
We study the reach control problem for affine systems on simplices, and the
focus is on cases when it is known that the problem is not solvable by
continuous state feedback. We examine from a geometric viewpoint the structural
properties of the system which make continuous state feedbacks fail. This
structure is encoded by so-called reach control indices, which are defined and
developed in the paper. Based on these indices, we propose a subdivision
algorithm and associated piecewise affine feedback. The method is shown to
solve the reach control problem in all remaining cases, assuming it is solvable
by open-loop controls
Algebraic Necessary and Sufficient Conditions for the Controllability of Conewise Linear Systems
The problem of checking certain controllability properties of even very simple piecewise linear systems is known to be undecidable. This paper focuses on conewise linear systems, i.e., systems for which the state space is partitioned into conical regions and a linear dynamics is active on each of these regions. For this class of systems, we present algebraic necessary and sufficient conditions for controllability. We also show that the classical results of controllability of linear systems and input-constrained linear systems can be recovered fromour main result. Our treatment employs tools both from geometric control theory and mathematical programming.
Hybrid modeling and control of mechatronic systems using a piecewise affine dynamics approach
This thesis investigates the topic of modeling and control of PWA systems based on two experimental cases of an electrical and hydraulic nature with varying complexity that were also built, instrumented and evaluated. A full-order model has been created for both systems, including all dominant system dynamics and non-linearities. The unknown parameters and characteristics have been identi ed via an extensive parameter identi cation. In the following, the non-linear characteristics are linearized at several points, resulting in PWA models for each respective setup.
Regarding the closed loop control of the generated models and corresponding experimental setups, a linear control structure comprised of integral error, feed-forward and state-feedback control has been used. Additionally, the hydraulic setup has been controlled in an autonomous hybrid position/force control mode, resulting in a switched system with each mode's dynamics being de ned by the previously derived PWA-based model in combination with the control structure and respective mode-dependent controller gains. The autonomous switch between control modes has been de ned by a switching event capable of consistently switching between modes in a deterministic manner despite the noise-a icted measurements. Several methods were used to obtain suitable controller gains, including optimization routines and pole placement. Validation of the system's fast and accurate response was obtained through simulations and experimental evaluation.
The controlled system's local stability was proven for regions in state-space associated with operational points by using pole-zero analysis. The stability of the hybrid control approach was proven by using multiple Lyapunov functions for the investigated test scenarios.publishedVersio