Static Sliding Mode Control Research Articles

On the Control of the 2D Navier–Stokes Equations with Kolmogorov Forcing

This paper is devoted to the control problem of a nonlinear dynamical system obtained by a truncation of the two-dimensional (2D) Navier–Stokes (N-S) equations with periodic boundary conditions and with a sinusoidal external force along the x-direction. This special case of the 2D N-S equations is known as the 2D Kolmogorov flow. Firstly, the dynamics of the 2D Kolmogorov flow which is represented by a nonlinear dynamical system of seven ordinary differential equations (ODEs) of a laminar steady state flow regime and a periodic flow regime are analyzed; numerical simulations are given to illustrate the analysis. Secondly, an adaptive controller is designed for the system of seven ODEs representing the approximation of the dynamics of the 2D Kolmogorov flow to control its dynamics either to a steady-state regime or to a periodic regime; the value of the Reynolds number is determined using an update law. Then, a static sliding mode controller and a dynamic sliding mode controller are designed for the system of seven ODEs representing the approximation of the dynamics of the 2D Kolmogorov flow to control its dynamics either to a steady-state regime or to a periodic regime. Numerical simulations are presented to show the effectiveness of the proposed three control schemes. The simulation results clearly show that the proposed controllers work well.

Static Sliding Mode Control of Systems With Arbitrary Relative Degree by Using Artificial Delay

Static output-feedback stabilization of systems with relative degree n with matched disturbances is considered. Assuming that the system is controllable, a static output-feedback sliding mode controller is designed, where the output derivatives up to the order (n-1) are approximated by using the current and the delayed values of the output. Numerical examples illustrate the efficiency of the method.

Introduction and realization of four fractional-order sliding mode controllers for nonlinear open-loop unstable system: a magnetic levitation study case

The concept of magnetic levitation attracts the attention of researchers and developers on the global platform for its serviceability in both industrial and research applications. Sliding mode controller is a nonlinear and robust control strategy to provide efficient control over variable structure systems. This paper is initiating with nonlinear modelling of magnetic levitation system dynamics. Various sliding mode controllers for controlling the current through electromagnetic coil to levitate the ferromagnetic ball are presented. This paper is mainly focusing on design robust and energy-efficient fractional sliding mode controller for a nonlinear system. Four novel controllers called fractional static sliding mode controller, fractional integral static sliding mode controller, fractional dynamic sliding mode controller and fractional integral dynamic sliding mode controller are proposed. Stability proof of Lyapunov criteria for the proposed controller has been done. Performance of the proposed controllers is analysed in comparison with the existing sliding mode controllers. Experimental validation is done on a benchmark Feedback 33–210 magnetic levitation system.

Robust Control of an Electrostatic Microelectromechanical Actuator

A continuing trend these days is the use of micro-electro-mechanical actuators with electronic circuitry to fab- ricate MEMS devices such as micro-switches, hard disks, optical micro-mirrors ... One of the problems with the electro- static MEMS actuator is that when an electrical voltage is applied to these devices, the micro-actuators undergo a residual vibration before reaching their permanent position. This paper addresses the control of an electrostatic microelectrome- chanical actuator to reduce the vibration effect on its performance. A feedback linearization controller, a static sliding mode controller and a dynamic sliding mode controller are designed for the microelectromechanical system. The stability of the closed loop system is proved. Simulation results indicate that the proposed control schemes work well.

Sliding mode control of coupled tanks

The paper deals with the level control of two coupled tanks. A static sliding mode control scheme is proposed for the system. To greatly reduce the chattering problem associated with the static sliding mode control scheme, two different dynamic sliding mode control schemes are proposed. The proposed control schemes guarantee the asymptotic stability of the closed loop system. To illustrate the developed control schemes, the performance of the closed loop system is simulated using MATLAB. Moreover the proposed control schemes are implemented using an experimental setup. The simulation as well as the implementation results indicate that the proposed control schemes work very well. In addition, robustness of the control schemes to change in system’s parameters as well as to disturbances are investigated.

Chattering‐free sliding mode control for a class of nonlinear mechanical systems

AbstractSecond‐order sliding mode control (2‐smc) and dynamic sliding mode control (dsmc) eliminate the disturbing characteristic of chattering in static sliding mode control under the assumption that the derivative of the sliding surface is available or complex inequalities at the acceleration level can be constructed. In this paper, passivity‐based adaptive and non‐adaptive chattering‐free sliding mode controllers are proposed assuming that the upper bound of the norm of the derivative of the sliding surface is available, a weaker and easy to implement assumption in comparison to those of 2‐smc and dsmc. The closed‐loop system accounts explicitly for the invariance condition without reaching phase, and therefore for a desired transient response with global exponential convergence of tracking errors. Preliminary experiments are presented. Copyright © 2001 John Wiley & Sons, Ltd.

Robustness of static sliding mode control for non-linear systems

Robustness of static sliding mode control based on affine non-linear state space models in regular form is considered. This is necessary because the stability of non-linear systems is usually a local property which can be destroyed by an additive uncertainty. Thus the uncertainty should be appropriately structured. A cone bounded uncertainty structure is assumed in this paper. In general, when a regular form is used to design a static sliding mode control, only matched uncertainty can be expelled. For the stability of the closed-loop system, a minimum phase assumption is necessary. It is shown that the sliding manifold is equivalent to the manifold determined by the zero dynamics and the minimum phase assumption relates to the compactness of the sliding manifold in the ideal sliding mode. It is also shown that the two phase separability, i.e. reaching mode and ideal sliding mode, which holds for linear systems, does not hold generally for non-linear systems. A pertinent example is given.