Design of tunable digital set-point tracking PID controllers for linear multivariable plants using step-response matrices

It is shown that the proportional, integral, and derivative controller matrices embodied in tunable digital PID controllers for linear multivariable plants can be directly determined from open-loop tests performed on asymptotically stable plants, thus circumventing the need for mathematical models. The class of multivariable plants for which digital PID controllers are superior to digital PI controllers is identified, and the effectiveness of the resulting design methodology is illustrated by designing a tunable digital set-point tracking PID controller for a distillation column.