Discrete Sliding Mode Control for Nonlinear Sampled Data Systems.

摘要

Nonlinear control theory has been successfully applied to continuous, nonlinear, autonomous plant models. Implementation of these continuous control laws, using digital computers, has relied upon high sample frequencies to approximate the performance of continuous control. This thesis extends the design of continuous sliding mode control to discrete and to sampled data systems. Continuous, nonlinear, autonomous, second order dynamic plant models are discretized using an approximation to a Taylor series expansion. The discretization process accounts for the Zero Order Hold circuit, used to convert the discrete control output of the digital computer, into a piecewise continuous control input to the plant. A Discrete Sliding Mode Control is developed using Feedback Linearization to account for plant model nonlinearities, and Lyapunov Stability analysis to guarantee convergence to the sliding manifold. A five step design process systematizes the design technique. The design technique was applied to two unstable nonlinear second order plant models. Stability was confirmed by simulation studies. Comparison with the Continuous Sliding Mode Control implemented digitally, at a sample rate five times the plant model fundamental frequency, showed that the Discrete Sliding Mode Control retained asymptotic stability while the Continuous Sliding Mode Control did not.