Showing 10 results for Fractional Order
Volume 12, Issue 1 (4-2012)
Abstract
Non-fragile observer design is the main problem of this paper. Using continuous frequency distribution, the stability conditions based on integer order Lyapunov theorem are derived for Lipschitz class of nonlinear fractional order systems. The proposed observer is stable beside the existence of both gain perturbation and input disturbance. For the first time, in this paper a systematic method is suggested based on linear matrix inequality to find an optimal observer gain to minimize both the effects of disturbance on the synchronization error and norm of the observer gain. A comparison has done between this observer and previous research on resilient observer design for nonlinear fractional order systems based on fractional order Lyapunov method. The comparison shows a much broader range of feasible response for the proposed method of this paper besides simpler computing. After presenting thediscussion, chaos synchronization is simulated to show the effectiveness of the proposed method in the end.
Volume 13, Issue 4 (1-2014)
Abstract
This paper proposes a new hierarchical identification method for fractional-order systems. In this method, a SISO (single input, single output) state space model has been considered in which parameters and also state variables should be estimated. By using a linear transformation and a shift operator, the system will be transformed into a form appropriate for identification of a fractional-order system. Then, the unknown parameters will be identified through a recursive least squares method and the states will be estimated using a fractional order Kalman filter. This identification method is based on the hierarchical identification principle that reduces the computational burden and is easy to implement on computer. The promising performance of the proposed method is verified using two stable fractional-order systems.
Iman Ghasemi, Abolfazl Ranjbar Noei, Seyed Jalil Sadati Rostami,
Volume 15, Issue 10 (1-2016)
Abstract
In this paper, a new type of iterative learning control systems with fractional order known as iterative learning control with fractional order derivative and iterative learning control with fractional proportional–derivative for linearized systems of single-link robot arm is introduced. First order derivative of classic Arimoto is used for tracking error in updating law of derivative iterative learning control. Suggested method in this paper implement tracking error for updating control law of iterative learning of fractional order. For the first time, nonlinear robot system is linearized by input feedback linearization. Then, convergence analysis of iterative learning control law of type PD^alpha is studied.In the next step, we define a criteria for parameters optimization of proposed controller by using Biogeography-based optimization algorithm. Both updating law of fractional order iterative learning control (D^alpha-type ILC and PD^alpha-type ILC) is applied on linearized robot arm and performance of both controller for different value of alpha is presented. For improving the performance of closed loop system, coefficient of fractional order iterative learning control (proportional and derivative coefficients) is optimized by BBO algorithm. Proposed iterative learning control is compared with common type of system.
Amir Hossein Asgharnia, Reza Shahnazi, Ali Jamali,
Volume 17, Issue 3 (5-2017)
Abstract
In this paper, an optimal Fractional-order Proportional-Integral-Derivative (FOPID) controller is proposed to control an offshore 5MW wind turbine’s pitch angle in above rated speed. The proposed pitch controller regulates the generator angular speed and consequently the generator power to its nominal value without any knowledge of the model. In order to find the parameters of the controller, a hybrid cost function is proposed, which consists of sum of absolute error signal and absolute rate of control signal in three different wind speeds. The wind speeds are chosen in the beginning, middle and at the end of the interval, thus, the optimized controller is able to show an acceptable performance in whole range of wind speeds, without any demand to nonlinear and complex controllers. To this end, the proposed cost function is minimized using three optimization algorithms: Differential Evolution (DE), Firefly algorithm and Particle Swarm Optimization (PSO). In order to evaluate the robustness of proposed FOPID, numerous wind profiles with different speeds and fluctuations are applied and the results are compared with the optimal integer order PID controller. The comparison demonstrates that the proposed FOPID has more effective performance and robustness than optimal integer order PID.
Hadi Delavari, Hamid Heydarinejad,
Volume 17, Issue 3 (5-2017)
Abstract
Magnetic levitation systems are widely used in various industries. These kind of systems are usually open-loop unstable and are described by highly nonlinear differential equations which present additional difficulties in controlling these systems in the presence of disturbance and sensor noise. We consider the stabilization and the tracking problems of a magnetic levitation system. In this paper an adaptive fractional order Backstepping sliding mode control schemes is proposed. Backstepping algorithm is based on the Lyapunov theory. The proposed controller in this paper is designed by a combination of a Backstepping algorithm, sliding mode control and fractional calculus to make more degree of freedom and robustness. The stability of the closed loop system is investigated by using the Lyapunov stability theorem and the new extension of Lyapunov stability theorem for fractional order systems. Simulations are performed to confirm the theoretical results of the proposed controller for the magnetic levitation system. The proposed controller is able to reject the sensor noise and disturbance with a chattering free control law. Finally the simulation results of the proposed controller are compared with the adaptive fast terminal sliding mode control.
