Ahmed Said Nouri

Repetitive sliding mode control for nondecouplable multivariable systems: Periodic disturbances rejection

Disturbances rejection is an important field of control theory. In this context, our paper is proposed to deal with asymptotic rejection of periodic disturbances affecting discrete multivariable systems with an interactor matrix. A multivariable repetitive sliding mode control is proposed to cancel the disturbances when the system is nondecouplable. To synthesis this control an interactor matrix is used. A numerical example shows that the proposed strategy gives good performance in terms of rejecting periodic disturbances for nondecouplable multivariable systems.

Stability analysis of discrete input output second order sliding mode control

The success of the sliding mode control (SMC) is due to the simplicity of its implementation and its robustness against external disturbances via state space and input output model. In spite of this characteristic, the sliding mode control (SMC) suffers from a main drawback known as the ‘chattering phenomenon’. In order to overcome this problem, a new discrete second order sliding mode control via input output model is proposed in this paper. A stability analysis of the proposed control was then studied. To illustrate the effectiveness of the proposed discrete second order sliding mode control law, a classical discrete sliding mode control and discrete second order sliding mode control were applied to a real discrete second order system via input output model. The experimental results of the proposed discrete sliding mode control law show good performances in terms of the rejection of the external disturbances and the reduction of the chattering phenomenon.

Multimodel Discrete Second Order Sliding Mode Control: Stability Analysis and Real Time Application on a Chemical Reactor

The variable structure control is principally characterized by its robustness with respect to the system’s modeling uncertainties and external disturbances (Decarlo et al. (1988); Filippov (1960); Lopez & Nouri (2006); Utkin (1992)). Sliding Mode Systems are a particular case of the Variable Structure Systems (VSS). They are feedback systems with discontinuous gains switching the system’ s structure according to the state evolution, in order to maintain the trajectory within some specified subspace called the sliding surface (Utkin (1992)). However, the application of this control law is confronted to a serious problem. In fact, sliding mode necessitates an infinite switching frequency which is impossible to realize in numerical applications because of the calculation time and of the sensors dynamics that can not be neglected. The discontinuous control generates in that case oscillations on the state and on the switching function (Utkin (1992)). Owing to the many advantages of the digital control strategy (Ben Abdennour et al. (2001)), the discretization of the sliding mode control (SMC) has become an interesting research field. Unfortunately, the chattering phenomenon is more obvious in this case, because the sampling rate is more reduced. Many approaches have been suggested in order to resolve this last problem. Most of them propose a reduction in the oscillation amplitude at cost of the robustness of the control law (Utkin et al. (1999)). In the eighties, a new control technique, called high order sliding mode control, have been investigated. Its main idea is to reduce to zero, not only the sliding function, but also its high order derivatives. In the case of the r-order slidingmode control, the discontinuity is applied on the (r-1) derivative of the control. The effective control is obtained by (r-1) integrations and can, then, be considered as a continuous signal. In other words, the oscillations generated by the discontinuous control are transferred to the higher derivatives of the sliding function. This approach permits to reduce the oscillations amplitude, the notorious sliding mode systems robustness remaining intact (Levant (1993)). Another problem of the SMC is its vulnerability to external disturbances, parametric variations and non linearity, essentially, during the reaching phase. A solution to this problem, based on the multimodel approach, was proposed by the authors in (Mihoub et al. (2009a)). The combination of the multimodel approach and the second order discrete sliding mode control (2-DSMC) allows resolving both the chattering problem and the vulnerability during Multimodel Discrete Second Order Sliding Mode Control: Stability Analysis and Real Time Application on a Chemical Reactor 25

A real time application of discrete second order sliding mode control to a semi-batch reactor: a multimodel approach

The esterification reaction requires a tight temperature control. As the different stages of this reaction (the heating, the reaction and the cooling) are characterised by different dynamics, a discrete second order sliding mode control using one global model of the system was not able to ensure the desired performances. We propose, in this paper, an application of the multimodel approach for the discrete second order sliding mode control. Experimental results on the reactor show better control performances both at tracking and disturbance rejection relative to the case where the conventional discrete second order sliding mode control is applied.

