A periodic fixed-architecture approach to multirate digital control design

Abstract

Publisher Summary This chapter discusses analog-to-digital conversions that are employed within a multirate setting to obtain periodically time-varying dynamics. The com, pensator is thus assigned a corresponding discrete-time periodic structure to account for the multirate measurements. It explains that the optimal reduced-order multirate dynamic compensator is characterized by a periodically time-varying system of four equations consisting of two modified Riccati equations and two modified Lyapunov equations corresponding to each intermediate point of the periodicity interval. Because of the time varying nature of the problem, the necessary conditions for optimality involve multiple projections corresponding to each intermediate point of the periodic interval and whose rank along the periodic interval is equal to the order of the compensator. Similar extensions to reduced-order multirate estimation are addressed. The chapter develops a periodic fixed-structure control framework (temporal) for multirate systems. An equivalent discrete-time representation is obtained for the given continuous-time system. Optimality conditions are derived for the problems of optimal multirate sampled-data static output-feedback as well as multirate fixed-order sampled-data dynamic compensation. A novel homotopy continuation algorithm is developed to obtain numerical solutions to the full-order design equations. Future work will use these results to develop numerical algorithms for reduced-order, multirate dynamic compensator design as well as extensions to decentralized (spatial) multirate controller architectures.