Designing Nonlinear Control Structures by Reference System Synthesis

Reference system synthesis, an equation-based method for designing nonlinear feedforward/feedback controllers for general dynamic systems is presented. The control objective is expressed as a desired closed loop behavior in the form of a set of integro-differential equations which can, by design, be nonlinear. Realization of the desired closed loop behavior depends upon the solution of an operator equation relating the open loop system to the desired closed loop system for computing the necessary manipulated variable action. Analytical solutions of this operator equation can be found for simple systems. In general, numerical solutions can be determined using Newton's method, for example. The advantages of reference system synthesis are (i) it provides a general method for designing nonlinear feedforward/feedback controllers, (ii) it is simple, and (iii) its loop-shaping capabilities allow for the design of deliberately nonlinear closed loop behavior for higher performance and constraint-avoiding control. In this paper, we introduce the reference system synthesis procedure, illustrate its application to simple dynamical systems, and discuss the relationship of reference system synthesis to PID and Internal Model Control design procedures.