Abstract. This paper addresses the modeling of a planar parallel robot including electric motors.The dynamic model of the system is derived by applying the substructure method and Lagrangian equations with multipliers in the form of redundant generalized coordinates. These equations are then transformed to the form of minimal coordinates of operational variables. Based on this form, a sliding mode controller (SMC) is designed for trajectory tracking in a task space. Numerical simulations in MATLAB are carried out based on the 3RRR parallel robot in order to show the effectiveness of the proposal approach. The obtained results show a good behavior of the proposed task space tracking controller.
In recent years, the application of hedge algebras in the field of control has been studied. The results show that this approach has many advantages. In additions, industrial robots are being well-developed and extensively used, especially in the industrial revolution 4.0. Accurate control of industrial robots is a class of problems that many scientists are interested in. In this paper, we design a controller based on hedge algebra for serial robots. The control rule is given by linguistic rule base system. The goal is to accurately control the moving robot arm which adheres given trajectories. Optimization of fuzzy parameters for the controller is done by genetic algorithms. The system has been simulated on the Matlab-Simulink software. The simulation results show that the orbital deviation is very small. Moreover, the controller worked well with correct control quality. This result once presents the simplicity and efficiency of the hedge algebras approach to control.
This paper presents the dynamic model and singularity-free simulation of electromechanical systems including closed loop multibody systems, massless gear transmission and electric motors. The dynamic model of these systems is established in matrix form and written in a Differential-Algebraic Equations form by applying the Lagrangian equation with multipliers and substructure method. Moreover, this paper deals with two difficult issues in the simulation of closed-loop multibody systems which are to overcome smoothly the singular configurations and to stabilize the constrained equations due to accumulated errors. The singularity-free simulation is solved by using null-space of Jacobian matrix to eliminate the constraint forces – Lagrangian multipliers in equations of motion. The drift in the constraint equation during simulation is restricted by a combination of Baumgarte’s stabilization and post-adjusting technique. Some numerical experiments are carried out to the planar 3RRR parallel manipulator driven by electric motors. Simulation results confirm the effectiveness of the proposed approach in overcoming the singular configurations and in stabilization of the constraint.
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