Urmia University of Technology

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Aghababa M.P.,Urmia University of Technology
Nonlinear Dynamics | Year: 2014

In this paper, a fractional calculus-based terminal sliding mode controller is introduced for finite-time control of non-autonomous non-linear dynamical systems in the canonical form. A fractional terminal switching manifold which is appropriate for canonical integer-order systems is firstly designed. Then some conditions are provided to avoid the inherent singularities of the conventional terminal sliding manifolds. A non-smooth Lyapunov function is adopted to prove the finite time stability and convergence of the sliding mode dynamics. Afterward, based on the sliding mode control theory, an equivalent control and a discontinuous control law are designed to guarantee the occurrence of the sliding motion in finite time. The proposed control scheme uses only one control input to stabilize the system. The proposed controller is also robust against system uncertainties and external disturbances. Two illustrative examples show the effectiveness and applicability of the proposed fractional finite-time control strategy. It is worth noting that the proposed sliding mode controller can be applied for control and stabilization of a large class of non-autonomous non-linear uncertain canonical systems. © 2013 Springer Science+Business Media Dordrecht.


Aghababa M.P.,Urmia University of Technology
Nonlinear Dynamics | Year: 2015

Chaos control and synchronization of second-order nonautonomous fractional complex chaotic systems are discussed in this paper. A novel fractional nonsingular terminal sliding surface which is suitable for second-order fractional systems is proposed. It is proved that once the state trajectories of the system reach to the proposed sliding surface, they will be converged to the origin within a given finite time. After establishing the desired terminal sliding surface, a novel robust single sliding mode control law is introduced to force the system trajectories to reach the terminal sliding surface over a finite time. The stability and robustness of the proposed method are proved using the latest version of the fractional Lyapunov stability theorem. The proposed method is implemented for synchronization of two uncertain different fractional chaotic systems to confirm the theoretical results. Moreover, the fractional-order gyro system is stabilized using the proposed fractional sliding mode control scheme. It is worth noticing that the proposed fractional sliding mode approach is still a general control method and can be applied for control of second- order uncertain nonautonomous/autonomous fractional systems. © 2014, Springer Science+Business Media Dordrecht.


Aghababa M.P.,Urmia University of Technology
Nonlinear Dynamics | Year: 2013

This paper concerns the problem of robust control of uncertain fractional-order nonlinear complex systems. After establishing a simple linear sliding surface, the sliding mode theory is used to derive a novel robust fractional control law for ensuring the existence of the sliding motion in finite time. We use a nonsmooth positive definitive function to prove the stability of the controlled system based on the fractional version of the Lyapunov stability theorem. In order to avoid the chattering, which is inherent in conventional sliding mode controllers, we transfer the sign function of the control input into the first derivative of the control signal. The proposed sliding mode approach is also applied for control of a class of nonlinear fractional-order systems via a single control input. Simulation results indicate that the proposed fractional variable structure controller works well for stabilization of hyperchaotic and chaotic complex fractional-order nonlinear systems. Moreover, it is revealed that the control inputs are free of chattering and practical. © 2013 Springer Science+Business Media Dordrecht.


Aghababa M.P.,Urmia University of Technology
Nonlinear Dynamics | Year: 2013

This paper introduces a finite-time control technique for control of a class of non-autonomous fractional-order nonlinear systems in the presence of system uncertainties and external noises. It is known that finite-time control methods demonstrate better robustness and disturbance rejection properties. Moreover, finite time control methods have optimal settling time. In order to design a robust finite-time controller, a new nonsingular terminal sliding manifold is proposed. The proposed sliding mode dynamics has the property of fast convergence to zero. Afterwards, a novel fractional sliding mode control law is introduced to guarantee the occurrence of the sliding motion in finite time. The convergence times of both reaching and sliding phases are estimated. The main characteristics of the proposed fractional sliding mode technique are (1) finite-time convergence to the origin; (2) the use of only one control input; (3) robustness against system uncertainties and external noises; and (4) the ability of control of non-autonomous fractional-order systems. At the end of this paper, some computer simulations are included to highlight the applicability and efficacy of the proposed fractional control method. © 2013 Springer Science+Business Media Dordrecht.


Aghababa M.P.,Urmia University of Technology
ISA Transactions | Year: 2013

The problem of active control of vibration structures has attracted much attention over the past decades. A general description of the control problem of vibration systems is to design an active controller to suppress the vibrations of the system induced by external disturbances such as an earthquake. In this paper, a novel fractional-order sliding mode control is introduced to attenuate the vibrations of structures with uncertainties and disturbances. After establishing a stable fractional sliding surface, a sliding mode control law is proposed. Then, the global asymptotic stability of the closed-loop system is analytically proved using fractional Lyapunov stability theorem. Finally, the robustness and applicability of the technique are verified using two examples, including a three degree of freedom structure and a two-story shear building. © 2013 ISA.Published by Elsevier Ltd. All rights reserved.


