| First, we present a new tool for the analysis and design of uncertain linear systems. A robustness measure is developed based on the characteristic equation root locations. The measure has a geometric interpretation and can be easily used in the controller design. Moreover, simple robust controller design can be accomplished by using this measure with pole placement techniques. Also, we illustrate that the ITAE and Bessel function prototype configurations are robust.; The perturbation technique can be extended to the phase and gain margins in the frequency domain. Then, the sensitivities of phase and gain margins are derived. Furthermore, the significance of these sensitivities can be interpreted geometrically. We present a new concept about the phase and gain margins for a system uncertainties. That is, the design of systems to resist parametric perturbations should include the gain and phase sensitivities as well as the margins themselves.; Moreover, we consider the uncertainties of nonlinearity for the actuator, for example, the saturation of the actuator. In this dissertation, the Lur'e problem is addressed from a root locus point of view. By partial fractional expansion, the sector for globally asymptotic stability can be easily determined. It is already known that for some system, the Popov and circle stability criterions fail to verify Aizerman's conjecture. Here, we present that for certain class transfer functions, the Hurwitz sector is equivalent to this stability sector for the Lur'e problem.; In this dissertation, the above analytical tools are used in the fine motion control: nanometer positioning of an XY table. The method is called dual mode control for the positioning of an XY table. This method has been developed to achieve nanometer-level resolution by adding a force actuation system to conventional, lead screw-actuated XY tables. The force actuation system is simple, economical, and easy to control. It operates in parallel with the conventional actuation, and is used after the lead screw motion has stopped. Unlike series, resolution enhancement devices, such as piezo-electric actuators, no modification is required of the loading-bearing portion of the table. We design a robust controller with the pole placement technique. (Abstract shortened by UMI.)... |
