Abstract:
A new control methodology is proposed for use with a class of nonlinear, single-input
discrete time systems. The technique is based on a discrete time approach that parallels
existing continuous time sliding surface concepts. Modifications to the basic algorithm
allow for system models with time-variant or uncertain parameters, time delays in
the control input, and external disturbances. A major feature of the method is its
straightforward extension to an adaptive control form which can be used to improve
performance and maintain stability in the presence of large parametric uncertainty
or time-variant behavior. Techniques are proposed for overcoming instabilities that
frequently arise when using adaptive control schemes based on reduced order system
models or in the presence of disturbances.
A framework is provided for the practical application of the methodology to continuous
time systems. The discrete time nature of the development makes it especially
well suited to applications where sensor data is infrequently available or computational
power is limited. An experimental study is performed using an underwater remotely
operated vehicle to verify the validity of the approach. The ability of the method to
use a nonlinear model and adapt to large parametric uncertainty is shown to result in
improved performance over the use of a linear or time-invariant model.
