Baran Alikoc

An Experimental Study for Delay-Independent State-Feedback Controller Design

Abstract In this study, a method for determining delay-independent stability zones of the general LTI dynamics with multiple delays against parametric uncertainties is presented. The method is utilized to design a delay-independent state-feedback controller and verified experimentally for a two-tank liquid level control system. The method is based on extended kronecker summation(EKS) to investigate controller parameter space for delay-independent stability(DIS) of the system. The main aim of the paper is recalling a new sufficient condition for determination of controller parameter space for DIS and presenting the application of methodology for a physical experimental case study.

Stability Analysis of Train Following Model with Multiple Communication Delays

Abstract In dense traffic regions, moving block railway signalization systems are utilized instead of fixed block systems. In a moving block approach, exact location of the consequent trains has to be determined which brings stability problem of keeping safe distance headway between the trains. In this study, the train following problem with multiple communication time delays between the trains and the wayside control unit is handled. The problem is modeled as a linear time invariant multiple time delay system (LTI-MTDS) for two different scenarios. Stability boundaries with respect to time delays for an appropriate following distance are obtained by using the Cluster Treatment of Characteristic Roots (CTCR) Technique with Extended Kronecker Summation Method and the results are validated via simulations.

A New Delayed Resonator Design Approach for Extended Operable Frequency Range

The operable frequency range of the Delayed Resonators (DR) is known to be narrow due to stability issues. This study presents a novel approach for DR design with a combined feedback strategy that consists of a delayed velocity and non-delayed position feedback to extend the operable frequency range of the DR method. The non-delayed position feedback is used to alter the natural frequency of the DR artificially while delayed velocity feedback is employed to tune the frequency of DR matching with the undesired vibrations. The proposed method also introduces an optimization parameter that provides freedom for the designer to obtain fast vibration suppression while improving the stability range of the DR. An 1 Corresponding Author * The author conducted this research in part while he was with Control and Automation Eng. Dept., Istanbul Technical University.

A Polynomial Method for Stability Analysis of LTI Systems Independent of Delays

A new method providing necessary and sufficient conditions to test delay-independent stability for general linear time-invariant systems with constant delays is proposed. The method is utilized for single delay and incommensurate multiple delay systems. The proposed method offers an approach to determine the exact boundaries of unknown parameters such as controller gains or system parameters ensuring delay-independent stability, in addition to exhibiting an efficient test for real parameters. The technique is based on nonexistence of unitary complex zeros of an auxiliary characteristic polynomial obtained via extended Kronecker summation. A special feature of the polynomial, i.e., the self-inversive property, is proved and utilized to check its unitary zeros to determine delay-independent stability by an efficient zero location test. The methodology is executed employing simple algebraic operations and inspection of the number of sign variations in the obtained sequence. For the single delay case, the pro...

Stability regions for synchronized τ-periodic orbits of coupled maps with coupling delay τ

Motivated by the chaos suppression methods based on stabilizing an unstable periodic orbit, we study the stability of synchronized periodic orbits of coupled map systems when the period of the orbit is the same as the delay in the information transmission between coupled units. We show that the stability region of a synchronized periodic orbit is determined by the Floquet multiplier of the periodic orbit for the uncoupled map, the coupling constant, the smallest and the largest Laplacian eigenvalue of the adjacency matrix. We prove that the stabilization of an unstable τ-periodic orbit via coupling with delay τ is possible only when the Floquet multiplier of the orbit is negative and the connection structure is not bipartite. For a given coupling structure, it is possible to find the values of the coupling strength that stabilizes unstable periodic orbits. The most suitable connection topology for stabilization is found to be the all-to-all coupling. On the other hand, a negative coupling constant may lead to destabilization of τ-periodic orbits that are stable for the uncoupled map. We provide examples of coupled logistic maps demonstrating the stabilization and destabilization of synchronized τ-periodic orbits as well as chaos suppression via stabilization of a synchronized τ-periodic orbit.

Level control of a coupled-tank system via eigenvalue assignment and LQG control

This paper presents the state-space modeling and control of a coupled-tank liquid level system. Observed-state feedback controller via eigenvalue assignment and LQG control are designed in discrete-time and implemented by an industrial controller PLC. Both control design methods are augmented with integral action for a reference tracking without steady-state error for step inputs. The aim of the study is to examine the control performances of the methods subject to reference tracking, noise attenuation, disturbance rejection. The experimental results are presented and discussed for this purpose.

Reduced order digital controller design for plants with large time delays

In process control, inherited large time delays both in feedback line and actuator dynamics compromise the stability and the performance of the system especially with the fast acting controllers. The new method utilizes Kronecker multiplication and palindromic polynomials to reduce the order of the characteristic equation to ease the digital controller design. Furthermore, the method facilitates rightmost root placement to implement controllers which increases the performance of the control action. In this study, we present the new controller design method and its application on an industrial experimental case.