SAMPLED-DATA CONTROL BASED ON DISCRETE-TIME EQUIVALENT MODELS

Abstract

This thesis focuses on the design and performance of sampled-data control of continuous-time systems. The philosophy of the control law design is based on stabilization of discrete-time equivalent models of the continuous-time system. The development in the thesis can be broadly classified into sampled-data stabilization of a class of underactuated linear systems and sampled-data stabilization of locally Lipschitz nonlinear systems. The class of underactuated linear systems considered in the thesis has time varying actuation characteristics. The system can be actuated with a short duration pulse during a fixed interval of time. The system is unactuated otherwise in the interval. Based on these actuation characteristics, a discrete-time equivalent model can be developed by integrating the continuous-time model. The equivalent model is time invariant and fully actuated thus discrete-time control law design for sampled-data control is facilitated. The closed form exact discrete-time equivalent model (obtained by integrating the continuous-time model over the sampling interval) cannot be obtained for nonlinear systems in general. As an alternative, the continuous-time model is discretized using the Euler method. Discretization using the Euler method has an associated discretization iv error. This error may become unbounded in certain cases for nonlinear systems. This provides the motivation for analysis of discretization error bounds for nonlinear systems. Analyses show that locally Lipschitz nonlinear systems discretized using the Euler method have bounded discretization error for sampling time less than the guaranteed interval of existence. The error bound is a function of Lipschitz constant and sampling time. The discrete-time control law is designed on the basis of system model discretized using the Euler method. The sampled-data closed loop performance of locally Lipschitz nonlinear systems is analyzed using discretization error bounds and Lyapunov method. Locally Lipschitz nonlinear systems with state feedback control are analyzed in general whereas performance of output feedback control using discrete-time observers is investigated for a sub-class of locally Lipschitz nonlinear systems. Asymptotic/exponential stability of closed loop sampled-data systems is established for arbitrarily small sampling time; moreover it is shown that asymptotic/exponential stability can be achieved for nonzero sampling time under some additional conditions. The results are demonstrated by sampled-data control of nonlinear systems