Overview

An intensive search is underway for a unified field theory that would bring together quantum and gravitational forces and provide the underlying truth behind physical laws. In this appendix we show that we are at least fortunate enough to have achieved a unification of Lambda, internal model control, the Ziegler-Nichols reaction curve, and ultimate oscillation tuning methods for bioprocess control. For the control of vessel temperature, concentration, and gas pressure, the controller tuning equations from diverse methods are reducible to a common form, in which the maximum controller gain (equation 3-3f in chapter 3) is proportional to the time-constant-to-dead-time ratio ( ?1 / ?d) and is inversely proportional to the open loop gain (K _o), commonly known as the process gain. This common form is easy to remember and provides insight into the relative effects of process dynamics on tuning and hence on loop performance. This appendix concludes with a derivation of the equation to predict the control error (integrated absolute error) in terms of the tuning settings (equation 2-2a in chapter 2) from a PI controller's response to load disturbances.

Lambda tuning provides stable results for any Lambda value. Normally, Lambda is set large enough to provide the degree of slowness desired to reduce interaction and promote the coordination of loops. If Lambda is set much smaller than normally expected, as outlined in this section, then the result is the common form, which provides maximum disturbance rejection and minimum integrated absolute error. Thus, Lambda tuning...