An asymptotic discrete second order sliding mode control law for highly non stationary systems

In this work, an asymptotic numerical second order sliding mode control (2-DSMC) is developed in order to reduce the chattering phenomenon that characterize the discrete first order sliding mode control. A comparative study with Bartolinipsilas numerical second order sliding mode control approach is realized. The obtained results in the case of the proposed approach denote the notable improvement of the closed loop performances in regulation and in tracking, essentially, in presence of the highly non stationary system.

A chattering free second order discrete sliding mode observer: An experimentation on a chemical reactor

In this paper, the chattering phenomenon that characterizes discrete sliding mode systems is analyzed and illustrated by a simulation example. In order to resolve this problem, in case of relatively large parameter variations and/or external disturbances, a second order discrete sliding mode observer (2-DSMO) is proposed. A stability analysis of the proposed observer is developed and a real time application on a semi batch reactor is realized. The experimental results show a good performance in terms of precision of the state estimation and of chattering reduction.

Discrete sliding mode control for time-varying delay systems: a multi-delay approach

Owing to its potential for real applications, many researchers have studied the problem of modelling and control of time-varying delay systems. In this paper, we propose a new strategy called multi-delay approach for modelling and control of these systems. In this new strategy, the time-varying delay systems are modelled by a multi-delay model representation in which each elementary model is characterised by a constant delay value varying between the lower and upper bounds of the delay term supposed to be known. A systematic elementary model reproducing the real output evolution is generated. Then, a discrete sliding mode control based on the multi-delay model representation (MD-DSMC) was developed to stabilise such systems. The proposed controller guarantees a finite time convergence of systems under consideration. The controller parameters are selected by solving linear matrix inequalities (LMIs). A comparative study with the classical discrete sliding mode control was also subject of this work.

Discrete T–S fuzzy systems with time-varying delays: a new discrete sliding mode control approach

The control of nonlinear systems has been the subject of extensive research. This interest is mainly due to its potential for real applications. In this paper, we investigated discrete sliding mode control for a class of nonlinear time-delay systems represented by T–S fuzzy models. In most existing fuzzy sliding mode control, a common input matrix is considered for all subsystems. This assumption is very restrictive. Therefore, we proposed a new sliding surface, which takes account of the system state and the control input in order to exclude the restrictive assumption. Furthermore, we have improved the latter sliding mode control scheme, by adding delayed states. Based on formulation of linear matrix inequalities, the parameters of the sliding function are obtained. Therefore, to further reduce the conservatism in the existing results, the Wirtinger-based integral inequality and Jensens inequality are employed. To show the applicability and effectiveness of the proposed controller design methodology, a numerical example is given for illustration.

Discrete Predictive Sliding Mode Control for multivariable systems

This paper shows the development of a Discrete Predictive Sliding Mode Controller (DPSMC) for multivariable systems. This is an extension of our previous works synthesized in the case of single input single output. The multivariable DPSMC consists on two loops, the primary loop is a Sliding Mode Control (SMC) and the secondary loop is a Model Predictive Control (MPC). This type of scheme improves the performances of the SMC and the MPC controllers. Simulation results demonstrate that the DPSMC gives better performances, for multivariable systems, in terms of strong robustness to external disturbance and parameters variation, chattering elimination and fast con- vergence, in comparaison with the SMC.

Adaptive sliding mode control for discrete uncertain systems using matrix RLS algorithm

Designing an adequate controller for plant with uncertainties is still an open area for research. In this paper, a discrete adaptive sliding mode control is proposed for the input-output systems with uncertain parameters. Its motivated by the use of recent new variations of Recursive Least Square algorithm (M-RLS). This algorithm is combined with sliding mode control. Simulation results show the effectiveness of the proposed method, in spite of the presence of parameter uncertainties.