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Comparison of linear control methods for an AMB system

Wojciech Grega, Adam Pilat (2005)

International Journal of Applied Mathematics and Computer Science

The contactless nature of active magnetic bearings brings about many advantages over the conventional bearing while industrial real-time applications are often limited by the significant complexity of control algorithms. This paper presents the application of an LQ controller to an active magnetic bearing system (AMB). Two control strategies are presented and compared: local and global. In the first case the rotor is modelled as two separated masses located at the bearing. In the second case rotor...

Computation of realizations composed of dynamic and static parts of improper transfer matrices

Tadeusz Kaczorek (2007)

International Journal of Applied Mathematics and Computer Science

The problem of computing minimal realizations of a singular system decomposed into a standard dynamical system and a static system of a given improper transfer matrix is formulated and solved. A new notion of the minimal dynamical-static realization is introduced. It is shown that there always exists a minimal dynamical-static realization of a given improper transfer matrix. A procedure for the computation of a minimal dynamical-static realization for a given improper transfer matrix is proposed...

Constrained robust adaptive stabilization for a class of lower triangular systems with unknown control direction

Jianglin Lan, Weijie Sun, Yunjian Peng (2014)

Kybernetika

This paper studies the constrained robust adaptive stabilization problem for a class of lower triangular systems with unknown control direction. A robust adaptive feedback control law for the systems is proposed by incorporating the technique of Barrier Lyapunov Function with Nussbaum gain. Such a controlled system arises from the study of the constrained robust output regulation problem for a class of output feedback systems with the unknown control direction and a nonlinear exosystem. An application...

Construction of algebraic and difference equations with a prescribed solution space

Lazaros Moysis, Nicholas P. Karampetakis (2017)

International Journal of Applied Mathematics and Computer Science

This paper studies the solution space of systems of algebraic and difference equations, given as auto-regressive (AR) representations A(σ)β(k) = 0, where σ denotes the shift forward operator and A(σ) is a regular polynomial matrix. The solution space of such systems consists of forward and backward propagating solutions, over a finite time horizon. This solution space can be constructed from knowledge of the finite and infinite elementary divisor structure of A(σ). This work deals with the inverse...

Continuous dependence on parameters and boundedness of solutions to a hysteresis system

Alexander M. Kamachkin, Dmitriy K. Potapov, Victoria V. Yevstafyeva (2022)

Applications of Mathematics

We analyze an ordinary differential system with a hysteresis-relay nonlinearity in two cases when the system is autonomous or nonautonomous. Sufficient conditions for both the continuous dependence on the system parameters and the boundedness of the solutions to the system are obtained. We give a supporting example for the autonomous system.

Continuous-time periodic systems in H 2 and H ∞ . Part I: Theoretical aspects

Patrizio Colaneri (2000)

Kybernetika

The paper is divided in two parts. In the first part a deep investigation is made on some system theoretical aspects of periodic systems and control, including the notions of H 2 and H ∞ norms, the parametrization of stabilizing controllers, and the existence of periodic solutions to Riccati differential equations and/or inequalities. All these aspects are useful in the second part, where some parametrization and control problems in H 2 and H ∞ are introduced and solved.

Controllability of linear impulsive matrix Lyapunov differential systems with delays in the control function

Vijayakumar S. Muni, Raju K. George (2018)

Kybernetika

In this paper, we establish the controllability conditions for a finite-dimensional dynamical control system modelled by a linear impulsive matrix Lyapunov ordinary differential equations having multiple constant time-delays in control for certain classes of admissible control functions. We characterize the controllability property of the system in terms of matrix rank conditions and are easy to verify. The obtained results are applicable for both autonomous (time-invariant) and non-autonomous (time-variant)...

Controlling a non-homogeneous Timoshenko beam with the aid of the torque

Grigory M. Sklyar, Grzegorz Szkibiel (2013)

International Journal of Applied Mathematics and Computer Science

Considered is the control and stabilizability of a slowly rotating non-homogeneous Timoshenko beam with the aid of a torque. It turns out that the beam is (approximately) controllable with the aid of the torque if and only if it is (approximately) controllable. However, the controllability problem appears to be a side-effect while studying the stabilizability. To build a stabilizing control one needs to go through the methods of correcting the operators with functionals so that they have finally...

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