5 research outputs found
Some Special Cases in the Stability Analysis of Multi-Dimensional Time-Delay Systems Using The Matrix Lambert W function
This paper revisits a recently developed methodology based on the matrix
Lambert W function for the stability analysis of linear time invariant, time
delay systems. By studying a particular, yet common, second order system, we
show that in general there is no one to one correspondence between the branches
of the matrix Lambert W function and the characteristic roots of the system.
Furthermore, it is shown that under mild conditions only two branches suffice
to find the complete spectrum of the system, and that the principal branch can
be used to find several roots, and not the dominant root only, as stated in
previous works. The results are first presented analytically, and then verified
by numerical experiments
Interpolatory -optimality Conditions for Structured Linear Time-invariant Systems
Interpolatory necessary optimality conditions for -optimal
reduced-order modeling of unstructured linear time-invariant (LTI) systems are
well-known. Based on previous work on -optimal reduced-order
modeling of stationary parametric problems, in this paper we develop and
investigate optimality conditions for -optimal reduced-order
modeling of structured LTI systems, in particular, for second-order,
port-Hamiltonian, and time-delay systems. We show that across all these
different structured settings, bitangential Hermite interpolation is the common
form for optimality, thus proving a unifying optimality framework for
structured reduced-order modeling.Comment: 20 page
TUNING PD AND PID CONTROLLERS VIA THE LAMBERT W FUNCTION FOR DOUBLE INTEGRATOR PLUS DEAD TIME PROCESSES
The paper explores the Proportional-derivative controller for a double integrator plus dead time processes, which is a challenging control problem, that is designed based on the existing Proportional-integrative controller for integrator plus dead time processes. The PD controller is extended with an integral action and an ideal PID controller is received. The parameters of both controllers are received by using the pole placement technique, whereby the transcendent characteristics equation of the closed loop system is solved by using the Lambert W function. The paper also examines the influence of the desired poles of the system with a closed feedback as well as the influence of the disturbance and the change of the DIPTD processes parameters onto the received control system performances. The results received by simulation, and the quantitative indicators, show that the proposed control system has better performances in comparison to the control systems obtained by other methods in literature