This work presents a research on intelligent civil structures, like bridges and buildings, which consists in the use of sensors and actuators to monitor and control some specific parameters of the structures. A recent technological breakthrough has been the development of piezoelectric actuators or sensors using special materials, such as Lead Zirconate Titanate (PZT), magnetorheological dampers, shape memory, and others. In particular, the use of smart materials in the structural control of buildings is an interesting and promising subject in civil engineering. The method of active control is used to reduce the negative effects of external forces or perturbations on the performance of the overall system. These forces can be expressed mainly in terms of the effects of winds or earthquakes. This article presents a case of study of a building-like structure perturbed in the ground-borne by an external force and controlled through an active control applied with a PZT actuator joined in a column of the structure. The scheme of control consists in a modal control known as Positive Position Feedback (PPF), which aims to reduce the vibrations in the building-like structure. The gains of PPF control are tuned using an optimization method known as Differential Evolution combined with the Interior Point Algorithm. Experimental and numerical results are shown with the purpose of analyzing the efficiency of the control in the presence of an exogenous force in the dynamics of the system. The numerical results of the optimized PPF control are interesting and promising, reducing the vibrations and lateral displacements by around 97% of the building-like structure.