Khadija Dehri

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.

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.

Conditions of Disturbances Rejection for Discrete First, Second Order and Repetitive Sliding Mode Controllers

Harmonic disturbance rejection is an important field of control theory and applications. In this paper a discrete first and second order sliding mode control for multivariable systems are investigated. The necessary conditions of harmonic disturbances rejection using first and second order sliding mode control laws are elaborated. In order to improve the performances of sliding mode control in periodic disturbances rejection, a discrete repetitive sliding mode control is presented. A necessary condition for the choice of the discontinuous terms in discrete repetitive sliding mode control is then developed. The different proposed control strategies have been tested on numerical simulation example. The obtained results are very satisfactory in terms of compensation of periodic disturbances using discrete repetitive sliding mode control.

Multimodel repetitive–predictive control of nonlinear systems: rejection of unknown non-stationary sinusoidal disturbances

ABSTRACT In the present work, we propose a supervised multimodel repetitive–predictive control scheme for discrete-time nonlinear systems in order to reject unknown non-stationary sinusoidal disturbances and to track reference trajectory. The nonlinear system is described by the decoupled state multimodel. Also, a non-stationary sinusoidal unknown input multi-observer is used to estimate the state and the unknown non-stationary sinusoidal disturbances simultaneously. The estimate of the disturbances is exploited by the magnitude–phase-locked loop (MPLL) approach to reconstruct the accurate disturbance period used to develop a robust supervised multi-rejector. The proposed control strategy provides good closed-loop performance despite the changes of the disturbance characteristics. A simulation example is provided to illustrate the significance of the proposed multi-rejector.

Discrete Variable Structure Model Reference Adaptive Control for Non Strictly Positive Real Systems Using Only I/O Measurements

Solving the problem of unpredictable transient responses and tracking reference trajectories has recently becomes one of the challenging aspects of Model Reference Adaptive Control (MRAC). In this paper, a Discrete Variable Structure Model Reference Adaptive Control using only input output measurements (D-VS-MRAC-IO) for linear non strictly positive real systems with relative degree two and relatively important parameter variations was proposed. The D-VSMRAC- IO was designed in order to improve the performances of the MRAC control. Simulation results show a good reference trajectory tracking in spite of the presence of parameter uncertainties.

Discrete fast terminal and integral sliding mode controllers

In this paper, we propose two methods of discrete sliding mode control. The first is the discrete fast terminal sliding mode control (DFTSM) and the second is the discrete integral sliding mode control (DISMC). These methods are proposed in order to overcome sliding mode problems, such as chattering phenomenon, convergence speed and rejection of external disturbance. An illustrative example is presented to prove the effectiveness of the proposed methods.

Discrete variable structure model reference adaptive control using only input-output measurements:

Designing an adequate controller for a plant with an arbitrary relative degree is still an active area of research. In this paper, a discrete variable structure model reference adaptive control using only input-output measurements (DVS-MRAC-IO) for not strictly positive real systems with a relative degree of two is proposed. In order to show the effectiveness of the proposed controller, a detailed stability analysis is studied using Lyapunov theory. Further, a straightforward generalization of DVS-MRAC-IO for systems with arbitrary relative degree is presented. Numerical results are used to show the effectiveness of the proposed methods.

Synthesis of an Optimal Sliding Function Using LMIs Approach for Time Delay Systems

During the reachability phase, the sliding mode control is sensitive to external disturbances and uncertainties. In this paper, we propose to determine coefficients of the sliding function using the technique of Linear Matrix Inequalities (LMIs) for single-input single-output time delay systems. This technique leads to an optimal choice of the sliding function to reduce the reachability phase. Using the proposed sliding function, a discrete second order sliding mode control is presented. The control law is based on an input–output model. Simulation results demonstrate that the proposed strategy leads to an optimal performance in terms of reduction of the reachability phase as well as the chattering phenomenon.