Digital Controller Design for Aliased Sampled-Data Systems
Abstract
Many of the dynamic systems in use today consist of an analog plant controlled by a digital controller. Design of these digital controllers assumes a system with no aliasing, and most, if not all, current design methods employ means to assure no aliasing is present. The drawbacks to these methods are unobservable and/or uncontrollable high frequency modes. This research effort provides a means to design a digital controller for systems with aliased modes. A model is developed in which both continuous and discrete portions of a sampled-data system are included. From this model, the unique digital controller function that will excite the analog plant is found. Moreover, as a result of the discrete-to-continuous manner of the model, the sample period allowing aliasing becomes a design parameter. Sampling frequencies providing improved response are determined and responses at these frequencies are explored. With aliasing allowed in the discrete-to-continuous system, stability for some systems is actually introduced and improved over the same systems in which aliasing is not allowed, as evidenced by increased gain margins and improved time domain responses. A deadbeat response controller is designed using proportional-integral control by placing one pole of a second-order system at the optimal position of the origin in the z-plane. The response of this controller is such that the desired position is obtained within a single sample period. Robustness of this controller is examined with favorable results. In a fourth-order system in which one mode is aliased, control of the aliased mode is accomplished simply by selecting the sample rate correctly. The resulting effects of the aliased mode are negligible, and design of the controller for the non-aliased mode follows traditional theory. Disturbance rejection for the second-order and fourth-orders systems was found to be excellent for disturbances with frequencies below that of the sampler.
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 01, 2000
- Accession Number
- ADA382580
Entities
People
- David S. Hansen
Organizations
- Brigham Young University