Departure angle based and frequency based compensator design in learning and repetitive control

Iterative learning control (ILC) and repetitive control (RC) have proved to be very effective at eliminating periodic disturbances and effective at achieving zero tracking error executing a periodic command in feedback control systems. To implement ILC or RC a compensator is usually required to achieve stability and good learning transients. This dissertation develops new methods to design such controllers and compensators in order to improve various performance characteristics or to design based on observed response properties. This dissertation has four major parts.; The first part addresses three main difficulties in linear discrete-time ILC: (1) The number of output variables for which zero tracking error can be achieved is limited by the number of input variables. (2) Every variable for which zero tracking error is sought must be a measured variable. (3) In a digital environment, the intersample behavior may have undesirable error from ripple. Methods to address these difficulties are provided. Three learning control laws are implemented to show the effectiveness of the methods.; The second part uses root locus departure angle information to design compensators in an RC system. The high dimensionality of RC systems makes typical classical design methods, such as Routh Criterion, Jury test, root locus plots and the Nyquist stability condition intractable. However, the departure angle can be computed easily in any RC system. The method presented in this part takes advantage of this fact to design compensators. A library of compensators is developed.; The third part extends the method in order to design compensators without needing to create a model. Unlike classical control, RC requires high accuracy model throughout the whole frequency range, which is difficult to obtain. Hence, this part develops a technique consisting of five stages to design compensators purely from the observed error history during repetitions.; The fourth part investigates the merits of higher order RC. It is concluded that higher order RC has an advantage with respect to the waterbed effect. The characteristics of pole and zero locations and departure angle information in higher order RC are summarized. Finally, another class of compensator inspired by higher order RC is developed.