8 research outputs found
Robust stability of integral delay systems with exponential kernels
"In this chapter the stability analysis via Lyapunov-Krasovskii method is extended to perturbed integral delay systems with exponential kernels. Several sufficient robust stability conditions given in the form of linear matrix inequalities are derived.
Stability conditions for integral delay systems
"In this paper we consider a special class of integral delay systems arising in several stability problems of timeâdelay systems. For these integral systems we derive stability and robust stability conditions in terms of LyapunovâKrasovskii functionals. More explicitly, after providing the stability conditions we compute quadratic functionals and apply them to derive exponential estimates for solutions, and robust stability conditions for perturbed integral delay systems.
New results on robust exponential stability of integral delay systems
"The robust exponential stability of integral delay systems with exponential kernels is investigated. Sufficient delay-dependent robust conditions expressed in terms of linear matrix inequalities and matrix norms are derived by using the LyapunovâKrasovskii functional approach. The results are combined with a new result on quadratic stabilisability of the state-feedback synthesis problem in order to derive a new linear matrix inequality methodology of designing a robust non-fragile controller for the finite spectrum assignment of input delay systems that guarantees simultaneously a numerically safe implementation and also the robustness to uncertainty in the system matrices and to perturbation in the feedback gain.
Output Strictly Passive Control of Uncertain Singular Neutral Systems
This paper concerns the problem of output strictly passive control for uncertain singular neutral systems. It introduces a new effective criterion to study the passivity of singular neutral systems. Compared with the previous approach, this criterion has no equality constraints. And the state feedback controller is designed so that the uncertain singular neutral systems are output strictly passive. In terms of a linear matrix inequality (LMI) and Lyapunov function, the strictly passive criterion is formulated. And the desired passive controller is given. Finally, an illustrative example is given to demonstrate the effectiveness of the proposed approach
A Review of Some Subtleties of Practical Relevance
This paper reviews some subtleties in time-delay systems of neutral type that are believed to be of particular relevance in practice. Both traditional formulation and the coupled differential-difference equation formulation are used. The discontinuity of the spectrum as a function of delays is discussed. Conditions to guarantee stability under small parameter variations are given. A number of subjects that have been discussed in the literature, often using different methods, are reviewed to illustrate some fundamental concepts. These include systems with small delays, the sensitivity of Smith predictor to small delay mismatch, and the discrete implementation of distributed-delay feedback control. The framework prsented in this paper makes it possible to provide simpler formulation and strengthen, generalize, or provide alternative interpretation of the existing results
Performance analysis of robust stable PID controllers using dominant pole placement for SOPTD process models
This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this recordThis paper derives new formulations for designing dominant pole placement based proportionalintegral-derivative
(PID) controllers to handle second order processes with time delays (SOPTD).
Previously, similar attempts have been made for pole placement in delay-free systems. The presence
of the time delay term manifests itself as a higher order system with variable number of interlaced
poles and zeros upon Pade approximation, which makes it difficult to achieve precise pole placement
control. We here report the analytical expressions to constrain the closed loop dominant and nondominant
poles at the desired locations in the complex s-plane, using a third order Pade
approximation for the delay term. However, invariance of the closed loop performance with different
time delay approximation has also been verified using increasing order of Pade, representing a closed
to reality higher order delay dynamics. The choice of the nature of non-dominant poles e.g. all being
complex, real or a combination of them modifies the characteristic equation and influences the
achievable stability regions. The effect of different types of non-dominant poles and the
corresponding stability regions are obtained for nine test-bench processes indicating different levels of
open-loop damping and lag to delay ratio. Next, we investigate which expression yields a wider
stability region in the design parameter space by using Monte Carlo simulations while uniformly
sampling a chosen design parameter space. The accepted data-points from the stabilizing region in the
design parameter space can then be mapped on to the PID controller parameter space, relating these
two sets of parameters. The widest stability region is then used to find out the most robust solution
which are investigated using an unsupervised data clustering algorithm yielding the optimal centroid
location of the arbitrary shaped stability regions. Various time and frequency domain control
performance parameters are investigated next, as well as their deviations with uncertain process
parameters, using thousands of Monte Carlo simulations, around the robust stable solution for each of
the nine test-bench processes. We also report, PID controller tuning rules for the robust stable
solutions using the test-bench processes while also providing computational complexity analysis of
the algorithm and carry out hypothesis testing for the distribution of sampled data-points for different
classes of process dynamics and non-dominant pole types.KH acknowledges the support from the University Grants Commission (UGC), Govt. of India under
its Basic Scientific Research (BSR) schem
Robust Predictive Extended State Observer for a Class of Nonlinear Systems with Time-Varying Input Delay
[EN] This paper deals with asymptotic stabilisation of a class of nonlinear input-delayed systems via dynamic output feedback in the presence of disturbances. The proposed strategy has the structure of an observer-based control law, in which the observer estimates and predicts both the plant state and the external disturbance. A nominal delay value is assumed to be known and stability conditions in terms of linear matrix inequalities are derived for fast-varying delay uncertainties. Asymptotic stability is achieved if the disturbance or the time delay is constant. The controller design problem is also addressed and a numerical example with an unstable system is provided to illustrate the usefulness of the proposed strategy.This work was partially supported by: Ministerio de EconomĂa y Competitividad, Spain (TIN2017-86520-C3-1-R); Universitat PolitĂšcnica de ValĂšncia (FPI-UPV 2014 PhD Grant); and Israel Science Foundation (Grant No. 1128/14).Sanz Diaz, R.; GarcĂa Gil, PJ.; Fridman, E.; Albertos PĂ©rez, P. (2020). Robust Predictive Extended State Observer for a Class of Nonlinear Systems with Time-Varying Input Delay. International Journal of Control. 93(2):217-225. https://doi.org/10.1080/00207179.2018.1562204S217225932Ahmed-Ali, T., Cherrier, E., & Lamnabhi-Lagarrigue, F. (2012). Cascade High Gain Predictors for a Class of Nonlinear Systems. IEEE Transactions on Automatic Control, 57(1), 221-226. doi:10.1109/tac.2011.2161795Artstein, Z. (1982). Linear systems with delayed controls: A reduction. 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