Xianhong Li, Haibin Yu, and Mingzhe Yuan
Optimal PI controller, Lyapunov theorems, NLCO problem, controlweight factor, coupled liquid level systemNomenclatureGp(s) process transfer functionN(s) numerator of process Gp(s)M(s) denominator of process Gp(s)a1, . . . , an system parameter of process Gp(s)b1, . . . , bw+1 system parameter of process Gp(s)r(s) command signaly(s) output signale(s) error signalu(t) control signalGc(s) PI controllerQc flow of control valve∗ Department of Information Service and Intelli
A systematic method is proposed to design optimal proportional- integral (PI) controller for different processes. An augmented integral squared error performance index is used to design optimal PI controller. The optimal control problem can be equivalently transformed into a nonlinear constraint optimization (NLCO) problem through Lyapunov theorems, therefore optimal PI controller can be obtained by solving NLCO problem. The proposed method is used to design optimal PI controllers for multiple processes. System performances of different tuning methods are studied. Control weight factor’s effects on dynamic performances are analyzed. Optimal PI controllers of the proposed method are applied for coupled liquid level system under various set points. Both simulation results and experiment results show effectiveness and usefulness of the proposed method.
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