Sliding-Mode Controller Based on Fractional Order Calculus for a Class of Nonlinear Systems

This  paper  presents  a  new  approach  of  fractional  order  sliding  mode controllers  (FOSMC)  for  a  class  of  nonlinear  systems  which  have  a  single input and two outputs (SITO). Firstly, two fractional order sliding surfaces S1 and S2 were proposed with an intermediate variable z transferred from S2 to S1 in order to hierarchy the two sliding surfaces. Secondly, a control law was determined  in  order  to  control  the  two  outputs.  A  sliding  control  stability condition  was  obtained  by  using  the  properties  of  the  fractional  order calculus.  Finally,  the  effectiveness  and  robustness  of  the  proposed  approach  were demonstrated by comparing its performance with the one of the conventional sliding mode controller (SMC), which is based on integer order derivatives. Simulation results were provided for the cases of controlling a ball-beam and inverted pendulum systems

Commande floue adaptative directe stable étendue appliquée à la machine asynchrone

Aujourd'hui, suite au progrès significatifs dans le domaine de la commande des machines électriques, de nouvelles techniques et approches ont émergées. Pour les systèmes non linéaires à paramètres non constants, les lois de commandes classiques peuvent être inadéquates car certaines performances ne peut pas être garanties en présence des variations structurelles ou perturbations externes. Il est alors nécessaire de synthétiser des lois de commandes robustes par rapport à ces perturbations. C'est dans ce contexte qu'on propose dans ce travail une nouvelle commande qui combine l'étude de l'adaptabilité à l'incertitude ce qui dérive les régulateurs flous adaptatifs. Cette étude vise la commande floue adaptative directe stable étendue, qui utilise la théorie de l’approximation et la théorie de Lyapunov pour établir une loi d’adaptation paramétrique assurant la stabilité et la bornitude de tous les signaux de commande et de l’erreur de poursuite. Les résultats obtenus montrent que la commande floue adaptative directe stable étendue a prouvé une grande efficacité et une bonne robustesse en présence des variations paramétriques et de perturbations.Mots clé: Machine asynchrone- Systèmes flous- Commande par logique floue- Commande adaptative- lois adaptative floue- analyse de stabilité- fonction de Lyapunov. Stable direct adaptive fuzzy control extended applied to the asynchronous machineToday, as a result of significant progress in the area of control of electrical machines, new techniques and approaches have emerged. In order nonlinear or having non constant parameters systems, conventional control laws may be inadequate because some performance can not be guaranteed in the presence of structural variations or external disturbances. It is then necessary to synthesize robust controls with respect to these disturbances. It is in this context that we propose in this work a new command combines the study of adaptivity with the uncertainty that derives adaptive fuzzy controllers. This study presents the direct adaptive fuzzy control stability extended, which uses the theory of approximation and the theory of Lyapunov to establish a parametric adaptation law ensuring the stability and boundedness of all the control signals and the tracking error. The obtained results show that direct adaptive fuzzy control stability extended has proved a great effectiveness and a strong robustness in the presence of parameter variations and disturbances.Keywords: Asynchronous machine- fuzzy Systems- fuzzy control- adaptive control- fuzzy adaptive law- Stability analysis- Lyapunov function.

Nonlinear PD plus sliding mode control with application to a parallel delta robot

In this paper, a hybrid nonlinear proportional-derivative-sliding mode controller (NPD-SMC) is developed for the trajectory tracking of robot manipulators. The proposed controller combines the advantage of the easy implementation of NPD control and the robustness of SMC. The gains of PD control are tuned on-line in order to increase the convergence rate, whereas the SMC term is introduced to reject the external disturbances without requiring to know the system dynamics. The stability of the NPD-SMC is proved using Lyaponuv theorem, and it is demonstrated that the tracking error and the tracking error rate converge asymptotically to zero. Experiments are carried out on the parallel Delta robot to illustrate the effectiveness and robustness of the proposed approach. It is also shown the superiority of the NPD-SMC control over the NPD control and PD-SMC control

