Contribuições ao Problema de Sintonia Ótima de Controladores PID de Ordens Inteira e Fracionária via Otimização Metaheurística

Abstract

The minimum jerk principle is often used for the purpose of planning robot trajectories. However, since the principle is formalized in terms of the robot’s kinematics, there is no guarantee that a PID-type controller tuned by classical methods (e.g. Ziegler-Nichols) will accurately track the planned profiles for acceleration and jerk. This is because the robot dynamics, necessary for the correct tuning of the controller, is not inserted in the formalism of the trajectory planning task. Bearing this in mind, this thesis introduces a method for optimal estimation of the gains of PID-like controllers for tracking robotic trajectories with minimum jerk constraints. The connection between the kinematics and dynamics of the robot for the purpose of optimum tuning of PID controllers, whether of integer or fractional order, occurs through the definition of a new performance index, called here jerk-based integral of absolute error (J-IAE), which extends the well-known IAE index for minimum jerk scenarios. Using a single J-IAE index as an objective function, the particle swarm optimization algorithm (PSO) is used to search for the optimal gains of the controllers of the joints of a vertical planar robot. Furthermore, beyond the application in robotics, this thesis also proposes a new methodology for the synthesis of PID-like controllers, which, in addition to seeking the optimum values for the controller’s gains, also seeks the optimal structure (i.e. optimal number of terms) of the controller to perform the task of interest. The combined optimization of the number of terms and the associated gains leads to a new class of PID controllers here called optimal selfconfiguring controllers. The PSO algorithm is used to investigate the feasibility of this methodology. Finally, a comprehensive performance evaluation is presented in order to evaluate the two proposals of this thesis, discussing their advantages and limitations for different robotic configurations and control plants.