Stabilizing a nonlinear controlled system for steady-state motions in the critical case of a double zero root

1967 ◽  
Vol 31 (5) ◽  
pp. 981-986 ◽  
Author(s):  
N.V. Stoianov
Keyword(s):  
Steady State ◽  
Critical Case ◽  
Double Zero ◽  
Controlled System ◽  
Nonlinear Controlled System

Induction Suspension of Conductive Microring and Its Gyroscopic Stabilization

2021 ◽  
Author(s):  
Dmitrii Skubov ◽  
Ivan Popov ◽  
Pavel Udalov
Keyword(s):  
Magnetic Field ◽  
Steady State ◽  
Eddy Current ◽  
Equilibrium Position ◽  
Critical Case ◽  
Conservative System ◽  
Critical Value ◽  
Main Task ◽  
Gyroscopic Stabilization

Abstract The main task of our work is determination of possible levitation of micro-ring with eddy current in magnetic field of down ring with set alternating current and determination of critical value of «ohmic» damping separated field of parameters, at which motions of suspension ring transit from divergent to meeting to steady-state equilibrium position. I. e. in this critical case the motion practically coincides with motions of conservative system. The possibility of gyroscopic stabilization of suspension ring taking into account initial set rotation is considered. Thereby it can serve as contactless micro-gyroscope.

LIMIT CYCLING IN AN OBSERVER-BASED CONTROLLED SYSTEM WITH FRICTION: NUMERICAL ANALYSIS AND EXPERIMENTAL VALIDATION

2004 ◽  
Vol 14 (09) ◽  
pp. 3083-3093 ◽  
Author(s):  
DEVI PUTRA ◽  
HENK NIJMEIJER
Keyword(s):  
Steady State ◽  
Numerical Analysis ◽  
Bifurcation Analysis ◽  
Laboratory Experiments ◽  
Experimental Validation ◽  
Friction Compensation ◽  
Controlled System ◽  
The Cost ◽  
Controlled Mechanical Systems ◽  
Cycling Behavior

This paper investigates limit cycling behavior of observer-based controlled mechanical systems with friction compensation. The limit cycling is induced by the interaction between friction and friction compensation, which is based on the estimated velocity. The limit cycling phenomenon, which is experimentally observed in a rotating arm manipulator, is analyzed through computational bifurcation analysis. The computed bifurcation diagram confirms that the limit cycles can be eliminated by enlarging observer gains and controller gains at the cost of a steady state error. The numerical results match well with laboratory experiments.

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