Model reaching adaptive-robust control law for vibration isolation systems with parametric uncertainty

Adaptive control has been used for active vibration isolation and vehicle suspensions systems. A model reference adaptive control law is used for the plant to track the ideal reference model. In a model reaching adaptive control approach, the ideal of a skyhook target without using a reference model is achieved. In this paper, a novel approach, a model reaching adaptive-robust control law is studied for active vibration isolation systems. A dynamic manifold for ideal system is defined using the ideal of a skyhook target model system parameters. First, a new Lyapunov function is defined. Based on the Lyapunov stability theory, a model reaching adaptive and a robust control laws are derived for the uncertain system to reach the ideal manifold. Parameters and upper bounding functions are estimated as a trigonometric function depending on the relative displacements, velocities and the defined manifold. The developed adaptive and the robust compensators are combined and this combination is proposed as an adaptive-robust control law. After that, the controller is applied to a vehicle suspension system and the ideal of a skyhook target without using a reference model is achieved. The results also show that the proposed robust control law can increase the comfort of the vehicle active suspension systems and the ride comfort is remarkably increased

Modelling of a logarithmic parameter adaptation law for adaptive control of mechanical manipulators

In the paper,(1) a new adaptive control law for controlling robot manipulators is derived based on the Lyapunov theory; trigonometric functions are used for the derivation of the parameter estimation law. In this note, we have derived a logarithmic parameter estimation law based on a previous paper, and the boundedness of tracking error has been shown

Design of adaptive compensators for the control of robot manipulators robust to unknown structured and unstructured parameters

In this paper, a new adaptive-robust control approach for robot manipulators is developed. The adaptive-robust control law is not only robust to unknown structured parameters but also robust to unknown unstructured parameters such as unstructured joint friction and disturbances. The bounded disturbances and unstructured model are taken into account in a dynamic model and it is assumed that the structured and unstructured parameters are unknown. The structured and unstructured parameters are distinguished between parameters and these parameters are treated separately. Next, new parameter estimation functions are developed for each of the 2 uncertainty groups. After that, the developed dynamic adaptive compensators for the unknown structured and unknown unstructured parameters are combined and the control law is formulated by the combination of the compensators, including the proportional-derivative feedforward control. Based on the Lyapunov theory, the uniform ultimate boundedness of the tracking error is obtained

Design of an adaptive control law using trigonometric functions for robot manipulators

In this study, a new approach of adaptive control law for controlling robot manipulators using the Lyapunov based theory is derived, thus the stability of an uncertain system is guaranteed. The control law includes a PD feed forward pail and a full dynamics feed forward compensation part with the unknown manipulator and payload parameters. The novelty of the obtained result is that an adaptive control algorithm is developed using trigonometric functions depending on manipulator kinematics, inertia parameters and tracking error, and both system parameters and adaptation gain matrix are updated in time

Upper bounding estimation for robustness to the parameter uncertainty with trigonometric function in trajectory control of robot arms

In this paper, a new robust control law is considered for controlling robot manipulators subjected to uncertainties. The control law is derived as a result of analytical solution from the Lyapunov function, thus stability of the uncertain system is guaranteed. Apart from previous studies, uncertainty bound and adaptation gain matrix are updated in time with the estimation law to control the system properly and uncertainty bound is determined using a trigonometric function of robot kinematics, inertia parameters and tracking error while adaptation gain matrix is determined using a trigonometric function of robot kinematics and tracking error. Application to a two-link robotic manipulator is presented and numerical simulations are included

Modelling of Bound Estimation Laws and Robust Controllers for Robustness to Parametric Uncertainty for Control of Robot Manipulators

In this paper, first, a new approach is proposed for derivation of bound estimation laws for robust control of robot manipulators. In this approach, functions depending on robot kinematics and control parameters and integration techniques can be used for derivation of the bound estimation laws based on the Lyapunov theory, thus, stability of the uncertain system is guaranteed. Five new bound estimation laws are proposed, and in this derivations, five novel functions depending on robot kinematics and control parameters and proper integration techniques, such as substitution method, integration by part and integration by partial fractions are used. Then, four new robust control inputs are proposed based on each derived bound estimation law. Lyapunov theory based on Corless and Leitmann (IEEE Trans Automat Contr 26:1139-1144, 1981) approach is used for designing the robust control input achieving uniform boundedness error convergence. This study also allows derivation of other bound estimation laws for robust controllers provided that appropriate novel functions and proper integration techniques are chosen