Solving the time-variant equality-constrained quadratic programming (TVECQP) problem extensively occurs in diverse applications, and thus many novel schemes have been developed, e.g., numerical algorithms and zeroing neural networks. However, few existing works consider the perturbations in a computing system which may cause inaccurate solution. To suppress the effect of perturbations, we try to employ the integral feedback control to design a new algorithm. Firstly, the control system model of the traditional algorithm, i.e., the Newton algorithm is presented. Hence, the correlation between the control system and algorithm has been established. Then, the integral control feedback is added to the system to construct the proportional-integral iterative (PII) algorithm. The PII algorithm is thus endowed with robustness against various perturbations that are proved in theory. Moreover, numerical simulations among the Newton algorithms, the zeroing neural network, and the proposed PII algorithm are performed for comparison, which verify the theoretical analyses and demonstrate the superior robustness of the PII algorithm. Finally, two applications are provided to illustrate the feasibility of the PII algorithm, where one investigating the distribution of surface water from satellite images and the other is about robotic manipulator control.