IRAQI JOURNAL OF COMPUTERS, COMMUNICATIONS, CONTROL AND SYSTEMS ENGINEERING

The objective of this paper is to design a robust controller for a system modeled as a two-mass system, with a flexible coupling. Here, the flexible Joint between two-mass systems is characterized by a spring. In fact, a two-mass system represents most of an industrial drive, like rolling mill drives, automated arms, conveyor belts, and so on, that has a flexible joint, for which oscillation suppression and robust control against model uncertainties and external disturbances are very important. The proposed controller is based on sliding mode control with a back-stepping approach. Two subsystems (upper and lower) strategies are proposed for two- mass systems. On this basis, the classical sliding mode controller for each subsystem based on Lyapunov stability theory and sliding mode control theory is addressed to eliminate the influences of the parametric uncertainties, nonlinearities, and external disturbance load with the aid of sliding mode perturbation observer. Finally, comprehensive simulations are conducted to demonstrate the excellent performance of the proposed method.

The design of an H2 sliding mode controller for a mobile inverted
pendulum system is proposed in this paper. This controller is conducted to stabilize
the mobile inverted pendulum in the upright position and drive the system to a
desired position. Lagrangian approach is used to develop the mathematical model
of the system. The H2 controller is combined with the sliding mode control to give a
better performance compared to the case of using each of the above controllers
alone. The results show that the proposed controller can stabilize the system and
drive the output to a given desired input. Furthermore, variations in system
parameters and disturbance are considered to illustrate the robustness of the
proposed controller.

Abstract:
In this paper two invariant sets are derived for a second order nonlinear affine system using a sliding mode controller. If the state started in these sets, it will not leave it for all future time. The invariant set is found function to the initial condition only, from which the state bound is estimated and used when determining the gain of the sliding mode controller. This step overcomes an arithmetic difficulty that consists of calculating suitable controller gain value that ensures the attractiveness of the switching manifold. Also, by using a differentiable form for the approximate signum function in sliding mode controller formula, the state will converge to a positively invariant set rather than the origin. The size of this set is found function to the parameters that can be chosen by the designer, thus, it enables us to control the size of the steady state error. The sliding mode controller is designed to the servo actuator system with friction where the derived invariant sets are used in the calculation of the sliding mode controller gain. The friction model is represented by the major friction components; Coulomb friction, the Stiction friction, and the viscous friction. The simulation results demonstrate the rightness of the derived sets and the ability of the differentiable sliding mode controller to attenuate the friction effect and regulate the state to the positively invariant set with a prescribed steady state error.