Finance

Combinatorics

Pure mathematics

Mathematics

Algorithm

Mathematical analysis

Polytope

Artificial intelligence

Position (finance)

Economics

Control (management)

Variable (mathematics)

Backlash

Computer science

Control theory (sociology)

State (computer science)

Affine transformation

This paper presents a Linear Parameter Varying (LPV) approach to model and control two-mass systems with backlash. The maximum amplitude of the backlash angle is assumed to be unknown and variable having no knowledge about the upper and lower bounds of it. Proper affine state space model together with the admissible variations of the LPV parameters is designed in order to realize a viable convex polytope. Utilizing H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> LPV lemmas and theories lead to a set of Linear Matrix Inequalities (LMIs). By solving these LMIs, appropriate scheduled state feedback gains are obtained. The designed robust control strategy can easily handle the variations of the backlash angle and load disturbance torque. A simulated two-mass backlash system verifies the efficiency of the designed control law.

LPV modeling and position control of two mass systems with variable backlash using LMIs