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A multi‐input/multi‐output optimal PI controller for redundant robots in the presence of flexible disturbances
Author(s) -
Barbieri Enrique
Publication year - 1994
Publication title -
optimal control applications and methods
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.458
H-Index - 44
eISSN - 1099-1514
pISSN - 0143-2087
DOI - 10.1002/oca.4660150104
Subject(s) - control theory (sociology) , pid controller , algebraic number , lti system theory , linear quadratic regulator , quadratic equation , controller (irrigation) , planar , optimal control , mathematics , set (abstract data type) , constant (computer programming) , algebraic equation , robot , invariant (physics) , linear system , algebraic riccati equation , computer science , riccati equation , mathematical optimization , control engineering , control (management) , engineering , nonlinear system , mathematical analysis , differential equation , artificial intelligence , computer graphics (images) , temperature control , biology , geometry , quantum mechanics , agronomy , programming language , physics , mathematical physics
The two‐stage synthesis of a multi‐input/multi‐output optimal proportional‐integral (PI) controller is described for linear, time‐invariant systems. In the first stage the PI controller is designed by solving a steady state algebraic Riccati equation. As a result, the optimal cost is expressed in terms of the system's constant output set‐points. In the second stage the cost is further reduced by optimally selecting the output set‐points to minimize a static quadratic performance index subject to linear algebraic constraints. The design framework is applied to a planar redundant robotic manipulator equipped with four joints and mounted at the tip of a long flexible arm. We then address the problem of self‐motion control in the presence of vibratory disturbances.