| The objective of this dissertation is to improve the feedback design of control system engineering using output from the open-loop system. With theories from linear algebra, especially the concepts of eigenvalues and eigenvectors, the procedure to obtain a design for output feedback is created by positioning the desired closed-loop poles in order to improve the performance of the system. Analysis shows that the closed-loop poles are more stable from the perturbation of any parameters in the closed-loop system when eigenvectors are selected so that the angles between them are as close as possible to 90°. This conclusion applies to both the state-feedback and the output-feedback designs. Assuming the open-loop system is controllable, the state-feedback design can be implemented to generate the control input when all states are available for measurement. If all states are not accessible for measurement, then the output-feedback design can be implemented, assuming the open-loop system is controllable and observable. An additional requirement to design the output feedback is that the total number of inputs ( m) and outputs (r) must be greater than the number of the open-loop system's order (n). When this additional requirement is not met, an observer with a reduced-order of n + 1 - m - r must be designed to estimate the additional required outputs. The condition number of closed-loop poles is used to evaluate the design in the s-domain and cost function in the time-domain. From these evaluations, the output-feedback and the observer designs with properly-selected eigenvectors will be able to achieve comparable performance compared to the state-feedback design. |
