| The concept of equivalent outputs for single input/single output nonlinear processes is introduced to aid in the synthesis of nonlinear controllers. The roots of this method are in linear inferential control, where a controller is designed on the basis of an auxiliary output, which must be inferred on-line. This output not only simplifies the controller design problem, but the resulting controller also solves the original control problem in terms of the primary output. Two types of equivalent outputs, statically equivalent and dynamically equivalent, are mathematically defined and a general control structure for use with either type is developed. A process with a statically equivalent output will have the same static gain as with its primary output, but may have different zero dynamics. A process with a dynamically equivalent output will have the same zero dynamics as with its primary output, but may have different static gain.;Statically equivalent outputs are applied to the problems of nonminimum phase compensation for nonlinear systems with unstable inverses and deadtime compensation for nonlinear processes. For control of a nonlinear system with an unstable inverse, the system with a statically equivalent output defined is minimum phase. For control of a nonlinear system with deadtime, a statically equivalent output that represents what the primary output would have been if there were no deadtime, is defined. In both cases, the statically equivalent output is inferred on-line and a nonlinear controller is synthesized using existing methods and combined with the estimator.;A dynamically equivalent output is applied to the difficult nonlinear problem of pH control. The dynamically equivalent output makes the system linear, and is interpreted physically as the Strong Acid Equivalent. The Strong Acid Equivalent is estimated on-line on the basis of a reduced model that depends on the titration curve of the process stream and combined with a linear PI controller. Results from laboratory experiments and an industrial process validate this method. |
