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EN
This paper proposes a generalized fractional controller for integer order systems with time delay. The fractional controller structure is so adopted to have a combined effect of fractional filter and Smith predictor. Interestingly, the resulting novel controller can be decomposed into fractional filter cascaded with an integer order PID controller. The method is applied to two practical examples i.e. liquid level system and Shell control fractionator system. The closed-loop responses resulting from the proposed method are compared with that of the available methods in the literature. For quantitative evaluations of the proposed method, Integral Absolute Error (IAE) and Integral Square Control Input (ISCI) performance criteria are employed. The proposed method effectively enhances the closed-loop response by improving the IAE values, reducing the control effort inputs to achieve the desired output. The disturbance rejection and robustness tests are also carried out. The robustness test reveals a significant improvement in the maximum absolute sensitivity measure. That is displayed in numerical simulations of the paper.
EN
This paper proposes a new method for the analysis of continuous and periodic event-based state-feedback plus static feedforward controllers that regulate linear time invariant systems with time delays. Measurable disturbances are used in both the control law and triggering condition to provide better disturbance attenuation. Asymptotic stability and L2-gain disturbance rejection problems are addressed by means of Lyapunov–Krasovskii functionals, leading to performance conditions that are expressed in terms of linear matrix inequalities. The proposed controller offers better disturbance rejection and a reduction in the number of transmissions with respect to other robust event-triggered controllers in the literature.
EN
This paper is aimed at reviewing the ring of retarded quasipolynomial meromorphic functions (RMS) that was recently introduced as a convenient control design tool for linear, time-invariant time delay systems (TDS). It has been found by the authors that the original definition does not constitute a ring and has some essential deficiencies, and hence it could not be used for an algebraic control design without a thorough reformulation which i.a. extends the usability to neutral TDS and to those with distributed delays. This contribution summarizes the original definition of RMS simply highlights its deficiencies via examples, and suggests a possible new extended definition. Hence, the new ring of quasipolynomial meromorphic functions RQM is established to avoid confusion. The paper also investigates and introduces selected algebraic properties supported by some illustrative examples and concisely outlines its use in controller design.
EN
This note addresses the stabilization problem of nonlinear chained-form systems with input time delay. We first employ the so-called σ-process transformation that renders the feedback system under a linear form. We introduce a particular transformation to convert the original system into a delay-free system. Finally, we apply a state feedback control, which guarantees a quasi-exponential stabilization to all the system states, which in turn converge exponentially to zero. Then we employ the so-called -type control to achieve a quasi-exponential stabilization of the subsequent system. A simulation example illustrated on the model of a wheeled mobile robot is provided to demonstrate the effectiveness of the proposed approach.
EN
This work introduces a novel approach to stability and stabilization of nonlinear systems with delayed multivariable inputs; it provides exponential estimates as well as a guaranteed cost of the system solutions. The result is based on an exact convex representation of the nonlinear system which allows a Lyapunov–Krasovskii functional to be applied in order to obtain sufficient conditions in the form of linear matrix inequalities. These are efficiently solved via convex optimization techniques. A real-time implementation of the developed approach on the twin rotor MIMO system is included.
EN
In this paper a parametric optimization problem for a linear neutral system with two delays with an integral quadratic performance index is formulated and solved. The method of computing of a performance index value bases on determining of a Lyapunov functional defined on a state space such that its value for an initial state is equal to a performance index value. In the paper a form of a Lyapunov functional is assumed and a method of computing its coefficients is given. An example illustrating the application of discussed theory is presented. It concerns the system with a PD-controller designed to control a plant with two delays both retarded and neutral type. For such system a value of considered performance index is determined.
EN
The paper presents a method to determine a Lyapunov functional for a linear time-invariant system with an interval time-varying delay. The functional is constructed for the system with a time-varying delay with a given time derivative, which is calculated on the system trajectory. The presented method gives analytical formulas for the coefficients of the Lyapunov functional.
8
Content available Funkcjonały Lapunowa dla układów z opóźnieniem
PL
W pracy przedstawiono zastosowanie funkcjonałów Lapunowa do badania stabilności układów z opóźnieniem oraz w procesie optymalizacji parametrycznej.
EN
In the paper was presented the application of the Lyapunov functionals to examination of the stability of the time delay systems and in the process of parametric optimization.
EN
The paper presents a method of determining the Lyapunov quadratic functional for linear tirne-invariant system with both lumped and distributed delay. The Lyapunov functional is constructed for its given time derivative, which is calculated on the trajectory of the system with both lumped and distributed delay. The method presented gives analytical formulas for the coefficients of the Lyapunov functional.
EN
In the paper the problem of parametric optimization of a linear neutral system with two delays accomplished with respect to the integral quadratic performance index is formulated and solved. A method of computing the value of performance index relies on determining such a Lyapunov functional defined on the state space that its value for the initial state is equal to that of performance index. In the paper the form of Lyapunov functional is assumed and a method of computing its coefficients is given. An example illustrating the application of the theory discussed is presented. It concerns a system with the P-controller designed to control a plant with two delays both retarded and neutral type. For such a system the value of the considered performance index is determined.
11
Content available remote Lyapunov functional for a system with k-non-commensurate neutral time delays
EN
The paper presents a method of determining the Lyapunov quadratic functional for linear time-invariant system with k-non-commensurate neutral type time delays. The Lyapunov functional is constructed for its given time derivative, which is calculated on the trajectory of the system with k-non-commensurate neutral type time delays. The presented method gives analytical formulas for the coefficients of the Lyapunov functional.
12
Content available remote Lyapunov functional for a linear system with two delays
EN
The paper presents a method of determining the Lyapunov functional for linear time-invariant LTI system with two lumped delays.
EN
The paper presents a method of determining of the Lyapunov quadratic functional for linear time-invariant system with two delays both retarded and neutral type. The Lyapunov functional is constructed for a given its time derivative which is calculated on the trajectory of the system with two delays both retarded and neutral type. The presented method gives analytical formulas for the coefficients of the Lyapunov functional.
EN
This paper concerns the issue of robust asymptotic stabilization for uncertain time-delay systems with saturating actuators. Delay-dependent criteria for robust stabilization via linear memoryless state feedback have been obtained. The resulting upper bound on the delay time is given in terms of the solution to a Riccati equation subject to model transformation. Finally, examples are presented to show the effectiveness of our result.
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