Sadrzadeh A.,Urmia University of Technology
Computers and Industrial Engineering | Year: 2012

The paper presents a genetic algorithm-based meta-heuristic to solve the facility layout problem (FLP) in a manufacturing system, where the material flow pattern of the multi-line layout is considered with the multi-products. The matrix encoding technique has been used for the chromosomes under the objective of minimizing the total material handling cost. The proposed algorithm produces a table with the descending order of the data corresponding to the input values of the flow and cost data. The generated table is used to create a schematic representation of the facilities, which in turn is utilized to heuristically generate the initial population of the chromosomes and to handle the heuristic crossover and mutation operators. The efficiency of the proposed algorithm has been proved through solving the two examples with the total cost less than the other genetic algorithms, CRAFT algorithm, and entropy-based algorithm. © 2011 Elsevier Ltd. All rights reserved.


Aghababa M.P.,Urmia University of Technology
Chinese Physics B | Year: 2012

The present paper investigates the existence of chaos in a non-autonomous fractional-order micro-electromechanical resonator system (FOMEMRS). Using the maximal Lyapunov exponent criterion, we show that the FOMEMRS exhibits chaos. Strange attractors of the system are plotted to validate its chaotic behavior. Afterward, a novel fractional finite-time controller is introduced to suppress the chaos of the FOMEMRS with model uncertainties and external disturbances in a given finite time. Using the latest version of the fractional Lyapunov theory, the finite time stability and robustness of the proposed scheme are proved. Finally, we present some computer simulations to illustrate the usefulness and applicability of the proposed method. © 2012 Chinese Physical Society and IOP Publishing Ltd.


In this paper, a novel fractional-order terminal sliding mode control approach is introduced to control/synchronize chaos of fractional-order nonautonomous chaotic/hyperchaotic systems in a given finite time. The effects of model uncertainties and external disturbances are fully taken into account. First, a novel fractional nonsingular terminal sliding surface is proposed and its finite-time convergence to zero is analytically proved. Then an appropriate robust fractional sliding mode control law is proposed to ensure the occurrence of the sliding motion in a given finite time. The fractional version of the Lyapunov stability is used to prove the finite-time existence of the sliding motion. The proposed control scheme is applied to control/synchronize chaos of autonomous/nonautonomous fractional-order chaotic/hyperchaotic systems in the presence of both model uncertainties and external disturbances. Two illustrative examples are presented to show the efficiency and applicability of the proposed finite-time control strategy. It is worth to notice that the proposed fractional nonsingular terminal sliding mode control approach can be applied to control a broad range of nonlinear autonomous/nonautonomous fractional-order dynamical systems in finite time. © 2011 Springer Science+Business Media B.V.


Pourmahmood Aghababa M.,Urmia University of Technology
Journal of Computational and Nonlinear Dynamics | Year: 2012

This paper concerns the problem of stabilization of uncertain fractional-order chaotic systems in finite time. On the basis of fractional Lyapunov stability theory, a robust finite-time fractional controller is introduced to control chaos of fractional-order chaotic systems in the presence of system uncertainties. The finite-time stability of the closed-loop system is analytically proved. An estimation of the convergence time is also given. Some numerical simulations are provided to illustrate the usefulness and applicability of the proposed robust finite-time control approach. It is worth noting that the proposed fractional control method is applicable for stabilizing a broad range of uncertain fractional-order nonlinear systems in a given finite time. © 2012 American Society of Mechanical Engineers.


In this paper, optimal paths in environments with obstacles for underwater vehicles are computed using a numerical solution of the nonlinear optimal control problem (NOCP). The underwater vehicle is modeled with six-dimensional nonlinear and coupled equations of motion, controlled by DC motors in all degrees of freedom. An energy performance index combined with a time consumption index is used. Both fixed and free final times are considered. Solving NOCP leads to a two point boundary value problem (TPBVP). Five intelligent evolutionary algorithms (EAs), which include genetic algorithm, memetic algorithm, particle swarm optimization, ant colony optimization and shuffled frog leaping algorithm, are applied to solve the NOCP. For comparison, a conjugate gradient penalty method is also used to solve the TPBVP. The simulation results show that the trajectories obtained by the intelligent methods are better than those of conjugate gradient method. After analyzing a simple path planning problem, the time-energy-optimal path planning problem in energetic environments is propounded and solved by EAs. The problem of static obstacle collision avoidance in an energetic environment is also studied. © 2012 Elsevier Ltd.

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