Minimal time deadbeat regulation and control of linear, stationary, sampled-date systems

• Main Author: de Barbeyrac, Jacques J.
• Format: Others
• Published: 1963
• Online Access: https://thesis.library.caltech.edu/6892/1/De_Barbeyrac_jj_1963.pdf; de Barbeyrac, Jacques J. (1963) Minimal time deadbeat regulation and control of linear, stationary, sampled-date systems. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/X0XR-4J34. https://resolver.caltech.edu/CaltechTHESIS:04052012-083321157 <https://resolver.caltech.edu/CaltechTHESIS:04052012-083321157>

<p>The problem of minimal time deadbeat regulation and control of linear, stationary, sampled-data systems is studied in this dissertation, assuming that only a limited number of the state variables are directly observable. The problem is first solved for the usual one-input one-output systems. The existing techniques for deadbeat digital compensation are all derived under the assumption that a specific initial state always exists; it will be shown that if this condition is violated and a digital controller is designed using the existing methods, the system has a transient response with time constants corresponding to the stable poles of the open-loop system. A technique to overcome this difficulty is developed using both a state-space and a z-transform approach to the problem. A digital controller which in a sense first identifies the complete state and then proceeds to control it in a deadbeat fashion is synthesized.</p> <p>The problem is next solved for multi-input, multi-output systems, using a state-space approach different from the one used for the one-input, one-output systems. It is first shown that if all the state variables are directly observable and the system is completely controllable in N sampling periods, there always exists at least one stationary, linear feedback law which will regulate the system in N sampling periods. If only a limited number of the state variables are directly observable, but the system is completely observable in N sampling periods, then there exist "discrete compensators" which will regulate the system in (N + N') sampling periods.</p>