Reference tracking in feedback control with saturating actuators

This dissertation addresses analysis and controller synthesis problems for systems with saturating actuators. Three problems are considered, namely: characterizing the quality of asymptotic tracking for deterministic references such as step, ramp, and parabolic inputs; characterizing the quality of tracking for band-limited random references; and developing a controller synthesis method for random reference tracking.; The solution to the first problem is based on extending the well-known notion of system type to systems with saturating actuators. It is shown that the roles of controller poles and plant poles are different, and, based on this, new system types are defined. Asymptotic tracking errors are characterized according to these system types. In addition, the notion of trackable domain is introduced, which characterizes limitations in asymptotic tracking due to actuator saturation. These results may be useful for selecting controllers and/or actuators that ensure desired trackable domains and steady state errors in feedback systems with saturating actuators.; The solution to the second problem is provided by introducing the notion of saturating random sensitivity function. This function, obtained using the method of stochastic linearization, characterizes the stationary tracking error for band-limited random references. Several of its functionals, referred to as tracking quality indicators, are introduced to characterize complex tracking behaviors that arise in feedback systems with saturating actuators. Various causes of poor tracking (e.g., static unresponsiveness, lagging, oscillatory responses, controller wind-up, and limitations due to finite trackable domains) can be identified by these indicators. The saturating random sensitivity function and tracking quality indicators are useful for predicting the quality of tracking in feedback systems with saturating actuators.; The solution to the third problem is given by extending the standard $H\infty$ technique to systems with saturating actuators. This extension, referred to as $SH\infty$ where ‘S’ stands for saturating, is utilized for shaping the saturating random sensitivity function in order to obtain desired tracking quality indicators. The effectiveness of this method is demonstrated by applying it to the problem of hard disk servo design.