Tuning of a First-Order Lag-Lead Compensator used with a Very Slow Second-Order Process

Lag-lead compensators are well known in automatic control engineering. They have 3 or 4 parameters to be adjusted (tuned) for proper operation depending on the compensator order. The frequency response of the control system or the root locus plot are traditionally used to tune the compensator in a lengthy procedure. A selected very slow second-order process has a time response to a unit step input of 150 seconds settling time is controlled using a first-order lag-lead compensator (through simulation). The lag-lead compensator is tuned by minimizing the sum of square of errors of the control system using MATLAB. Four functional constrains are used to control the performance of the lag-lead compensated control system. The result was reducing the settling time to only 0.666 seconds. The steady-state characteristics of closed-loop control system using the first-order lag-lead compensator were excellent. It was possible reduce the steady-state error to less than 0.01 using the tuned first-order lag-lead compensator.