Output feedback sampled-data control of nonlinear systems using high-gain observers

This thesis presents a separation principle for sampled-data control of a class of nonlinear systems. The basic ingredients of this technique are: a continuous-time high-gain observer that robustly estimates the derivatives of the output, a global bounded state feedback control, and a discrete-time implementation of the high-gain observer. For sufficiently small sampling period and sufficiently high observer gain, the sampled-data controller recovers the performance of the continuous-time state feedback controller. The high-gain observer is discretized using different discretization methods to achieve the best discretization algorithm and parameters choice.; Analysis of the discretized high-gain observer as a numerical differentiator provides answers to a number of important questions such as: what is the best discretization method? what are the best choices for the observer parameters and how do they relate to the sampling period? and what is the effect of the order of the observer on the estimation of the output derivatives. This is done for noisy as well as noise-free measurements. We also show how other numerical differentiators are special cases of the high-gain observer discretized by the bilinear discretization method. The closed-loop analysis shows that the sampled-data output feedback controller recovers the performance of the continuous-time state feedback controller as the sampling frequency and the observer gain become sufficiently large. Performance recovery is shown in two steps. First we show boundedness of trajectories, which come arbitrarily close to the desired equilibrium point as time progress. Second, we show convergence to the equilibrium point.; Finally, we experimentally test the use of the discretized high-gain observer in controlling an electromechanical system of (the pendubot). We show how saturation is used to overcome peaking and the effect of increasing the observer gain on the steady-state error. The experimental results confirm our analysis and show that the discretized high-gain observer outperforms the Euler formula as a means for calculating velocities from optical encoder.