Modeling, analysis, and design of multirate systems

Multirate systems refer to the class of control systems where digital signals and systems updating at different rates are utilized. These systems have been the subject of extensive research for many decades. This work focuses on the class of multirate systems where the controller update rate is faster than the measurement update rate. This class of systems can be found in several applications of electro-mechanical and chemical processes.;The classical model matching problem that is studied in the literature requires the input-output properties of the closed-loop multirate system to match those of a desired single-rate linear time-invariant system. The model matching problem from an input-state viewpoint is considered in this work: Given a desired linear time-invariant system, find conditions and provide a controller design procedure to achieve matching between the closed-loop system and the desired system state variables at the measurement update rate. The advantage of solving this input-state model matching problem derives from the opportunity to select a desired behavior for the closed-loop system state variables. Necessary and sufficient conditions are given to solve this problem and, at the same time, to avoid the presence of ripples in the steady-state output of the continuous-time plant. In addition, a procedure is provided to design linear time-varying controllers for this control problem.;The second part of this work focuses on the design of linear time-invariant controllers for multirate systems. A new frequency-domain approach to model multirate systems is developed. This approach facilitates the design and the parametrization of linear time-invariant controllers. The new modeling approach is based on the use of up-sampling and down-sampling operators. The developed parametrization procedure is utilized to parametrize the set of stabilizing linear time-invariant controllers for which model matching is achieved at the fast control update rate with a desired single-rate system. Even though the use of up-sampling and down-sampling operators facilitates the parametrization of linear time-invariant controllers, this may cause ripples in the closed-loop system response. Therefore, necessary and sufficient conditions are also derived to guarantee ripple-free response to step reference signals. The conditions are given in terms of the constraints on the coefficients of finite impulse response filters included at the input of the feedback and feed-forward controllers.