| The goal of control systems design is to make a physical system (the plant) act in a pre-specified manner as closely as possible. When the plant dynamics are not well understood or time-varying in an unknown way, such a goal may not be achieved satisfactorily by a fixed controller. An adaptive controller can adjust its parameters upon observing the plant's response such that the design goal can be better accomplished over time. This better performance usually comes at the cost of increased system complexity, both structurally and algorithmically.; Adaptive inverse control has been previously proposed as a simple yet general design approach to attack certain adaptive control problems from a signal processing viewpoint. A subproblem of inverse control is adaptive plant disturbance cancellation. The goal is to reduce disturbance level at the plant output without altering the plant's dynamics. An adaptive plant disturbance canceler consists of two adaptation processes, one for plant modeling, the other for disturbance canceling, operating at the same time. The effects of simultaneous adaptation on system behavior have been to a large extent unknown. This work examines the interactions between the two adaptation processes using the method of averaging analysis.; Averaging analysis can approximate a complex adaptive system by a simpler averaged system, and properties of the averaged system can be extended to the original adaptive law under certain regularity conditions. With the help of averaging analysis, this work studies two previously proposed disturbance cancellation schemes and gives sufficient conditions under which they work properly.; Provided the sufficient conditions are satisfied, interactions between plant modeling and disturbance canceling, though exist, do not have a detrimental effect on the disturbance canceler's performance; when the sufficient conditions are violated, simulation examples show the possibility of system malfunctioning. Situations satisfying the sufficient conditions are also pointed out. |
