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Number of results: 10
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Abstract

In the paper a Lyapunov matrices approach to the parametric optimization problem of a time-delay system with two commensurate delays and a PI-controller is presented. The value of integral quadratic performance index is equal to the value of the Lyapunov functional for the initial function of the time-delay system. The Lyapunov functional is determined by means of the Lyapunov matrix. In the paper is presented the example of a scalar system with two delays and a PI controller.

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Authors and Affiliations

Jozef Duda
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Abstract

This paper deals with the problem of stabilization by an estimated state feedback for a family of nonlinear time-delay Takagi-Sugeno fuzzy parameterized systems. The delay is supposed to be constant where the parameter-dependent controls laws are used to compensate the nonlinearities which are formulated in terms of linear matrix inequalities (LMIs). Based on the Lyapunov- Krasovskii functionals, global exponential stability of the closed-loop systems is achieved. The controller and observer gains are able to be separately designed even in the presence of modeling uncertainty and state delay. Finally, a numerical example is given to show the applicability of the main result.
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Authors and Affiliations

Nizar Hadj Taieb
1
Mohamed Ali Hammami
2
François Delmotte
3

  1. University of Sfax, IPEIS Sfax, Tunisia
  2. University of Sfax, Faculty of Sciences of Sfax, Tunisia
  3. University of Artois, Bethune, France
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Abstract

The stability analysis for discrete-time fractional linear systems with delays is presented. The state-space model with a time shift in the difference is considered. Necessary and sufficient conditions for practical stability and for asymptotic stability have been established. The systems with only one matrix occurring in the state equation at a delayed moment have been also considered. In this case analytical conditions for asymptotic stability have been given. Moreover parametric descriptions of the boundary of practical stability and asymptotic stability regions have been presented.

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Authors and Affiliations

Andrzej Ruszewski
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Abstract

The time delay element present in the PI controller brings dead-time compensation capability and shows improved performance for dead-time processes. However, design of robust time delayed PI controller needs much responsiveness for uncertainty in dead-time processes. Hence in this paper, robustness of time delayed PI controller has been analyzed for First Order plus Dead-Time (FOPDT) process model. The process having dead-time greater than three times of time constant is very sensitive to dead-time variation. A first order filter is introduced to ensure robustness. Furthermore, integral time constant of time delayed PI controller is modified to attain better regulatory performance for the lag-dominant processes. The FOPDT process models are classified into dead-time/lag dominated on the basis of dead-time to time constant ratio. A unified tuning method is developed for processes with a number of dead-time to time constant ratio. Several simulation examples and experimental evaluation are exhibited to show the efficiency of the proposed unified tuning technique. The applicability to the process models other than FOPDT such as high-order, integrating, right half plane zero systems are also demonstrated via simulation examples.
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Bibliography

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Authors and Affiliations

Arun R. Pathiran
1
R. Muniraj
2
ORCID: ORCID
M. Willjuice Iruthayarajan
3
ORCID: ORCID
S.R. Boselin Prabhu
4
T. Jarin
5
ORCID: ORCID

  1. Department of Electrical and Electronics Technology, Ethiopian Technical University, Addis Ababa, Ethiopia
  2. Department of Electrical and Electronics Engineering, P.S.R. Engineering College, Sivakasi, Virudhunagar District, Tamilnadu, India
  3. Department of Electrical and Electronics Engineering, National Engineering College, Kovilpatti, India
  4. Department of Electronics and Communication Engineering, Surya Engineering College, Mettukadai, India
  5. Department of Electrical and Electronics Engineering, Jyothi Engineering College, Thrissur, India
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Abstract

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.

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Authors and Affiliations

Shaival Hemant Nagarsheth
Shambhu Nath Sharma
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Abstract

Extremal problems for multiple time delay hyperbolic systems are presented. The optimal boundary control problems for hyperbolic systems in which multiple time delays appear both in the state equations and in theNeumann boundary conditions are solved. The time horizon is fixed. Making use of Dubovicki-Milutin scheme, necessary and sufficient conditions of optimality for the Neumann problem with the quadratic performance functionals and constrained control are derived.
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Authors and Affiliations

Adam Kowalewski
1

  1. AGH University of Science and Technology, Institute of Automatic Control and Robotics, 30-059 Cracow, al. Mickiewicza 30, Poland
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Abstract

