Tuning Proportional-Integral controllers to approximate simplified predictive control performance

An exact equivalence between PI (Proportional-Integral) and two-parameter SPC (Simplified Predictive Control) is developed to provide identical control of first order linear plants. A relationship between the PI control parameters and the SPC control parameters is described. This relationship that allows the same control in the case of first order linear plants is also found to provide tuning formulas that yield PI control which approximates SPC performance in the case of second order linear plants with widely separated Eigenvalues. Finally, an extension of the PI control algorithm to include future errors provides another exact PI–SPC equivalence for networked control of first order plants.