Point mapping method in investigating the dynamics of relay stabilization with account for nonlinearity of the speed sensor, delays, and time-independent perturbation

2021 ◽  
Author(s):  
R.P. Simonyants ◽  
V.N. Bulavkin
Keyword(s):  
Limit Cycles ◽  
Dead Zone ◽  
Mapping Method ◽  
General Purpose ◽  
Point Mapping ◽  
Speed Sensor ◽  
Literary Sources ◽  
The Dead ◽  
Phase Surface ◽  
Analytical Expressions

Using the point mapping method, we obtained analytical expressions for the first return functions for determining simple and complex attractors in the stabilization mode by a general-purpose relay controller with the linear formation of the control signal. We investigated self-oscillations with account for the operating members’ aftereffect, the dead zone of the speed sensor, and the time-independent perturbation action. The study shows that the dead zone of the speed sensor introduces significant changes in the behavior of the system, giving it new properties. The analysis of dynamic processes on a three-sheet phase surface revealed a wide variety of limit cycles and their dependence on the system’s parameters. Complex limit cycles are represented by combining simple cycles of two types, which allowed for a simplifying approach to their search based on the theory of multidimensional transformations of Yu.I. Neymark. A more complete result was obtained in comparison with the well-known literary sources.

Improved Pole-placement Control with Feed-forward Dead Zone Compensation for Position Tracking of Electro-Pneumatic Actuator System Improved Pole-placement Control with Feed-forward Dead Zone Compensation for Position Tracking of Electro-Pneumatic Actuato

2021 ◽  
Vol 20 (2) ◽  
pp. 25-32
Author(s):  
Noorhazirah Sunar ◽  
Mohd Fua’ad Rahmat ◽  
Ahmad ‘Athif Mohd Fauzi ◽  
Zool Hilmi Ismail ◽  
Siti Marhanis Osman ◽  
...  
Keyword(s):  
Dead Zone ◽  
Pneumatic Actuator ◽  
Pole Placement ◽  
Position Tracking ◽  
Zone Model ◽  
Feed Forward ◽  
The Dead ◽  
Chattering Effect ◽  
Pole Placement Controller ◽  
Pole Placement Control

Dead-zone in the valve degraded the performances of the Electro-Pneumatic Actuator (EPA) system.  It makes the system difficult to control, become unstable and leads to chattering effect nearest desired position.  In order to cater this issue, the EPA system transfer function and the dead-zone model is identified by MATLAB SI toolbox and the Particle Swarm Optimization (PSO) algorithm respectively.  Then a parametric control is designed based on pole-placement approach and combine with feed-forward inverse dead-zone compensation.  To reduce chattering effect, a smooth parameter is added to the controller output.  The advantages of using these techniques are the chattering effect and the dead-zone of the EPA system is reduced.  Moreover, the feed-forward system improves the transient performance.  The results are compared with the pole-placement control (1) without compensator and (2) with conventional dead-zone compensator.  Based on the experimental results, the proposed controller reduced the chattering effect due to the controller output of conventional dead-zone compensation, 90% of the pole-placement controller steady-state error and 30% and 40% of the pole-placement controller with conventional dead-zone compensation settling time and rise time.

Piecewise Nonlinear Energy Sink

2015 ◽  
Author(s):  
Mohammad A. Al-Shudeifat
Keyword(s):  
Dead Zone ◽  
Linear Structure ◽  
Nonlinear Energy Sink ◽  
Viscous Damping ◽  
Nonlinear Stiffness ◽  
Flexible Design ◽  
Energy Inputs ◽  
Energy Sink ◽  
The Dead ◽  
Nonlinear Energy

Symmetric piecewise nonlinearities are employed here to design highly efficient nonlinear energy sink (NES). These symmetric piecewise nonlinearities are usually called in the literature as dead-zone nonlinearities. The proposed dead-zone NES includes symmetric clearance about its equilibrium position in which zero stiffness and linear viscous damping are incorporated. At the boundaries of the symmetric clearance, the NES is coupled to the linear structure by either linear or nonlinear stiffness components in addition to similar viscous damping to that in the clearance zone. By this flexible design of the dead-zone NES, we obtain a considerable enhancement in the NES efficiency at moderate and severe energy inputs. Moreover, the dead-zone NES is also found here through numerical simulations to be more robust for damping and stiffness variations than the linear absorber and some other types of NESs.

scholarly journals Experimental investigation on steady granular flows interacting with an obstacle down an inclined channel: study of the dead zone upstream from the obstacle. Application to interaction between dense snow avalanches and defence structures

2002 ◽  
Vol 2 (3/4) ◽  
pp. 187-191 ◽  
Author(s):  
T. Faug ◽  
P. Lachamp ◽  
M. Naaim
Keyword(s):  
Experimental Investigation ◽  
Dead Zone ◽  
Granular Flows ◽  
Friction Angle ◽  
Snow Avalanches ◽  
Zone Length ◽  
Inclined Channel ◽  
Zone Of Influence ◽  
The Dead ◽  
Obstacle Height

Abstract. An experimental investigation with dry granular flows passing over an obstacle down a rough inclined channel has been performed. The aim is to improve our understanding of the interaction between dense snow avalanches and defence structures. Specific attention was directed to the study of the zone of influence upstream from the obstacle, linked to the formation of a dead zone. The dead zone length L was systematically measured as a function of the obstacle height H and the channel inclination θ, for several discharges. In a whole range of channel inclinations, all the data are shown to collapse into a single curve when properly scaled. The scaling is based on the introduction of a theoretical deposit length (depending on H, θ and the internal friction angle of the material, φ) and a Froude number of the flow depending on the obstacle height.

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