A new computer graphics approach to parameter space design of control systems

This paper presents a new approach to parameter space design of linear multivariable control systems. The complete solution of a pole region assignment problem for single-input systems is obtained as an admissible region in then-dimensional parameter space of state feedback gains. We develop a new modeling technique for these admissible parameter space regions which is superior to previous ones because it permits unambiguous and efficient graphical display of slices in 2D and 3D subspaces. In an interactive computer graphics implementation, this method provides an environment where the influence of stability, performance, robustness, integrity, and control constraints on design parameters can be directly visualized and complex tradeoffs are resolved in an interactive way. By judicious combination of overlays, color, and/ or animation, admissible ranges of up to five or six design parameters can be displayed simultaneously. A sequential decomposition technique which selects slices for full parameter space design of lower dimensional subsystems such that the remaining eigenvalues are invariant is used for systems of arbitrarily high order. Parameter space design of unity rank feedback for multiinput systems is done in exactly the same fashion, while systematic sequential design of full rank feedback is achieved as the sum of dyadic stages to which the single-input modeling techniques apply. Examples are given for all presented methods to show the flexibility and potential as a computer-aided control system design framework with a novel integration of computer graphics technology.