scholarly journals T-S Fuzzy Control of Uncertain Fractional-Order Systems with Time Delay

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Yilin Hao ◽  
Xiulan Zhang
Keyword(s):  
Time Delay ◽  
Fractional Order ◽  
Control Method ◽  
Fuzzy Model ◽  
Linear Structure ◽  
Adaptive Method ◽  
Delay Systems ◽  
Robust Controller ◽  
External Disturbances ◽  
Fuzzy Adaptive

In this article, the adaptive control of uncertain fractional-order time-delay systems (FOTDSs) with external disturbances is discussed. A Takagi-Sugenu (T-S) fuzzy model with if-then rules is adopted to characterize the dynamic equation of the FOTDS. Besides, a fuzzy adaptive method is proposed to stabilize the model. By utilizing the Lyapunov functions, a robust controller is constructed to stabilize the FOTDS. Due to the uncertainty of system parameters, some fractional-order adaptation laws are designed to update these parameters. At the same time, some if-then rules with linear structure based on the fuzzy T-S adaption concept are established. The designed method not only guarantees that the state of closed-loop system asymptotically converges to origin but also keeps the signal in the FOTDS bounded. Finally, the applicability of the control method is proved by simulation examples.

Control of Time-Delay Systems Using Robust Fractional-Order Control and Robust Smith Predictor Based Control

2005 ◽  
Author(s):  
Patrick Lanusse ◽  
Alain Oustaloup
Keyword(s):  
Time Delay ◽  
Fractional Order ◽  
Control Plant ◽  
Smith Predictor ◽  
Delay Systems ◽  
Time Delay Systems ◽  
Robust Controller ◽  
Fractional Order Control ◽  
And Performance ◽  
Performance Tradeoff

Many modifications have been proposed to improve the Smith predictor structure used to control plant with time-delay. Some of them have been proposed to enhance the robustness of Smith predictor based controllers. They are often based on the use of deliberately mismatched model of the plant and then the IMC method can be used to tune the controller. This paper compares the performance of two Smith predictor based controllers including a mismatched model to the performance provided by a fractional order Crone controller which is well known for managing well the robustness and performance tradeoff. It is shown that even if it can simplify the design of (robust) controller, the use of an improved Smith predictor is not necessary to obtain good performance.

Asymptotic stabilization of a class of uncertain nonlinear time-delay fractional-order systems via a robust delay-independent controller

2017 ◽  
Vol 24 (19) ◽  
pp. 4541-4550 ◽  
Author(s):  
T. Binazadeh ◽  
M. Yousefi
Keyword(s):  
Time Delay ◽  
Fractional Order ◽  
Sliding Mode ◽  
Robust Stabilization ◽  
Delay Systems ◽  
Time Varying ◽  
State Variables ◽  
Parameter Uncertainties ◽  
External Disturbances ◽  
Sliding Manifold

This paper studies the robust stabilization for a class of nonlinear time-delay fractional order (FO) systems in the presence of some practical aspects. The considered aspects in the FO system include: nonlinear Lipschitz functions; time-varying norm-bounded uncertain terms; and time-delays in the state variables. A major challenge in the control of time-delay systems is that the value of delay is usually not perfectly known or it may be even time-varying. In this paper, a novel asymptotic stabilizing control law is proposed which is delay independent and also has a robust manner in the presence of uncertain terms in the model which may be due to model uncertainties (parameter uncertainties or model simplification) and/or external disturbances. The proposed controller is a FO sliding mode controller that is designed such that the closed-loop system is asymptotically delay-independent stable. For this purpose, a FO sliding manifold is introduced and the occurrence of the reaching phase in a finite time is proved. Finally, in order to validate the theoretical results, an example is given and simulation results confirm the appropriate performance of the proposed controller.

Fractional-Order Optimal Control of Fractional-Order Linear Vibration Systems with Time Delay

2018 ◽  
Vol 7 (3) ◽  
pp. 72-93
Author(s):  
Saeed Balochian ◽  
Nahid Rajaee
Keyword(s):  
Optimal Control ◽  
Time Delay ◽  
Fractional Order ◽  
Control Method ◽  
Linear Structure ◽  
Control Input ◽  
Linear Vibration ◽  
Order Linear ◽  
Input Control ◽  
Delayed System

