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Öğe A new variable structure PID-controller design for robot manipulators(IEEE-Inst Electrical Electronics Engineers Inc, 2005) Jafarov, EM; Parlakçi, MNA; Istefanopulos, YIn this brief, a new variable structure proportional-integral-derivative (PID) controller design approach is considered for the tracking stabilization of robot motion. The work corroborates the utility of a certain PID sliding mode controller with PID sliding surface for tracking control of a robotic manipulator. Different from the general approach, the conventional equivalent control term is not used in this controller because that needs to use the matching conditions and exact full robot dynamics knowledge, which involves unavailable parameter uncertainties. Though the sliding surface includes also the integral error term, which makes the robot tracking control problem complicated, the existence of a sliding mode and gain selection guideline are clearly investigated. Moreover, different from uniformly ultimately boundedness, the global asymptotic stability of the robot system with proposed controller is analyzed. The sliding and global stability conditions are formulated in terms of Lyapunov full quadratic form and upper and lower matrix norm inequalities. Reduced design is also discussed. The proposed control algorithm is applied to a two-link direct drive robot arm through simulations. The simulation results indicate that the control performance of the robot system is satisfactory. The chattering phenomenon is handled by the use of a saturation function replaced with a pure signum function in the control law. The saturation function results in a smooth transient performance. The proposed approach is compared with the existing alternative sliding mode controllers for robot manipulators in terms of advantages and control performances. A comparative analysis with a plenty of simulation results soundly confirmed that the performance of developed variable structure PID controller is better under than those of both classical PID controller and an existing variable structure controller with PID-sliding surface.Öğe New variable structure PD-controllers design for robot manipulators with parameter perturbations(Acta Press/I A S T E D, 2004) Parlakci, MNA; Jafarov, EM; Istefanopulos, YIn this article two types of new variable structure PD controllers with and without full dynamics knowledge are designed for position and tracking stabilization of robot manipulator systems with parameter perturbations. The main contribution of this work is the design of the tracking PD-controller for robot manipulators without using full dynamics knowledge. The position PD-controller is built upon the conventional equivalent control approach when full robot dynamics model is well known. In this case, equivalent control cancelled the robot dynamics almost completely, and switching part of the controller is used only for establishing the sliding mode and for providing global asymptotical stability of the robot system. However, the tracking PD-controller does not use an equivalent control term and requires no exact information about the robot manipulator dynamics, and employs only the measurable joint variables and bounds of some robot perturbed parameters. The sufficient conditions for the existence of a sliding mode and the rate of convergence are investigated. Moreover, as this approach is different from existing ones, the global asymptotical stability conditions are also derived with a Lyapunov full quadratic form used for the first time. Linear matrix inequalities are often addressed. Reduced design conditions are also derived. Both analytical and numerical comparisons with the Qu and Dorsey control laws and stability results are also emphasized. Simulations are carried out with a two-link direct drive robot arm model. The simulation results have shown that the control performance of the designed system is better than that of existing systems.
