Optimum Controller Adjustments from Ultimate Gain and Frequency

The ultimate characteristics of a process control system are obtained readily by closing the loop through a proportional controller, and increasing the gain on the controller to the minimum proportional gain at which the system oscillates steadily. Johnson and Bay (J4) describe tests of both the ultimate gain approach and the reaction curve approach applied to pneumatic analog systems. 

The techniques for treating the synthesis of simple control systems are generally applicable to complex systems if the complexity arises from multiplicity of loops rather than intransigence of loop elements. 

A common kind of complicated system is the cascaded control system, in which a master controller reacts to disturbances in the controlled variable by manipulating the set point of a secondary controller, which in turn manipulates a control agent affecting the process. Franks and Worley (F3) present a quantitative analysis of a cascade control system simulated on an analog computer. 

Among other kinds of complex systems are those which incorporate high speed computers in the control loop to generate the command signals for the controllers on the basis of broad scale appraisals of operating performance, output requirements, and other pertinent variables. Such systems are not yet completely in being in the process industries, but 

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