Fixed-structure robust controller synthesis based on symbolic-numeric computation: design algorithms with a CACSD toolbox

We propose a new method with a software tool for parametric robust control synthesis by symbolic-numeric computation. The method is a parameter space approach and it is especially effective for analysis and design of fixed structure controllers of rational type. The real quantifier elimination (QE), which is one of the recent progresses in the symbolic computation, plays a key role in our development The QE-based approach can uniformly deal with a lot of important design specifications for robust control such as frequency restricted H_∞ norm constraints, stability (gain/phase) margin and stability radius specifications, and pole location requirement by reducing such specifications to a particular type of formulas called a "sign definite condition (SDC)". This is also useful for improving the efficiency of QE computations since we can utilize an efficient QE algorithm specialized to the SDC. We have developed a MATLAB toolbox for robust parametric control based on a parameter space approach accomplished by QE. The QE-based parameter space approach and numerical simulation of specifications for specific controller parameter values taken from a controller parameter space are integrated conveniently in our toolbox with the assistance of a graphical user interface. This enables control engineers to achieve multi-objective robust controller synthesis smoothly. We also discuss how to merge the numerical computation and the symbolic operation to make our new design methods more efficient in practical control design.