A pole-placement design for linear time-invariant multivariable feedback systems

This dissertation presents a pole placement method for designing linear time-invariant multivariable feedback systems. The idea of this proposed method is based on the fact that the internal signals of a feedback control system can be eliminated by performing row operations on a governing matrix. After choosing proper closed-loop poles, the new design procedure can be implemented by solving a Diophantine equation easily and insightfully. Simplification and systematization are the merits of the proposed method. Applied to multi-input multi-output (MIMO) systems, the proposed design method requires the plant to be in a strictly proper, right-coprime matrix fraction description (MFD). Therefore, if these prerequisites are not met, then additional manipulations are needed. Some rules to insure matrix non-singularity are presented to improve the MFD conversion. This new modified MFD conversion method is used as one of the preparatory tools of the proposed method. Instead of resulting in a solution which is not under the control of the designer as is the case with traditional methods, this novel MFD conversion method offers diverse choices of degrees in a reasonable range. With these rules to insure matrix non-singularity, a quick method for solving the Diophantine equation is also developed as part of a design tool. The newly developed linear time-invariant feedback systems design method makes the MIMO design easier and more flexible. More specifically, less computation and fewer cumbersome formulas are the attractive features of this method. Examples are conducted to validate the effectiveness of the method in both the SISO and MIMO cases. Based on the analytical and operator-based design procedure of the proposed method, extension of this new approach to the control of linear time-varying MIMO systems is possible.