Three mode control as an optimal control

Three mode control with Ziegler-Nichols or Cohen-Coon controller settings is shown to be the solution to an optimal control problem for a linear first order system with dead time and a quadratic cost functional. The implication of this result is that in the absence of an economically meaningful cost criterion there is no reason to prefer the results of optimal control theory to traditional design procedures for feedback control systems. The multivariable generalization of the optimal control problem solved here provides the means for extending classical control experience in design of single loop processes to multivariable control systems