Sliding Mode Control: The Delta-Sigma Modulation Approach by Hebertt Sira-Ramírez
By Hebertt Sira-Ramírez
This monograph offers a singular approach to sliding mode keep an eye on for switch-regulated nonlinear structures. The Delta Sigma modulation procedure permits one to enforce a continuing regulate scheme utilizing one or a number of, self sustaining switches, therefore successfully merging the to be had linear and nonlinear controller layout strategies with sliding mode regulate. Sliding Mode keep watch over: The Delta-Sigma Modulation technique, combines rigorous mathematical derivation of the original positive aspects of Sliding Mode regulate and Delta-Sigma modulation with a number of illustrative examples from assorted components of engineering. furthermore, engineering case experiences show the applicability of the method and the convenience with which you'll enforce the uncovered effects. This booklet will entice researchers up to the mark engineering and will be used as graduate-level textbook for a primary direction on sliding mode control.
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Extra info for Sliding Mode Control: The Delta-Sigma Modulation Approach
5 In this ﬁgure, we have also plotted the equivalent control just to check that the sliding mode existence conditions are not violated with the speciﬁed trajectory. 3 In this example it is interesting to assess the eﬀects of a violation of the existence condition 0 < ueq U < U . 5 as in the previous simulation), then the time derivative of the reference trajectory is accordingly increased during the maneuver. 0. The sliding mode is no longer sustained during this open interval and, as a consequence, the tracking of the reference trajectory is temporarily lost.
This virtual feedback control constitutes the equivalent control. The existence conditions of a sliding regime on a given sliding manifold simply demand that the equivalent control must be bounded within the interval determined by the two extreme numerical values assigned to the switch position function. The equivalent control law must be realizable as an intermediate smooth feedback control action with respect to the available switching control extremes. Such virtual control actions are responsible for sliding surface invariance, a concept that is intimately related to the ideal controlled behavior of the system on the restriction, or sliding, manifold.
We remark that if S is such that, locally, Lg σ < 0. The simple sliding surface coordinate change σ = −˜ σ makes all the previous assumptions valid. There is no loss of generality, then, in locally taking the transversal condition as: Lg σ > 0. Henceforth, all our statements about existence of a sliding regime are meant in a local sense. This locality assumes that its validity occurs in a suﬃciently large region of S for guaranteeing an eﬀective, sustainable, controlled motion of the system on the sliding surface.