Gradient Projection Anti-windup Scheme on Constrained Planar LTI Systems
MASSACHUSETTS INST OF TECH CAMBRIDGE AEROSPACE CONTROLS LAB
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The gradient projection anti-windup GPAW scheme was recently proposed as an anti-windup method for nonlinear multi-input-multi-output systemscontrollers, the solution of which was recognized as a largely open problem in a recent survey paper. This report analyzes the properties of the GPAW scheme applied to an input constrained first order linear time invariant LTI system driven by a first order LTI controller where the objective is to regulate the system state about the origin. We show that the GPAW compensated system is in fact a projected dynamical system PDS, and use results in the PDS literature to assert existence and uniqueness of its solutions. The main result is that the GPAW scheme can only maintainenlarge the exact region of attraction of the uncompensated system. We illustrate the qualitative weaknesses of some results in establishing true advantages of anti-windup methods, and propose a new paradigm to address the anti-windup problem, where results relative to the uncompensated system are sought.
- Theoretical Mathematics
- Operations Research