Solenoid actuators are well-known components that convert electromagnetic energy into mechanical energy. For control purposes, it is requested to have a high magnetic force that stays almost constant in the working region of the actuator. To meet these requirements, it is necessary to have an optimal geometrical design of the actuator. In this study, the following steps are performed to optimize the geometry of the solenoid actuator. The Finite Element Analysis (FEA) is performed, and the results of the simulation is verified with the experimental data. The effect of all geometrical parameters on the characteristics of the magnetic force is investigated. The parameters that highly affect the magnetic force are chosen as design optimization parameters. Then, the Particle Swarm Optimization (PSO) algorithm is realized to find optimal parameters. The algorithm consists of two objective functions being combined into a single objective function. It includes a higher and more consistent magnetic force in the effective working region of the solenoid. Finally, the solenoid actuator with optimized parameters is manufactured, and the results are compared. They show that the optimized solenoid actuator satisfies one of the objective functions, and magnetic force stays almost constant in the working region of the solenoid actuator.

The identification of nonlinear terms existing in the dynamic model of real-world mechanical systems such as robotic manipulators is a challenging modeling problem. The main aim of this research is not only to identify the unknown parameters of the nonlinear terms but also to verify their existence in the model. Generally, if the structure of the model is provided, the parameters of the nonlinear terms can be identified using different numerical approaches or evolutionary algorithms. However, finding a non-zero coefficient does not guarantee the existence of the nonlinear term or vice versa. Therefore, in this study, a meticulous investigation and statistical verification are carried out to ensure the reliability of the identification process. First, the simulation data are generated using the white-box model of a direct current motor that includes some of the nonlinear terms. Second, the particle swarm optimization (PSO) algorithm is applied to identify the unknown parameters of the model among many possible configurations. Then, to evaluate the results of the algorithm, statistical hypothesis and confidence interval tests are implemented. Finally, the reliability of the PSO algorithm is investigated using experimental data acquired from the UR5 manipulator. To compare the results of the PSO algorithm, the nonlinear least squares errors (NLSE) estimation algorithm is applied to identify the unknown parameters of the nonlinear models. The result shows that the PSO algorithm has higher identification accuracy than the NLSE estimation algorithm, and the model with identified parameters using the PSO algorithm accurately calculates the output torques of the joints of the manipulator.

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