Iterative learning control for trajectory tracking of a parallel Delta robot

This paper proposes an iterative learning controller (ILC) under the alignment condition for trajectory tracking of a parallel Delta robot, that performs various repetitive tasks for palletization. Motivated by the high cadence of our application that leads to significant coupling effects, where the traditional PD/PID fail to satisfy the requirements performances. A PD-type ILC is combined with a PD controller in order to enhance the performance through iterations during the whole operation interval. The traditional resetting condition is replaced by the practical alignment condition, then the convergence of the tracking error is derived based on the Lyapunov's theory. We definitely point out that the position and velocity errors decrease as the number of iterations increases. Experiments are carried out to demonstrate the effectiveness of the proposed controller

An Enhanced Adaptive Time Delay Control-Based Integral Sliding Mode for Trajectory Tracking of Robot Manipulators

This article proposes an enhanced adaptive time delay controller (ATDC) for robot manipulators subjected to external disturbances. This approach is model-free and uses time delay estimation (TDE) to estimate complex and unknown robot dynamics. First, to remove the reaching phase and improve the robustness of the control, an integral sliding surface (ISS) is used. Second, to speed up the convergence and compensate for the TDE errors and external disturbances, the gains of time delay control and the sliding mode have been made adaptive. In this article, we clearly point out using the Lyapunov method that the position and velocity tracking errors are guaranteed to be uniformly ultimately bounded (UUB). The effectiveness and the robustness of the designed controller over existing methods are experimentally verified on a parallel Delta robot. The novel model-free proposed control is robust and highly accurate, which is appropriate and recommended for industrial robotic applications

Iterative learning control of multivariable uncertain nonlinear systems with nonrepetitive trajectory

Iterative learning control (ILC) theory is based on the traditional assumptions of resetting condition and repetitive trajectory. To overcome these restrictions, a novel ILC is developed in this paper for MIMO uncertain nonlinear systems subject to external disturbances and performing nonrepetitive trajectory. The proposed ILC scheme works under alignment condition and nonrepetitive trajectory that can be varied from iteration to iteration in time interval length, in magnitude scale as well as in initial and final positions. A time-scale transformation is introduced and combined with Lyapunov method to synthesise the control law and to prove the asymptotic convergence. The tracking error converges to zero as the number of iterations increases. Simulation of pick-and-place operations is carried out on a parallel Delta robot in order to show the feasibility and the effectiveness of the proposed approach

A comparative study between feedforward control and iterative learning control for trajectory tracking of Delta robot

This paper presents a comparative study between feedforward control (FF) and iterative learning control (ILC) with application to a parallel Delta robot performing repetitive trajectory. In order to improve the tracking trajectory of the Delta robot, a model-based feedforward compensation combined with the proportional derivative (PD) controller is introduced. As the Delta robot is affected by important frictions that are not taken into account in the dynamic model, the performance of the FF can be degraded considerably. To overcome these issues, a model-free control represented by the PD-type ILC controller is used instead the FF compensation. Experimental results show that the two strategies can ensure good tracking performance with better accuracy of ILC

Optimized Fractional Order Based Droop Control with Improving the Flexibility of a Microgrid

This work presents an improved four-levels hierarchical control strategy for flexible microgrid based on three-phase voltage source inverters (VSIs) connected in parallel. In the proposed strategy, zero-level control is required to handle current and voltage control of VSIs. The primary-level that consists of a decentralized controller is based on a modified universal droop control by introducing a fractional-order derivative. It is used to enhance the power sharing quality during islanded mode and the desired power generation in grid-connected mode. In the secondary centralized control, the voltage and frequency deviations caused by the primary-control are restored. Also, this level includes the synchronization control loop that enables a seamless transition between both operation modes. In order to improve the flexibility of the microgrid, a sequential logic approach is proposed in the tertiary level. It is exploited to manage both the restoration and the synchronization loops at each transition, as well as the static switch (SS) which is used to connect/disconnect the microgrid to/from the main grid. The control parameters are optimized by using the self-learning particle swarm optimizer (SLPSO) algorithm. Simulations were performed to highlight the performances of the proposed hierarchical control approach compared with the well-known three-levels control scheme