By B. Bandyopadhyay
Sliding mode keep an eye on is an easy and but powerful regulate strategy, 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 earlier, discrete-time structures and laptop dependent keep watch over became very important themes. This monograph provides an output suggestions sliding mode keep an eye on philosophy which might be utilized to just about all controllable and observable structures, whereas even as 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 inspiration and the idea that of discrete-time sliding mode control.
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Additional info for Discrete-time Sliding Mode Control: A Multirate Output Feedback Approach
20) where, ˜ ≤ νu ε νl ≤ eT Md η(µ) νu + ν l ε ν0 = 2 νu − ν l fl = ρ 2 v(µ)| κ fl . However, when v(µ)) whenever |¯ The value of sgn(v(µ)) = sgn(¯ the value of |¯ v(µ)| p fl , the sign of v(µ) cannot be determined accurately as v(µ) is in the range of v¯(µ) ± fl . Hence, in order to assure quasi sliding mode band in spite of this uncertainty, the width of the quasi-sliding mode band should be such that it encompasses this ambiguous band of |v(µ)| ≤ 2fl . 4) with an additional uncertainty. 22) (µ)ρ Choosing the sliding surface v(µ) = −0ρ8 1 (µ) = 0 and P = 2, the various controller parameters can be computed to be η0 = 0ε fd = 0ρ01ε j0 = 0ε fg = 0ρ0086ε ν0 = 0ε fl = 0ρ0105ε and the value of > satisfying the condition for recrossing, for τ = 2 is calculated as 2 (fd + fg ) (1 − τz ) > = 1ρ63 κ = 1ρ49ρ τz 2 This gives a quasi-sliding mode bound of fy = >z + fd + fg = 0ρ182ρ The resultant control is of the form (µ) = −1ρ56 1ρ66 T −0ρ182sgn k + 0ρ857(µ − 1) −1ρ2 0ρ35 T k + 1ρ05(µ − 1) ρ The simulation results can be seen in Fig.
4) where vd (µ) is a priori known function such that the following apply. 2 MROF-DSMC for Matched Uncertainty 29 The positive integer µ ∗ is chosen by the designer to achieve a good trade oﬀ between faster convergence and magnitude of the control ρ One possible deﬁnition of vd (µ) when |v(0)| κ 2fd is µ∗ − µ v(0)ε µ = 0ε 1ε · · · ε µ ∗ ε µ∗ |v(0)| ρ µ∗ p 2fd vd (µ) = The control law which satisﬁes the reaching law in Eqn. 4) can be computed by using Eqn. 3) as (µ) = − eT Hτ −1 eT Sτ (µ) + η0 − vd (µ + 1) ρ The control law so designed guarantees that for any µ ≥ µ ∗ ε the system states satisfy the inequality |v(µ)| = |η(µ − 1) − η0 | ≤ fd Hence, the states of the system settle within a quasi-sliding mode band whose width is less than half of the width of the band achieved by the control law proposed in .
4 Comparative Study State Feedback based Control Using the state feedback based control algorithm proposed in , a control signal was generated such that the quasi-sliding mode band is minimum. 25) 40 3 MROF-DSMC in Uncertain Systems For, the example considered the following control achieves the minimum possible quasi-sliding mode band of width ss = 0ρ7530 for a disturbance magnitude of k = 0ρ7529. 26) The simulation results for the control law proposed in  are shown below in Figs. 8). 1 0 Sliding Function ss(k) −1 −2 −3 −4 −5 −6 0 10 20 30 40 50 60 Sampling Instants (k) 70 80 90 100 Fig.