Hidden modes of two degrees of freedom systems in control design

1990 ◽  
Vol 35 (4) ◽  
pp. 502-506 ◽  
Author(s):  
O.R. Gonzalez ◽  
P.J. Antsaklis
Keyword(s):  
Degrees Of Freedom ◽  
Control Design ◽  
Two Degrees Of Freedom

Lyapunov Functions and Sliding Mode Control for Two Degrees-of-Freedom and Multidegrees-of-Freedom Fractional Oscillators

2016 ◽  
Vol 139 (1) ◽  
Author(s):  
Youan Zhang ◽  
Jian Yuan ◽  
Jingmao Liu ◽  
Bao Shi
Keyword(s):  
Differential Equations ◽  
Sliding Mode Control ◽  
Lyapunov Functions ◽  
Degrees Of Freedom ◽  
Sliding Mode ◽  
Equations Of Motion ◽  
Control Design ◽  
State Equations ◽  
Two Degrees Of Freedom ◽  
Mode Control

This paper addresses the Lyapunov functions and sliding mode control design for two degrees-of-freedom (2DOF) and multidegrees-of-freedom (MDOF) fractional oscillators. First, differential equations of motion for 2DOF fractional oscillators are established by adopting the fractional Kelvin–Voigt constitute relation for viscoelastic materials. Second, a Lyapunov function candidate for 2DOF fractional oscillators is suggested, which includes the potential energy stored in fractional derivatives. Third, the differential equations of motion for 2DOF fractional oscillators are transformed into noncommensurate fractional state equations with six dimensions by introducing state variables with physical significance. Sliding mode control design and adaptive sliding mode control design are proposed based on the noncommensurate fractional state equations. Furthermore, the above results are generalized to MDOF fractional oscillators. Finally, numerical simulations are carried out to validate the above control designs.

The scientific bases of autocontrol with vibration phase for a resonance beating-vibration system with two degrees of freedom driven by debalances

1996 ◽  
Vol 18 (2) ◽  
pp. 43-48
Author(s):  
Tran Van Tuan ◽  
Do Sanh ◽  
Luu Duc Thach
Keyword(s):  
Degrees Of Freedom ◽  
Regulation System ◽  
Vibration System ◽  
Two Degrees Of Freedom ◽  
System Operating

In the paper it is introduced a method for studying dynamics of beating-vibrators by means of digital calculation with the help of the machine in accordance with the needs by the helps of an available auto regulation system operating with high reability.

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