Frequency Domain Design for Maximal Rejection of Persistent Bounded Disturbances

A frequency domain methodology for synthesizing controllers for SISO systems under persistent bounded disturbances is presented. The control objective is to maximize the disturbance magnitude without violating prespecified state, control and bandwidth constraints. These constraints are treated explicitly in the design process. State and control constraints expressed in the time domain are first mapped into a set of equivalent frequency domain design specifications. The latter specifications define a set of frequency domain constraints on admissible loop transfer functions. These constraints are then displayed on a Nichols chart highlighting the dependency of the loop gains on phase and frequency. The final step in the process is to follow a loop shaping procedure to satisfy the frequency domain constraints. In the proposed methodology, the structure of the controller emerges naturally as a consequence of loop shaping and is not preconceived. The design procedure is semi-graphical and clearly demonstrates the design trade-offs at each frequency of interest. The effectiveness of the design method is illustrated by synthesizing a controller for a third order boiler-turbine set.