Proposed Variable Structure Control Research Articles

High-performance discrete-time chattering-free sliding mode-based speed control of induction motor

This paper presents a new approach to induction motor (IM) speed controller design with indirect field-oriented control structure. The designed discrete-time variable structure (VS) speed controller uses elements of reduced-order and full-order (integral) sliding mode (SM) control, and acts as a nonlinear equivalent of conventional PI control. The controlled plant is approximated by a first-order dynamical model. Therefore, the proposed approach leads to an output feedback-based SM control (SMC) system. To improve its disturbances rejection and tracking capability, the controller is supplied with a first-order disturbance compensator based on the switching function measurement. The proposed VS control structure provides a high-performance chattering-free discrete-time SMC system. Numerous experiments have been carried out to test the proposed control method and to compare its performance with the conventional PI control approach. The experimental results demonstrate high tracking accuracy and robustness of the proposed system.

INVARIANT SLIDING SECTOR FOR VARIABLE STRUCTURE CONTROL

A sliding sector has been defined as a subset of the state space, inside which a norm of state decreases with zero control input [1]. In this paper, an invariant sliding sector is defined to be such a kind of sliding sector inside which with a suitable control law, the norm keeps decreasing and the system state stays there since then after entering the sector, i.e. the sector defined in the paper is an invariant subset of the state space. Design algorithms of the invariant sliding sector and the Variable Structure (VS) controller with the sector are given. The proposed VS controller with the invariant sliding sector ensures that the system state moves from the outside to the inside of the sector in a finite time and stays inside it forever after being moved into it, and that the norm of state keeps decreasing in the state space. The resulted VS control system is quadratically stable with a smooth VS control law. The experimental results with the inverted pendulum show the invariance of the sector and the robustness of the proposed VS control system with the invariant sliding sector.

Variable structure control with sliding sector based on hybrid switching law

AbstractIn general, a variable structure (VS) control system should be designed such that a sliding mode (or a boundary layer, or a high‐order sliding mode, or a sliding sector), where the reduced‐order system is stable, is reached in finite time, i.e. a reaching movement is necessary for VS control systems. This paper proposes a VS controller without the requirement of reaching movement. With the proposed controller, a system is stabilized by switching the system control input among a set of feedback control laws no matter whether a sliding mode happens or not. Each feedback control law is easy to be designed, because it uses only one of state variables with a fixed plus or minus feedback gain. For an n‐order system, 2n feedback control laws are needed to realize the proposed VS control. The concept of the sliding sector is used in the paper to show that there exists an area for each feedback control law, inside which a Lyapunov function decreases with the control law although the system may not be stabilized by it alone. A common Lyapunov function for all control laws exists if the system is controllable. Based on the extremum seeking control algorithm, a switching function is defined as the variation between the Lyapunov function and a pre‐determined decrease function. Then a VS control rule is designed such that a series of sliding modes happen with the switching function being a constant and the Lyapunov function decreases in every period after switching once through all control laws. The proposed VS control system is quadratically stable. Simulation results are given to show the convergence of the proposed VS control algorithm. Copyright © 2007 John Wiley & Sons, Ltd.

VS‐CONTROL WITH TIME‐VARYING SLIDING SECTOR — DESIGN AND APPLICATION TO PENDULUM —

ABSTRACTIn general, a Variable Structure (VS) system is designed with a sliding mode. Recently a sliding sector, designed by an algebraic Riccati equation, has been proposed to replace the sliding mode for chattering‐free VS controllers. In this paper we extend the design algorithm for the sliding sector to a time‐varying sliding sector. The time‐varying sliding sector is defined by functions dependent on both state and time, hence time‐varying uncertainty can be considered. The VS controller is designed to stabilize an uncertain system, quadratically. The design procedure for real systems is introduced via an implementation to the control of “Furuta pendulum”. To enhance the stability it is necessary to compensate the time‐varying nonlinear static friction of the actuator adequately, hence this problem is a good example to demonstrate the performance of the proposed VS control method. In the experiment, it will be shown that the VS control with the time‐varying sliding sector is superior to an orthodox chattering‐free VS control.

Variable structure control of continuous-time system with sliding sector

For any control systems, it is shown that in the state space there exists a subset around a hyperplane, inside which a norm of the state decreases without any control action. Therefore it is possible to use this natural feature of control systems to design a VS controller. In this paper, such subset is named the sliding sector. An algorithm to design the sliding sector using Riccati equation is given for controllable systems. A variable structure (VS) controller with the sliding sector for continuous-time system is proposed. With the VS control law designed in the paper, the state will move to the inside of the sliding sector and the norm of the state, i.e. some Lyapunov function decreases in all of the state space. Therefore the VS controller with the sliding sector quadratically stabilizes the system. A rotational pendulum system is used as a simulation model. The simulation results show that the proposed VS controller is chattering-free and with good control performance.

VS control of nonlinear system using sliding sector

A variable structure (VS) controller is designed for a class of nonlinear systems with parameter uncertainty by using sliding sector. The control problem is to let the output track a desired trajectory by state feedback. Based on a linear autonomous system, the sliding sector is defined as a subset of the state space Rn, where some norm of the state decreases. The VS control law designed in the paper transfers the system state from the outside to the inside of the sliding sector and ensures that some norm of the tracking error keeps decreasing in all of the state space even if there exists parameter uncertainty. Simulation results are given to shown the robustness of the proposed VS controller.