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Figure 7 Sliding variable with inaccurate assumption of initial condition Conclusion

Figure 7 Sliding variable with inaccurate assumption of initial condition Conclusion

Related Figures (7)

Consider a system with structure (2) with 4.1 System description and controller design Example and simulation results
Consider a system with structure (2) with 4.1 System description and controller design Example and simulation results
Figure 1 States x1 and x2 (with matched uncertainty) 2. Simulation based on systems with both matched ane unmatched uncertainty: The trajectories of the state variable: and the sliding function are shown in Figs. 4-6.
Figure 1 States x1 and x2 (with matched uncertainty) 2. Simulation based on systems with both matched ane unmatched uncertainty: The trajectories of the state variable: and the sliding function are shown in Figs. 4-6.
Figure 2 State x3 and sliding variable s (with matched uncertainty) In this case we have € = 0.5 and A is chosen as 0.7. The system trajectory is kept within a band of +1 x 107 around the sliding surface in the presence of the unmatched uncertainty. A quasi-sliding mode is shown. The closed-loop dynamic is determined by x(&+1)= (A + (GB) 'BG — BK)x(&) + w(2). Fig. 6 shows an example of the how states are impacted by w(&). As K is designed according to Proposition 2 and Remark 4, the closed-loop dynamic is stable even in the presence of w(A). Figs. 4—6 also supports the analysis given after Proposition 2. The states stay within a band around the origin. Fig. 7 shows he trajectory of the sliding variable when the assumption bout the initial condition deviates from its true value. The liding variable does not start from the sliding surface but a uasi-sliding mode is still realised finally because of the effect of the controller which is in the form of (20). Q 27,7.
Figure 2 State x3 and sliding variable s (with matched uncertainty) In this case we have € = 0.5 and A is chosen as 0.7. The system trajectory is kept within a band of +1 x 107 around the sliding surface in the presence of the unmatched uncertainty. A quasi-sliding mode is shown. The closed-loop dynamic is determined by x(&+1)= (A + (GB) 'BG — BK)x(&) + w(2). Fig. 6 shows an example of the how states are impacted by w(&). As K is designed according to Proposition 2 and Remark 4, the closed-loop dynamic is stable even in the presence of w(A). Figs. 4—6 also supports the analysis given after Proposition 2. The states stay within a band around the origin. Fig. 7 shows he trajectory of the sliding variable when the assumption bout the initial condition deviates from its true value. The liding variable does not start from the sliding surface but a uasi-sliding mode is still realised finally because of the effect of the controller which is in the form of (20). Q 27,7.
Figure 4 States x1 and x2 (with matched and unmatched uncertainties) Figure 5 State x3 and sliding variable s (with matched and unmatched uncertainties)
Figure 4 States x1 and x2 (with matched and unmatched uncertainties) Figure 5 State x3 and sliding variable s (with matched and unmatched uncertainties)
Figure 6 State x2 (magnified) (with matched anc unmatched uncertainties)
Figure 6 State x2 (magnified) (with matched anc unmatched uncertainties)
Related topics:
EngineeringMechanical EngineeringApplied MathematicsSliding mode controlRobustness (evolution)Electrical and Electronic Engineering
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