O f S l I d I n g M o d e C o n t r o l R e c e n t A d v a n t a g e s O f S l I d I n g M o d e C o n t r o l Europian Embedded Control Insttitute SUPELEC March 19-23, 2012

- Introduction (prehistory) - Discrete-time sliding modes - Observers and estimators - Chattering problem - High order sliding modes

Introduction of Sliding Mode Control First Stage – Control in Canonical Space

Introduction of Sliding Mode Control ■ Concept of Sliding Mode ( Second order relay system ) Upper semi-plane : Lower semi-plane : • State trajectories are towards the line switching line s=0 • State trajectories cannot leave and belong to the switching line s=0 : sliding mode • After sliding mode starts, further motion is governed by : sliding mode equation Sliding Mode n m In sliding mode, the system motion is governed by 1st order equation (reduced order). depending only on ‘c’ not plant dynamics. Sliding Mode Equation

Trajectories should be oriented towards the switching surface

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Introduction of Sliding Mode Control ■ Concept of Sliding Mode ( Variable Structures System ) 1 2 1 2 State planes of two unstable structures

State planes of Variable Structure System Introduction of Sliding Mode Control • If c<c0, the state trajectories are towards the line switching line s=0 • State trajectories cannot leave and belong to the switching line s=0 : sliding mode • After sliding mode starts, further motion is governed by : sliding mode equation State planes of Variable Structure System 1 2 In sliding mode, the system motion is governed by 1st order equation (reduced order). depending only on ‘c’ not plant dynamics.

Dubrovnik 1964 IFAC Sensitivity Conference

Dubrovnik 1964 IFAC Sensitivity Conference

Dubrovnik 1964 IFAC Sensitivity Conference