Janos Turi

Frequency domain analysis and robust control design for an ideal flexible beam

We study the problem of designing a feedback controller for a highly flexible Euler-Bernoulli beam using a distributed-parameter H∞-method. Employing skew Toeplitz theory, we derive the H∞-optimal controller for a weighted mixed sensitivity design for the beam. Based on the structure of the optimal controller we obtain suboptimal, finite-dimensional, linear, time-invariant controllers. With this approach we are able to include the added difficulties of a pure time delay and a noncollocated actuator/sensor pair directly into the design process.

Approximate stability charts for milling processes using semi-discretization

Unwanted relative vibrations between the tool and the workpiece represent significant challenges in high-speed machining. In order to avoid this problem, one needs to specify ranges for system parameters (spindle speed, depth of cut) for which the process is stable, i.e., to obtain a so-called stability chart. Such stability charts usually can only be given by numerical means which is illustrated in the paper for a single degree of freedom model of milling. In this paper, we establish the convergence of the semi-discretization approximation method for a class of delay equations modeling the milling process. Moreover, we show that semi-discretization preserves asymptotic stability of the original equation, thus it can be used to obtain good approximations for the stability charts.

Numerical approximations for a class of differential equations with time- and state-dependent delays

Abstract We establish limiting relations between solutions for a large class of functional differential equations with time- and state-dependent delays and solutions of appropriately selected sequences of approximating delay differential equations with piecewise constant arguments. The approximating equations, generated in the above process, lead naturally to discrete difference equations, well suited for computational purposes, and thus provide an approximation framework for simulation studies.

Applications of exact linearization techniques for steady-state stability enhancement in a weak AC/DC system

A nonlinear control strategy to improve the steady-state stability of a weak AC/DC power system is presented. The approach is based on the extension of feedback linearization techniques to nonlinear descriptor system models. This method produces a nonlinear control strategy which is capable of enhancing system performance for various system operating conditions. The control law is determined and simulation results are given. >

On existence, uniqueness and numerical approximation for neutral equations with state-dependent delays

Abstract We consider a class of neutral functional differential equations with state-dependent delays, and discuss existence, uniqueness, and numerical approximation of solutions of corresponding initial value problems.

State dependent regenerative delay in milling processes

Traditional models of regenerative machine tool chatter use constant time delays assuming that the period between two subsequent cuts is a constant determined definitely by the spindle speed. These models result in delay-differential equations with constant time delay. If the vibrations of the tool relative to the workpiece are also includedin thesurface regenerationmodel, thentheresulted time delay is not constant, but it depends on the actual and a delayed position of the tool. In this case, the governing equation is a delay-differential equation with state dependent time delay. Equations with state dependent delays can not be linearized in the traditional sense, but there exists linear equations that can be associated to them. This way, the local behavior of the system with state dependent delays can be investigated. In this study, a two degree of freedom model is presented for milling process. A thorough modeling of the regeneration effect results in the governingdelay-differentialequationwith state dependent time delay. It is shown through the linearization of the nonlinear equation that an additional term arises in the linearized equation of motion due to the state-dependency of the time delay.

DYNAMICS OF PIECEWISE LINEAR DISCONTINUOUS MAPS

In this paper, the dynamics of maps representing classes of controlled sampled systems with backlash are examined. First, a bilinear one-dimensional map is considered, and the analysis shows that, depending on the value of the control parameter, all orbits originating in an attractive set are either periodic or dense on the attractor. Moreover, the dense orbits have sensitive dependence on initial data, but behave rather regularly, i.e. they have quasiperiodic subsequences and the Lyapunov exponent of every orbit is zero. The inclusion of a second parameter, the processing delay, in the model leads to a piecewise linear two-dimensional map. The dynamics of this map are studied using numerical simulations which indicate similar behavior as in the one-dimensional case.

Robust control design for a flexible beam using a distributed-parameter H/sup infinity /-method

A skew Toeplitz theory is used to derive the H/sup infinity /-optimal controller for a weighted mixed sensitivity design for a free-free Euler-Bernoulli beam. On the basis of the structure of the optimal controller, low-order, suboptimal, finite-dimensional, linear, time-invariant controllers are designed for the beam with and without a pure time delay.<<ETX>>

Stability, instability in delay equations modeling human respiration.

A system of delay equations describing a simple model of the respiratory control mechanism in humans is considered and conditions guaranteeing stability, instability of steady-state equilibrium solutions of that system are presented.

An observer for a nonlinear descriptor system

The present study is motivated by previous work which sought input-output linearizing control laws for AC/DC power systems, which are modeled in the nonlinear DAE framework. Simulation studies verified the effectiveness of these control strategies when all the descriptor variables were assumed available for feedback. In the present work, the authors consider measurement limitations and attempt to reconstruct the descriptor variables with a nonlinear observer. Sufficient conditions are derived for the construction of an asymptotic observer and, although these conditions are somewhat restrictive for large-scale systems, they provide some insight toward a design for the particular application considered here (a) single-machine AC/DC power system). Some simulation results are provided along with a discussion of some interesting features of this problem which may warrant further investigation.<<ETX>>