Analytical design of proportional-integral controllers for the optimal control of first-order processes with operational constraints

A novel analytical design method of industrial proportional-integral (PI) controllers was developed for the optimal control of first-order processes with operational constraints. The control objective was to minimize a weighted sum of the controlled variable error and the rate of change in the manipulated variable under the maximum allowable limits in the controlled variable, manipulated variable and the rate of change in the manipulated variable. The constrained optimal servo control problem was converted to an unconstrained optimization to obtain an analytical tuning formula. A practical shortcut procedure for obtaining optimal PI parameters was provided based on graphical analysis of global optimality. The proposed PI controller was found to guarantee global optimum and deal explicitly with the three important operational constraints.