TY - CHAP
T1 - Sliding mode order and accuracy in sliding mode adaptation and convergence acceleration
AU - Dvir, Yaniv
AU - Levant, Arie
N1 - Publisher Copyright:
© Springer International Publishing Switzerland 2015.
PY - 2015
Y1 - 2015
N2 - Fundamental properties of Sliding Mode (SM) Control (SMC) are considered. The best and worst possible SM accuracy of Single-Input Single-Output (SISO) and Multi-Input Multi-Output (MIMO) systems is shown to be directly determined by the number of continuous derivatives of the sliding variables. The best SM accuracy is obtained in the both SISO and MIMO cases by homoneous SMs. SM adaptation is to be based on the detection of a real SM. Such detection is based on the observation of the above best possible accuracy in the presence of noises and discrete sampling. Convergence to SM is accelerated by control, which is piecewise homogeneous on successive time segments. It allows feedback application of homogeneous SM-based differentiators with piece-wise constant parameters, providing for arbitrarily fast convergence and preserving the optimal accuracy featuring homogeneous SMs. Simulation results show the feasibility of the proposed methods and demonstrate their asymptotic accuracy.
AB - Fundamental properties of Sliding Mode (SM) Control (SMC) are considered. The best and worst possible SM accuracy of Single-Input Single-Output (SISO) and Multi-Input Multi-Output (MIMO) systems is shown to be directly determined by the number of continuous derivatives of the sliding variables. The best SM accuracy is obtained in the both SISO and MIMO cases by homoneous SMs. SM adaptation is to be based on the detection of a real SM. Such detection is based on the observation of the above best possible accuracy in the presence of noises and discrete sampling. Convergence to SM is accelerated by control, which is piecewise homogeneous on successive time segments. It allows feedback application of homogeneous SM-based differentiators with piece-wise constant parameters, providing for arbitrarily fast convergence and preserving the optimal accuracy featuring homogeneous SMs. Simulation results show the feasibility of the proposed methods and demonstrate their asymptotic accuracy.
UR - http://www.scopus.com/inward/record.url?scp=85010788750&partnerID=8YFLogxK
U2 - 10.1007/978-3-319-18290-2_7
DO - 10.1007/978-3-319-18290-2_7
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AN - SCOPUS:85010788750
T3 - Studies in Systems, Decision and Control
SP - 129
EP - 153
BT - Studies in Systems, Decision and Control
PB - Springer International Publishing
ER -