A New CAD Method and Associated Architectures for Linear Controllers

S. Boyd, V. Balakrishnan, C. Barratt, N. Khraishi, X. Li, D. Meyer, and S. Norman

IEEE Transactions on Automatic Control, 33(3):268-283, March 1988.
Shorter version appeared in Proceedings of the American Control Conference, pages 611-616, June 1987, and Proceedings Annual Allerton Conference on Communication, Control and Computing, pages 889-898, 1986.

A new CAD method and associated architectures are proposed for linear controllers. The design methods and architecture are based on recent results which parametrize all controllers which stabilize a given plant. With this architecture, the design of controllers is a convex programming problem which can be solved numerically. Constraints on the closed-loop system such as asymptotic tracking, decoupling, limits on peak excursions of variables, step responses, setting time, and overshoot, as well as frequency domain inequalities are readily incorporated in the design. The minimization objective is quite general, with LQG, {bf H}_infty, and new ell_1 types as special cases. The constraints and objectives are specified in a control specification language which is natural for the control engineer, referring directly to step response, noise powers, transfer functions, and so on. This control specification language will be the input to a compiler which will translate the specifications into a standard convex program in {bf R}^L, which is then solved by some numerical convex program solver. A small but powerful subset of the language has been specified and its associated compiler implemented. The architecture proposed simplifies not only design of the controller but also its implementation. These controllers can be built right now from off the shelf components or integrated using standard VLSI cells.