Proportional Integral Switching Surface Research Articles

Microscopic chaos control of chemical reactor system using nonlinear active plus proportional integral sliding mode control technique

This paper puts forward the microscopic chaos control in the deterministic dynamics of the chemical reactor system. First, the dynamic behavior of the chemical reactor system is explored for some of the parameters and chaotic behavior is investigated. Phase plane, bifurcation plots and Lyapunov exponents are presented to verify the chaotic behavior. Second, nonlinear active plus proportional integral sliding mode control (NA-PISMC) is proposed to control microscopic chaos in the chemical reactor system. A proportional integral switching surface is proposed to achieve the stability condition of the error dynamics and controller is designed by using the relevant variables of the chemical system. Unlike the open loop and open plus closed loop control techniques, the design of proposed controller does not require the parameter perturbation. The required stability condition is derived based on Lyapunov stability theory. Simulation is done in MATLAB environment. Numerical simulation results are presented in order to show the effective performances of the proposed controller design. Simulation results correspond that the objectives of chaos existence and chaos control are achieved successfully.

Chaos control in biological system using recursive backstepping sliding mode control

This paper puts forward the control of chaos in the biological system. A new controller based on recursive backstepping sliding mode control is proposed such that it can control the chaotic dynamics in the biological system to stabilize at any position or to track any trajectory that is a smooth function of time. A proportional integral switching surface is proposed to achieve the stability condition of the error dynamics. Unlike the open loop and open plus closed loop control techniques, the design of proposed controller does not require the parameter perturbation. The required stability condition is derived based on Lyapunov stability theory. Simulation is achieved in MATLAB environment. Numerical simulation results are presented in order to show the effective verification of the proposed controller design. Simulation results correspond that the objective of chaos control is achieved successfully.

Single input sliding mode control for hyperchaotic Lu system with parameter uncertainty

In this paper, design of sliding mode controller (SMC) is presented to investigate the stabilization, complete synchronization and adaptive synchronization of four dimensional hyperchaotic Lu systems with parameter uncertainty. To achieve this goal, sliding mode control scheme along with Lyapunov stability theory is utilized. A proportional integral switching surface is proposed to ensure the stability of the closed-loop system in sliding motion. The SMC has been proposed to guarantee the occurrence of the sliding motion. It has also been shown that by proper choice of the adaptation laws for parameters, systems can be synchronized in conventional manner in master-slave configuration, in uncertain environment. The proposed adaptation laws also ensure the convergence of uncertain parameters to their true value in all the cases. Finally, numerical simulations are performed to demonstrate the effectiveness of the proposed approach.

Robust chaos synchronisation for a class of disturbed Rössler systems with multiple time-delays

This paper investigates the robust synchronisation problem for a class of Rössler systems with multiple time delays. Based on the proportional-integral switching surface, a sliding mode control (SMC) is derived to not only guarantee synchronisation between the master and slave Rössler systems with multiple time delays but also have a H∞ noise perturbation attenuation performance. The parameter matrix necessary for constructing both PI switching surface and the SMC can be easily solved by linear matrix inequality optimisation technique. The simulations results are presented to show the effectiveness of the proposed method.

Sliding mode control-based stabilisation and secure communication scheme for hyperchaotic systems

In this paper, design of a sliding mode control (SMC)-based control scheme is proposed for hyperchaotic systems. Further, the proposed procedure is extended to study robust synchronisation and secure communication scheme for hyperchaotic systems in master–slave configuration. To achieve this goal, a proportional-integral (PI) switching surface is proposed to simplify the task of assigning the performance of the closed-loop error system in sliding motion. Having established the PI switching surface, a sliding mode controller is designed. The proposed controller guarantees the occurrence of sliding motion and achieves asymptotic synchronisation of hyperchaotic systems in master– slave configuration. Then, as an application, the proposed SMC scheme is applied to construct an hyperchaotic secure communication scheme. Finally, numerical simulations are presented to show the efficacy of the proposed approach.

Adaptive synchronization of fractional-order chaotic system via sliding mode control

Based on sliding mode control theory and adaptive control theory, this paper investigates the synchronization of three-dimensional chaotic systems, designs a fractional order proportional integral switching surface, and proposes a single adaptive-feedback controller for fractional-order chaos synchronization. Simulation results for fractional-order unified chaotic system and Arneodo chaotic systems are provided to illustrate the effectiveness of the proposed scheme.

