The use of multiple surface sliding controllers for robust control of nonlinear systems with mismatched uncertainties has produced a number of impressive applications, but also raised a few theoretical questions. Among the latter are the use of numerical differencing to obtain derivatives of desired trajectories, robustness to uncertainties in the gain terms and the common practice of filtering desired trajectories for implementation. This paper seeks to address these issues through the concept of a Dynamic Surface Controller, in which filters form an integral part of the structure. This filtering removes the need for numerical differencing and guarantees a certain smoothness, enabling other assumptions of smoothness to be relaxed. In this paper, the Dynamic Surface Controller is coupled with a sequential design procedure that carves a system workspace out of the state space. Within this bounded region, bounded tracking performance can be rigorously guaranteed in the presence of uncertainties and constraints such as rate limits and saturation can be systematically avoided. The design of a Dynamic Surface Controller and the advantages of the workspace concept are demonstrated in the context of engine speed control.
“Loop-at-a-Time” Design of Dynamic Surface Controllers for Nonlinear Systems
Contributed by the Dynamic Systems and Control Division for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received by the Dynamic Systems and Control Division April 29, 1998. Associate Editor: G. Rizzoni.
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Gerdes, J. C., and Hedrick, J. K. (April 29, 1998). "“Loop-at-a-Time” Design of Dynamic Surface Controllers for Nonlinear Systems ." ASME. J. Dyn. Sys., Meas., Control. March 2002; 124(1): 104–110. https://doi.org/10.1115/1.1433804
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