This paper presents two applications of an alternative formulation for one-layer real time structure for control and optimization. This new formulation have arisen from predictive controller QDMC (Quadratic Dynamic Matrix Control), a type of predictive control (Model Predictive Control - MPC). At each sampling time, the values of the outputs of process are fed into the optimization-control structure which supplies the new values of the manipulated variables already considering the best conditions of process. The variables of optimization are both set-point changes and control actions. The future stationary outputs and the future stationary control actions have both a different formulation of conventional one-layer structure and they are calculated from the inverse gain matrix of the process. This alternative formulation generates a convex problem, which can be solved by less sophisticated optimization algorithms. Linear and nonlinear economic objective functions were considered. The proposed approach was applied to two linear models, one SISO (single-input/single output) and the other MIMO (multiple-input/multiple-output). The results showed an excellent performance

Introduction: Orthodontic retraction of the anterior teeth is indicated when the patient has a malocclusion with protrusion of the incisors. Several mechanics are indicated to perform this retraction. Objective: The objective of this study was to compare the strains generated by four different types of retraction mechanics along the roots of the anterior teeth. Methods: A photoelastic model simulating an arch with first premolars extraction was made. Sixty retraction archwires were prepared, including fifteen for each type of mechanics evaluated: sliding, teardrop loop spring, T-loop spring and double key loop archwire. The strains were observed in two perspectives: occlusal and oblique. In the occlusal perspective, strains were compared among the six anterior teeth. From the oblique perspective, strains were compared among the thirds of the left canine root. Results: In the occlusal perspective, the teardrop loop spring mechanics presented greater strains, followed by T-loop spring, double key loop archwire and sliding mechanics. In all mechanics, strains were more concentrated in the canines than in the incisors. From the oblique perspective, the teardrop loop mechanics generated greater strains in the cervical regions of the canine, and in the apical regions, no differences were found in strains among the four types of mechanics. In the same mechanics, greater strains were present in the cervical zones. Conclusion: The teardrop loop spring retraction mechanic presented the greatest mean strain, and the sliding retraction mechanic presented the lowest mean strain on the root of anteroinferior teeth in the occlusal and oblique perspectives.