Optimization of linear systems with integral control for time-weighted quadratic performance indices

The necessary conditions to be satisfied by the feedback control constructed by available variables, minimizing time-weighted quadratic performance indices for linear systems incorporating integral action, are developed using the parameter optimization technique. To remove the dependence of the solution on a reference input and an external disturbance, a performance index based on the statistical expectation and a minimax solution are considered. An algorithm based on a gradient technique is given to solve the necessary conditions of the minimax solution. Numerical examples are given to illustrate the effect of a time-weighted performance index on the transient response of the output, and they show that the integral-square-time-square error performance index is acceptable for a reference input.