Relative Stability Analysis of Closed-Loop SISO Dead-Time Systems: non-imaginary axis case

Continuation Based Computation of Root-Locus for SISO Dead-Time Systems

We present a numerical method to plot the root-locus of Single-Input-Single-Output (SISO) dead-time systems on a given right half-plane up to a predefined controller gain. We compute the starting and intersection points of root-locus inside the region and we obtain the root-loci of each root based on a predictor-corrector type continuation method. The method is effective for high-order SISO dead-time systems.

Root Locus for SISO Dead-Time Systems: A Continuation Based Approach

We present a numerical method to plot the root locus of Single-Input-Single-Output (SISO) dead-time systems with respect to the controller gain or the system delay. We compute the trajectories of characteristic roots of the closed-loop system on a prescribed complex right half-plane. We calculate the starting, branch and boundary crossing roots of root-locus branches inside the region. We compute the root locus of each characteristic root based on a predictor-corrector type continuation method. To avoid the high sensitivity of roots with respect to the locus parameter in the neighborhood of br…

Computation of Extremum Singular Values and the Strong H-infinity Norm of SISO Time-Delay Systems

We consider the computation of H-infinity norms for Single-Input-Single-Output (SISO) time-delay systems, which are described by delay differential algebraic equations. Unlike the iterative level set methods in the literature, we present a novel numerical method to compute the H-infinity norm. This method requires solving one eigenvalue problem of at most twice the size of the eigenvalue problem in every iteration of a level set method, but in practice often considerably lower. We first show that the computation of extrema of the transfer function can be turned into the computation of the imag…

On the achievable degree of stability in strictly negative imaginary state feedback control

In this paper we study the problem of determining the largest degree of stability that can be achieved for SISO systems using negative imaginary state feedback control. A state feedback result is given for synthesising a controller for a plant such that a given closed-loop transfer function is strictly negative imaginary with a prescribed degree of stability. By varying a parameter, the placement of the closed-loop system poles can be adjusted to give a prescribed degree of stability. We show the achievable degree of stability is related to the zero locations of the transfer function from the …

从稳定区域到认证控制器：消除时滞对象统一PID/PI分析中的选择缺口

From Stabilizing Regions to Certified Controllers: Closing the Selection Gap in Unified PID/PI Analysis for Time-Delay Plants

针对时滞对象统一PID调参方法中手动测试不稳定性极点计数和控制器选择的问题，本文提出解析极点计数、基于最小调节时间的时域选择规则，并揭示中性类型陷阱，实现完全自动化与控制器认证。