Sliding mode control design for generalized projective synchronization of unified chaotic systems containing nonlinear inputs

The problem of generalized projective synchronization for unified chaotic systems coupled with sector nonlinear inputs is investigated. Using the sliding mode control technique, a control scheme containing a new proportional–integral switching surface is developed to guarantee generalized projective synchronization even when the uncertainties and sector nonlinearity are present. Numerical simulations are included to demonstrate the effectiveness of the proposed synchronization scheme.

Adaptive sliding mode control of a high-precision ball-screw-driven stage

High-precision position control has been widely used in scientific instruments and semiconductor fabrication equipment. Traditionally, controllable displacements with sub-micron and nano-level resolution are usually achieved by piezoelectric actuators because of their high bandwidth and ease of control. However, the travel range of piezoelectric actuator is usually small. In this paper, the ball-screw-driven system is studied to provide long-range and high-precision performance for positioning and tracking control. In such a system, the friction dynamics are divided into the static and the dynamic regimes to describe the dynamic behavior of a conventional ball-screw-driven x-y stage. The same form of adaptive sliding mode controllers are designed in the static and dynamic regimes to obtain the precision performance for controlled stage. A proportional-integral switching surface is proposed to make it easy to assign the performance of the systems in the sliding mode motion and the controller is robust without knowing the bound of disturbance in advance. An illustrative example is included to demonstrate that the system achieves high precision (10 nm) and long-range (10 cm) positioning performance with repeatability and robustness by the proposed control approach.

Robust chaos suppression for the family of nonlinear chaotic systems with noise perturbation

This paper investigates the robust chaos suppression problem for some classical Rössler systems using the sliding mode controller (SMC). Based on the proportional-integral (PI) switching surface, a SMC is derived to not only guarantee asymptotical stability of the equilibrium points of the Rössler systems but also reduce the effect of noise perturbation to an H ∞ -norm performance. The parameter matrix necessary for constructing both PI switching surface and the SMC can be easily solved by the linear matrix inequality (LMI) optimization technique. Finally, two illustrative examples are provided to demonstrate the efficacy of the proposed control methodology.

H∞ controlling hyperchaos of the Rössler system with input nonlinearity

Based on the concept of variable structure control, this paper investigates the controller design for suppressing hyperchaos of the Rössler system with H ∞ norm constraint. A proportional-integral (PI) switching surface is newly adopted so that it becomes easy to solve the H ∞ control problem for such chaotic systems in the sliding mode. Based on this PI switching surface, a variable structure controller (VSC) is derived to guarantee the occurrence of sliding mode motion in finite time, even when the system is undergoing both input nonlinearity and external disturbance. Furthermore, a modified continuous controller is proposed to reduce the chattering phenomenon due to the conventional switching type VSC. An illustrative example is given to show the applicability of the proposed VSC design approach.

Sliding Mode Control for Uncertain Neutral Delay-Differential Systems.

This paper investigates the problems of stability analysis and sliding mode control for a class of uncertain neutral delay-differential systems. First, we develop a new delay dependent condition such that uncertain neutral systems are not only asymptotically stable but also with a prescribed stability degree. Then, a proportional-integral switching surface is newly proposed such that the sliding mode motion is robustly stable with a prospective stability degree. This type of switching surface does not allow for a reduction of system order as it is the case with most sliding mode control. This property of switching surface makes it easy to design a sliding mode controller for the considered neutral systems. Based on the switching surface, a sliding mode controller is derived to guarantee the occurrence of sliding mode motion in finite time. Last, two illustrative examples are included to demonstrate the superiority of the obtained results.

Robust Stabilization of Singular Systems Including State Delay via Sliding Mode Control.

The present paper concerns with the silding mode control for uncertain singular time-delay systems.First, a proportional-integral switching surface is newly proposed such that the sliding mode motion is not only asymptotically stable but also with a prospective stability degree.This type of switching surface does not allow for a reduction of order as it is the case with most sliding mode control.This property of switching surface make it easy to design a sliding mode controller for the considered singular time-delay systems.Then based on the switching surface, a sliding mode controller is derived to guarantee the occurrence of sliding mode motion in finite time.Finally, a numerical example is given to show the design procedures.