Advances in Sliding Mode Control: Concept, Theory and by Branislava Draženović, Čedomir Milosavljević (auth.), B PDF

By Branislava Draženović, Čedomir Milosavljević (auth.), B Bandyopadhyay, S Janardhanan, Sarah K. Spurgeon (eds.)

ISBN-10: 3642369855

ISBN-13: 9783642369858

ISBN-10: 3642369863

ISBN-13: 9783642369865

The sliding mode keep watch over paradigm has develop into a mature strategy for the layout of strong controllers for a large type of structures together with nonlinear, doubtful and time-delayed structures. This ebook is a suite of plenary and invited talks added on the 12th IEEE

International Workshop on Variable constitution process held on the Indian Institute of expertise, Mumbai, India in January 2012. After the workshop, those researchers have been invited to advance ebook chapters for this edited assortment with a purpose to mirror the most recent effects and open examine questions within the area.

The contributed chapters were geared up through the editors to mirror a number of the subject matters of sliding mode keep an eye on that are the present components of theoretical examine and purposes concentration; particularly articulation of the basic underpinning concept of the sliding mode layout paradigm, sliding modes for decentralized approach representations, regulate of time-delay platforms, the better order sliding mode suggestion, effects appropriate to nonlinear and underactuated structures, sliding mode observers, discrete sliding mode keep an eye on including innovative learn contributions within the software of the sliding mode thought to genuine global problems.

This ebook presents the reader with a transparent and entire photo of the present developments in Variable constitution structures and Sliding Mode keep an eye on Theory.

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Extra resources for Advances in Sliding Mode Control: Concept, Theory and Implementation

Example text

The following commands generate the reduced order SM model: [n,m]=size(B) [n,r]=size(G) [q,n]=size(H) P=eye(n)-B*(B*C)ˆ-1*C [U,S,V]=svd(P) SYSeq=ss(P*A,P*G,H,zeros(q,r)) SYStr=ss2ss(SYSeq,U’) SYSsm=modred(SYStr,[n-m+1:n],’truncate’) [Asm,Gsm,Hsm,Dsm]=ssdata(SYSsm) Asm = %Projector matrix %SVD of P %Equivalent system %Transformed system %Trunc. of m variab. 5 , Dsm = 0. 6ı) e−5T e−7T e−10T ]. 1806 ⎦ . 7894 Reduced order CT optimal SM design: The chosen optimization matrices are R = I3 , Q = I5 .

Below we will show that in the general case the adaptation of the gain-parameter k (t) only is sufficient to minimize the chattering effect on sliding mode phase since the suggested “learning law” for k (t) variation automatically takes into account the presence of this term. I. S. 28) If sliding mode does not exist, then [sign (σ (x))]eq = 1 and the gain k(t) will be equal to k+ which results in the occurrence of this motion in the surface σ (x (t)) = 0. 2 Analysis of the δ -Stability for the Adaptive Version The following theorem describes the main stability property of the sliding mode controller with the gain adaptation based on the “equivalent control method”.

39) is z(t) = m 1 t− α¯ k0 α¯ k0 + m (α¯ k0 )2 − x0 e−α¯ k0t and one can conclude that t = (k0 )−1 q 1 α¯ = √ x0 q 1 α¯ < t1∗ for a large enough α¯ . Here t is the solution of the transcendent algebraic equation z(t ) = 0 and q (s) → 0 when s → 0. I. S. 46) 1 q α¯ Last two inequalities permit to formulate the following result. 1. 5β¯ . Note that the system is not even asymptotically stable for φ0 ≥ β¯ . 35) in this case y (t) is constant or diverging, if the disturbance φ is such that |φ (t)| ≥ β¯ , and has sign opposite to control u (t).

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Advances in Sliding Mode Control: Concept, Theory and Implementation by Branislava Draženović, Čedomir Milosavljević (auth.), B Bandyopadhyay, S Janardhanan, Sarah K. Spurgeon (eds.)

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