Vibration control of fractional-order linear systems in the presence of time delays has been dealt in this article. Considering a delayed n-degree-of freedom linear structure that is modeled by fractional order equations, a fractional-order optimal control is provided to minimize both control input and output of delayed system via quadratic objective function. To do this, first the fractional order model of system that is subject to time delay is rewritten into a non-delay form through a particular transformation. Then, a fractional order optimal controller is provided using the classical optimal control theory to find an optimal input control. A delayed viscose system is then presented as a practical worked-out example. Numerical simulation results are given to confirm the efficiency of the proposed control method.

scholarly journals Fractional-Order Controller Design for Oscillatory Fractional Time-Delay Systems Based on the Numerical Inverse Laplace Transform Algorithms

2015 ◽  
Vol 2015 ◽  
pp. 1-10
Author(s):  
Lu Liu ◽  
Feng Pan ◽  
Dingyu Xue
Keyword(s):  
Time Delay ◽  
Laplace Transform ◽  
Fractional Order ◽  
Control Method ◽  
Delay System ◽  
Inverse Laplace Transform ◽  
Delay Systems ◽  
Time Delay System ◽  
Numerical Inverse Laplace Transform ◽  
Fractional Order Controller

Fractional-order time-delay system is thought to be a kind of oscillatory complex system which could not be controlled efficaciously so far because it does not have an analytical solution when using inverse Laplace transform. In this paper, a type of fractional-order controller based on numerical inverse Laplace transform algorithm INVLAP was proposed for the mentioned systems by searching for the optimal controller parameters with the objective function of ITAE index due to the verified nature that fractional-order controllers were the best means of controlling fractional-order systems. Simulations of step unit tracking and load-disturbance responses of the proposed fractional-order optimalPIλDμcontroller (FOPID) and corresponding conventional optimal PID (OPID) controller have been done on three typical kinds of fractional time-delay system with different ratio between time delay (L) and time constant (T) and a complex high-order fractional time delay system to verify the availability of the presented control method.

scholarly journals Design of a Nonlinear Predictive Controller for a Fractional-Order Hydraulic Turbine Governing System with Mechanical Time Delay

Energies ◽  
2019 ◽  
Vol 12 (24) ◽  
pp. 4727
Author(s):  
Yuqiang Tian ◽  
Bin Wang ◽  
Diyi Chen ◽  
Shaokun Wang ◽  
Peng Chen ◽  
...  
Keyword(s):  
Time Delay ◽  
Prediction Model ◽  
Fractional Order ◽  
Control Method ◽  
Moving Average ◽  
Fuzzy Model ◽  
Hydraulic Turbine ◽  
Governing System ◽  
Order Part ◽  
Predictive Controller

A nonlinear predictive control method for a fractional-order hydraulic turbine governing system (HTGS) with a time delay is studied in this paper. First, a fractional-order model of a time-delay hydraulic turbine governing system is presented. Second, the fractional-order hydraulic servo subsystem is transformed into a standard controlled autoregressive moving average (CARMA) model according to the Grünwald-Letnikov (G-L) definition of fractional calculus. Third, based on the delayed Takagi-Sugeno fuzzy model, the fuzzy prediction model of the integer-order part of the HTGS is given. Then, by introducing a fourth-order Runge-Kutta algorithm, the fuzzy prediction model can be easily transformed into the CARMA model. Furthermore, a nonlinear predictive controller is proposed to stabilize the time-delay HTGS. Finally, the experiment results are consistent with the theoretical analysis.

Transient Response Control by Fractional-Order PI Controllers

2011 ◽  
Author(s):  
Serdar Ethem Hamamci ◽  
Serhat Obuz
Keyword(s):  
Time Delay ◽  
Fractional Order ◽  
Transient Response ◽  
Stability Region ◽  
Control Method ◽  
Settling Time ◽  
Delay Systems ◽  
Response Control ◽  
Pi Controllers ◽  
And Control

Consideration of the transient response is one of the key topics in control system design for time delay systems. In this paper, an efficient method to control the transient response of the first order plus time delay stable (FOPTD) systems using the fractional-order PI (PIλ) controllers is presented. The main characterization of the method is first to construct the global stability region in the (kp, ki)-plane for any fixed value of λ and then to obtain ts and Mp curves corresponding to special settling time and maximum overshoot values in this region. Finally, by intersection of these curves, the Dλ-stability region in the (kp, ki)-plane is found. Changing the value of λ in the range of (0, 2), a set of Dλ-stability regions is obtained. These regions involve the controller parameters providing the closed loop settling time and maximum overshoot specifications together in the acceptable values. Therefore, the designer can easily decide to the selection of suitable values of kp, ki and λ. The simulation results indicate that the presented transient response control method is effective and practically useful in the analysis and control of the stable FOPTD systems by means of fractional-order PI controllers.

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