Download Discrete-time Sliding Mode Control: A Multirate Output by B. Bandyopadhyay PDF

By B. Bandyopadhyay

Sliding mode regulate is a straightforward and but powerful regulate process, the place the approach states are made to restrict to a particular subset. With the expanding use of pcs and discrete-time samplers in controller implementation within the contemporary previous, discrete-time platforms and computing device dependent regulate became vital themes. This monograph provides an output suggestions sliding mode regulate philosophy which are utilized to just about all controllable and observable structures, whereas whilst being basic adequate as to not tax the pc an excessive amount of. it truly is proven that the answer are available within the synergy of the multirate output sampling thought and the concept that of discrete-time sliding mode control.

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Additional info for Discrete-time Sliding Mode Control: A Multirate Output Feedback Approach

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20). 1) where, v(µ) = eT (µ) is the sliding function, τ and > are controller parameters satisfying the relationship 1 − τz κ 0ε > κ 0. 1 (The Quasi Sliding Mode Band). The quasi-sliding motion has been defined in [27] as a motion in which the system states approaches monotonically to the vicinity of the sliding surface v(µ) = 0 and on reaching a band termed as the quasi-sliding mode band (QSMB), it moves about the sliding surface in a zigzagging motion, crossing and re-crossing the sliding surface in subsequent time steps, with the magnitude of the zig-zag motion being within the band in subsequent time steps.

5) It is assumed here, without loss of generality that the pair (A0 ε B0 ) is controllable and (A0 ε C) is observable. 1), when discretized at a sampling time of z sec, with z such that zx = µx zε zu = µu zε zy = µy z where {µx ε µu ε µy } ∈ W, W denoting the set of whole numbers, would yield the following best-approximated discrete-time model [2, 11]. 1. It is obvious from the equations that the boundedness of η(y) would ensure the boundedness of ηd (µ). This can be proved in the following manner.

The analysis is restricted to systems wherein φd ≤ q ≤ φ. 29) starting at the same initial condition. The input 0 (µ) is the control that would drive the system in a desired manner. The point to be noted is that this is not a tracking problem as both systems start from the same initial condition and have almost the same dynamics. 30) where 0 (µ) is the ideal control and 1 (µ) is used to reject the perturbations. 31) where, v(µ) = 0 is a function representing a stable manifold, designed based on system states in a manner similar to ordinary sliding mode.

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