On Performance Based Design of Smooth Sliding Mode Control

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Title

On Performance Based Design of Smooth Sliding Mode Control

Abstract

The Sliding Mode Control (SMC), being famous for remarkable robustness, uses a discontinuous controller and is established in two phase, namely, reaching phase and sliding phase. The sliding phase, represented by reduced order dynamics, offers certain benefits like invariance with respect to parameters and disturbances. However, the discontinuous nature of the controller and imperfection of physical systems imposes the undesirable high frequency oscillations called chattering. In addition, the reaching phase has been reported to be sensitive to uncertainties and disturbances which may degrade the performance or even cause stability problems in some sensitive applications.

The Smooth SMC (SSMC), known for chattering eradication, do not approximate the actual sense of sliding modes. In addition, the Integral SMC (ISMC) eliminated the reaching phase and hence any sensitivity to any unwanted phenomenon in the reaching phase. However, the SSMC such as Smooth Super Twisting Algorith (SSTA) has no theoretical measures for the performance and/or robustness while the ISMC still suffers due to chattering, though reduced, and loses parameter invariance property due to no order reduction in the sliding phase.

In this thesis, a novel Lyapunov function based analysis of the SSTA is proposed and by the virtue of stability analysis, novel performance and robustness parameters are developed which include, analytical expressions for choosing the gains of the controller, settling time of the closed loop system and stability bounds for a class of uncertainties. The proposed settling time formulation suggests a methodical approach to SSTA design in contrast to the available rules of thumb. The proposed design framework is validated against a challenging problem of the Underground Coal Gasification (UCG) process control.

On the other hand, the ISMC has been investigated for chattering removal and possible performance degradation due to parametric variations in the sliding phase. In this regard, the discontinuous part of the ISMC is made smooth to eliminate chattering and the continuous part of the controller is proposed as a Linear Matrix Inequality (LMI) based LPV gain scheduling state feedback controller which deals with the possible performance degradation due to parametric variations. The results are proved mathematically and are validated experimentally on laboratory test bench ball on a beam balancer.

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