A control scheme is designed for the purpose of suppression of vibratory motion of a dynamical system. The efficacy and robustness of the controller vis a vis unknown but bounded disturbances and state measurement errors is investigated analytically and numerically. As an example of a dynamical system we consider a single degree of freedom mass—spring—damper system that is excited by an unknown force. The control scheme presupposes that the spring and damping coefficients can be varied within prescribed bounds, albeit not independently. The construction of such a semiactive controller can be realized by using the properties of so calledelectrorheological fluids (see [1] for relevant experimental investigations). The called for changes in spring and damping properties can be effected in microseconds since the control does not involve the separate dynamics (inertia) of usual actuators. The design of the controller is based on Lyapunov stability theory which is also utilized to investigate the stabilizing properties of the controller. To accommodate state measurement errors the proposed control scheme is combined with afuzzy control concept. Simulations are carried out for examples of periodic, continuous nonperiodic, discontinuous periodic and random excitation forces.
[1]
Peter Hagedorn,et al.
On the Active Control of Rotors with Uncertain Parameters
,
1986
.
[2]
Eduard Reithmeier,et al.
Semiaktive Regelung zur Amplitudenunterdrückung von Schwingungssystemen unter Einsatz elektrorheologischer Flüssigkeiten
,
1993
.
[3]
Witold Pedrycz,et al.
Fuzzy control and fuzzy systems
,
1989
.
[4]
F. Küçükay,et al.
Optimierung des Isolationsverhaltens von Lagerungen bei Maschinenbauteilkomplexen
,
1988
.
[5]
G. Leitmann.
On the Efficacy of Nonlinear Control in Uncertain Linear Systems
,
1981
.
[6]
H. Conrad,et al.
Vibration Characteristics of a Composite Beam Containing an Electrorheological Fluid
,
1990
.
[7]
G. Leitmann.
Guaranteed Asymptotic Stability for Some Linear Systems With Bounded Uncertainties
,
1979
.