This paper proposes a design procedure for observer-based controllers of discrete-time switched systems, in the presence of state’s time-delay, nonlinear terms, arbitrary switching signals, and affine parametric uncertainties. The proposed switched observer and the state- feedback controller are designed simultaneously using a set of linear matrix inequalities (LMIs). The stability analysis is performed based on an appropriate Lyapunov–Krasovskii functional with one switched expression, and in the meantime, the sufficient conditions for observer-based stabilization are developed. These conditions are formulated in the form of a feasibility test of a proposed bilinear matrix inequality (BMI) which is a non-convex problem. To make the problem easy to solve, the BMI is transformed into a set of LMIs using the singular value decomposition of output matrices. An important advantage of the proposed method is that the established sufficient conditions depend only on the upper bound of uncertain parameters. Furthermore, in the proposed method, an admissible upper bound for unknown nonlinear terms of the switched system may be calculated using a simple search algorithm. Finally, the efficiency of the proposed controller and the validity of the theoretical results are illustrated through a simulation example.

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Authors and Affiliations

N.A. Baleghi
M.H. Shafiei
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Abstract

In this paper we deal with the problem of uniform exponential stabilization for a class of distributed bilinear parabolic systems with time delay in a Hilbert space by means of a bounded feedback control. The uniform exponential stabilization problem of such a system reduces to stabilizing only its projection on a suitable finite dimensional subspace. Furthermore, the stabilizing feedback control depends only on the state projection on the finite dimensional subspace. An explicit decay rate estimate of the stabilized state is given provided that a nonstandard weaker observability condition is satisfied. Illustrative examples for partial functional differential equations are displayed.
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Authors and Affiliations

Azzeddine Tsouli
1
Mostafa Ouarit
2

  1. Laboratory of Mathematics and Applications, ENSAM, Hassan II University of Casablanca, Morocco
  2. Laboratory of Fundamental and Applied Mathematics LAMFA, Faculty of Sciences Ain Chock, Hassan II University of Casablanca, Morocco
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Abstract

In order to solve the problem of large error of delay estimation in low SNR environment, a new delay estimation method based on cross power spectral frequency domain weighting and spectrum subtraction is proposed. Through theoretical analysis and MATLAB simulation, among the four common weighting functions, it is proved that the cross-power spectral phase weighting method has a good sharpening effect on the peak value of the cross-correlation function, and it is verified that the improved spectral subtraction method generally has a good noise reduction effect under different SNR environments. Finally, the joint simulation results of the whole algorithm show that the combination of spectrum subtraction and crosspower spectrum phase method can effectively sharpen the peak value of cross-correlation function and improve the accuracy of time delay estimation in the low SNR environment. The results of this paper can provide useful help for sound source localization in complex environments.

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Authors and Affiliations

Feng Bin
Xu Lei
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Abstract

An active inerter-based suspension with acceleration feedback control is proposed in this paper, the time delay generated in the controllers and actuators is considered, which constitutes the time-delayed active inerter-based (TDA-IB) suspension. The dynamic equation of the TDA-IB suspension is established and is a neutral type of delay differential equation (NDDE) in which the time delay exists in the highest-order derivative. The stability analysis is conducted by calculating the number of unstable characteristic roots based on the definite integral stability method, the stable and unstable regions are determined. The effect of time delay and feedback gain on the dynamic performance of the TDA-IB suspension under harmonic, random, and shock excitations is studied in detail and compared with the parallel-connected inerter-based (PC-IB) and traditional suspensions. The results show that the TDA-IB suspension is asymptotically stable for smaller feedback gain and time delay, through increasing the feedback gain, the stable regions shrink, and a smaller time delay could cause the system to become unstable. Furthermore, the time delay could regulate the resonance peak around the unsprung mass natural frequency and generate multiple high-frequency resonance peaks. If the time delay is chosen appropriately and falls into the stable range, the TDA-IB suspension could improve the dynamic performance for the suspension stroke and dynamic tire load while having a deterioration for the vehicle body acceleration compared with the PC-IB and traditional suspensions.
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Authors and Affiliations

Yong Wang
1 2 3
ORCID: ORCID
Xian-Yu Jin
1
Yun-Shun Zhang
1
Hu Ding
4
Li-Qun Chen
4

  1. Automotive Engineering Research Institute, Jiangsu University, Zhenjiang 212013, China
  2. Vehicle Measurement, Control and Safety Key Laboratory of Sichuan Province, Xihua University, Chengdu 610039, China
  3. Provincial Engineering Research Center for New Energy Vehicle Intelligent Control and Simulation Test Technology of Sichuan, Xihua University, Chengdu 610039, China
  4. School of Mechanics and Engineering Science, Shanghai University, Shanghai 200444, China

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