Marzeh Kamali, Mehdi Farhadi, Javad Askari,
Volume 17, Issue 5 (7-2017)
Abstract
Quadrotors are types of Unmanned Aerial Vehicles (UAVs) which have unique features compared to conventional aircrafts because of its vertical take-off and landing capability, flying in small areas and its high maneuverability. Also the relatively simple, economical and easy flight system of quadrotors, makes it to widely used as a good platform for development, implementation and testing a variety of control methods. One of the robust control methods is sliding mode control. In spite of the high capabilities of this approach, it has a main problem which is high frequency switching of the control signal witch is known the chattering phenomenon. In the past several decades, fractional order differential equations have been implemented in engineering application field, including controllers design and provided the possibility of using controllers for improving the performance of system. In this paper, a fractional order sliding surface has been employed for designing sliding mode control rule for quadrotors. The main objective of this study is to improve the performance and reduce the chattering phenomenon in sliding mode method. In this regard, by introducing sliding 〖PD〗^α surface, the control rule is designed in two different modes of 0
Sayed Bagher Fazeli Asl, Seyyed Sajjad Moosapour,
Volume 17, Issue 5 (7-2017)
Abstract
In this paper, a fractional order backstepping type of fast terminal sliding mode controller is proposed for controlling a micro-electro-mechanical triaxial gyroscope with parameter uncertainty and internal and external disturbances. To compensate uncertainties and also incoming disturbances to the system used combination of sliding mode and backstepping robust nonlinear controllers. In the proposed approach, the sliding surface is selected in the form of fractional order. To increase the speed of convergence the system states to equilibrium points or the error to zero, the fast terminal sliding mode controller is used. The globally stability of the closed loop system will prove by Lyapunov stability theorem. Also in addition to the above proposal controller, a fractional order backstepping sliding mode controller designed and implemented for the gyroscope system. In order to evaluate the performance of designed controllers, these controllers compared with backstepping sliding mode controller and the backstepping fast terminal sliding mode controller. The results shown that the proposed controller has a faster transient response than the other controllers. Another advantage of the proposed controller is simplicity designed and implemented, increase system stability and acceptable tracking than the other controllers. Also unlike the other two controllers the chattering phenomenon completely removed in the fractional order designed controllers.
Hadi Delavari, Atefeh Azizkhani, Pooya Shiuooei,
Volume 17, Issue 10 (1-2018)
Abstract
Energy saving, low robot mass to carried mass ratio, more ability to work in various environments, easier delivery of parts and lower production costs in flexible robots make these robots more attractive than rigid robots to many researchers and industries. But due to nonlinearities in flexible robot system and high vibration in operation points and also more sensitivity against external disturbances, control of these robots is more difficult and complex. In this paper a controller for a flexible link manipulator based on fractional calculus is practically implemented. At first the dynamic model of a single flexible-link robot is introduced. Then various controllers such as fuzzy control, PID control, and fractional order PID torque control are practically implemented on a single flexible-link robot made in laboratory, and then the performance of each controllers in decreasing of arm vibration in final desired point and tracking error reduction are investigated. Further, to compare the robustness of the designed controllers, a same constant disturbance is applied to all controllers and their performance are compared. Finally, the simulation results and experimental results show that the fractional order PID torque controller has the best results among the implemented controllers.
Vahid Momeni, Mahdi Sojoodi, Vahid Johari Majd,
Volume 18, Issue 8 (12-2018)
Abstract
The main purpose of this paper is to the distributed formation tracking for fractional order multi agent systems with the leader-follower approach. First, it discusses the Lyapunov candidate function used to check the stability of the controlled system. The introduced candidate function is based on the properties of the matrix representing the desired system graph of the system. In this phase, the Lyapunov direct method is used to determine the stability of fractional order systems. Then, using sliding mode control, a decentralized controller design for tracking in fractional multi agent systems is presented in which it introduces and verifies the introduced control inputs. In the model, the input system is also considered as a disturbance type, and the control efficiency designed in turbulence mode is shown. In this section, it is shown that the controller introduced in the previous section has a desirable efficiency due to the sliding mode control. In the second section, the stability of the system, such as the first section, is investigated. at the end of this paper, several simulation examples are developed for controlling the performance of the controller.
M. Khamar, M. Edrisi,
Volume 18, Issue 9 (12-2018)
Abstract
Recently, a vast variety of wearable robots with various applications, including rehabilitation, have been produced, but a very challenging part of exoskeleton designing which is its motion control system still requires further investigation to be completed. Due to the nonlinearity in the dynamics of human-exoskeleton, uncertainty in parameters, unmodeled or simplified structures, and external disturbances (such as interaction of exerted human forces and movements), the use of robust control strategies is inevitable. Thus, in this research, a nonlinear disturbance rejection observer was used to estimate all of those as total disturbances. Then, a fractional order backstepping sliding mode (FOBSC) was utilized for enhanced tracking plus a Linear Quadratic Regulator (LQR) method to optimize the convergence to the equilibrium points. The advantage of using LQR is the optimum selection of the control input, and the FOBSC guarantees the robustness of the controller against uncertainties and disturbances. The combination of fractional order theory and control methods causes less chattering in the human-exoskeleton interactions. Moreover, particle swarm algorithm was used in order to select the coefficients of the cost function of LQR. In order to calculate the effect of the exoskeleton on human muscles and bones, the human parameters and knee motions, OpenSim was used. Matlab was used to implement the control strategy through OpenSim. The proposed method was then compared with the normal backstepping, fractional order system and LQR methods. The results show the superiority of this method compared to the classical methods.
