Download Abstracts

acta mechanica et automatica, vol.2 no.2 (2008)
ABSTRACTS
Mikołaj Busłowicz
Robust stability of convex combination of two fractional degree characteristic polynomials
The paper considers the problem of robust stability of convex combination of two fractional degree characteristic polynomials. This problem
is equivalent to the problem of robust stability of linear continuous-time fractional systems with characteristic polynomial linearly dependent
on one uncertain parameter. Frequency domain methods for robust stability analysis of such a combination are given. The methods proposed
are based on the Zero Exclusion Condition known from the theory of robust stability of families of natural degree polynomials. The considerations
are illustrated by numerical example.
Giancarlo Genta , Andrea Festini, Xavier Delepine
From oil to magnetic fields: active and passive vibration control
When a reduction of vibration amplitude usually designers resort to dampers based either on dry friction, internal material damping or fluid viscosity,
each one of these mechanisms having its peculiar field of application. To improve performance while at the same time reducing costs
and environmental load, electromagnetic damping devices are finding new applications, beyond the fields where they have a long history. Moreover,
electromagnetic dampers can be easily controlled, obtain active or even ‘intelligent’ vibration control. Three examples from the internal combustion
engines, automotive and gas turbine fields are discussed in some detail to show the potential advantages of this technology.
Keywords: Vibration control, eddy current dampers, active damping.
Zdzisław Gosiewski
Control-oriented modeling and control of rotor vibration
Deep analysis of the control plant brings many useful information for the designer of the control system. The analysis is also important part
in the design of active vibration control system. The coupling of different dynamical phenomena in rotating machinery leads to unstable vibrations.
Usually, the coupling effects are caused by changing parameters. Angular speed or rotor unbalance in some applications are such parameters which
change in the wide range. The problem is to find for which angular speeds we have unstable torsional/lateral vibrations. Usually, the unstable regions
are in the vicinity of angular speeds where maps of natural frequencies for both dynamical systems cross each other. In the paper there was explained
which intersection of torsional and lateral natural frequencies are unstable and why. The root locus method was used to explain the phenomenon.
It indicated such control procedures which amplify the positive (stabilizing) mechanisms in the rotor dynamics. Such procedures can also lead to
the energy saving control laws. In the case of lateral vibrations there were considered four control strategies. And these strategies were compared
to indicate optimal one.
Zdzisław Gosiewski, Grzegorz Michałowski
H∞ control of robot arm with hydraulic drive
In the paper an H∞ velocity control of the robot arm in combination with the hydraulic drive is presented. The open-loop system consists
of a manipulator with one rotary degree of freedom, a hydraulic servomotor, and an electrohydraulic amplifier. The mathematical model
of the system is derived. Due to the nonlinearity in the model, which is caused by varying operating point parameters and the direction of the
servomotor motion, the model of multiplicative uncertainty was defined. The plant model transfer function parameters were assumed to be variable.
To limit error signal, control signal, and output signal three weighting functions were designed. The simulation results of the designed H∞ optimal
closed-loop system were compared to the standard PID closed-loop system. The solution ensuring robust performance was achieved and proved.
Tadeusz Kaczorek
Realization problem for singular positive single-input single-output continuous-time systems with delays in state and in inputs
The positive realization problem for singular continuous-time linear single-input single-output systems with delays in state and in inputs is addressed.
The notion of canonical forms of matrices are extended for singular linear systems with delays. Necessary and sufficient conditions for positivity
of the singular continuous-time systems with delays and sufficient conditions for the existence of a positive singular realization are established.
A procedure for computation of a positive singular realization of a given transfer function is proposed and illustrated by a numerical example.
Tadeusz Kaczorek
Positive different orders fractional 2D linear systems
A new class of positive different orders fractional 2D linear systems is introduced. A notion of (α, β) orders difference of 2D function is proposed.
Fractional 2D state equations of linear systems are given and their solutions are derived using 2D Z-transform. The classical Cayley-Hamilton
theorem is extended to the 2D fractional linear systems. Neccesary and sufficient conditions for the positivity, reachability and controllability to zero
of the fractional 2D linear systems are established.
Tadeusz Kaczorek, Vladimir Marchenko, Łukasz Sajewski
Solvability of 2D hybrid linear systems – comparison of three different methods
A class of positive hybrid linear systems is introduced. Three different methods for computation of solutions of the hybrid system are proposed.
The considerations are illustrated by numerical example. Simulations of solution have been shown for the methods.
89
acta mechanica et automatica, vol.2 no.2 (2008)
Jerzy T. Sawicki
Rationale for mu-synthesis control of flexible rotor-magnetic bearing systems
The emergence of sophisticated formal control synthesis tools provokes important questions for any prospective user: why learn to use these new
tools, what will they offer me? In synthesis of magnetic bearing controllers, it turns out that the range of stabilizing controllers is often quite narrow
so that the difference between a poor controller and an “optimal” one may be small. Hence, the product of formal control synthesis tools often looks
and performs much like what a reasonably clever control engineer would produce by hand. This paper demonstrates that the real value of these tools
lies in a) generation of a performance benchmark which can be used to firmly establish the best performance relative to a specification and b) change
of design parameter space to one which is relatively easy to maintain and represents a durable investment from an engineering process view.
Krzysztof Sibilski
Microelectromechanical flying robots - state of the art
Micro Air Vehicles (MAVs) are miniature airplanes constructed from state-of-the-art materials, designed to be small, light, and highly resilient.
Current applications include surveillance, reconnaissance, and munitions. Many of the planes, because of their size, have unconventional designs
with respect to the wings and control surfaces. Instability introduced by the small non-traditional aircraft designs must be addressed, to eliminate
the need for an expert pilot for aircraft control and navigation. In this paper we present a state-of-the-art technology development focused
on the technologies and components required to enable flight at small scales, including flight control, power and propulsion, navigation,
multi-purpose structures, advanced communications and information systems, Micro-electro-mechanical Systems (MEMS), advanced sensors,
and lightweight, efficient high-density power sources.
90