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In this paper, an effective method to calculate the reduced-order model (ROM) of high-order linear time-invariant system is elaborated; this is done by evaluating time moments of the original high-order model (HOM).

The developed method has been applied to a hydraulic actuator of antiroll bar mechanism dedicated to heavy vehicle semi-active suspension. And as the actuator is a large-scale system; and that in this case, the only control applied is a classical control and with trial and error procedure (like PID), the use of an order reduction method is necessary. Hence, the actuator that has an eighth-order transfer function with uncontrollable states has been approximated by fully controllable second-order model, which is suitable for feedback controllers (RST, LQR […]). The RST control is applied to control the roll angle of the actuator and simulations are carried out to show the effectiveness of the procedure.

It is clear that RST shows good tracking as compared to PID. For further work, the given RST controller has a discrete character and can be easily implemented on the real process and then as a further simulation, one can use another controller such as fractional adaptive controller.

In the recent years, the technological need of modeling order, thus the complexity of the systems, directed the researchers toward the reduction of order of these systems, not only to facilitate the analysis but also to find a suitable approximation of the high-order systems while keeping the same important characteristics as closely as possible. Several methods are available but they fail to give stable transfer functions or important characteristics of the original system.

Cable-based Robots are new type of parallel robots that use cables instead of metallic cylinders. They have good properties that can be used for various applications. The main objective of this work is: the first is to use the direct and inverse geometric model to study and simulate the end effector position of the robot with three and four cables. A graphical user interface has been implemented in order to visualizing the position of the robot. Secondly, we present the determination of static and dynamic tensions and lengths of cables required to flow different trajectories. At the end, we study the response of our systems in closed loop with a Proportional-Integrated-Derivative (PID) and Proportional-Integrated (PD) controllers then this last are compared the results for the same examples using MATLAB/Simulink.; we found that the PID method gives the better performance, such as rapidly speed response, settling time, compared to PD controller.

This paper presents a modeling and control of new model in a spatial coordinates (x, y, z), from this structures we choose: regular pyramid of a square basis manipulated by five cables and eight cables for a cubic shape. The main objective of this work is to integrate the axe (z) on the horizontal plane (x, y) i-e the plan 3D. This last their intervention especially when we obliged to transfer the end effector from point to point, for that we used the direct and inverse geometric model to study and simulate the end effector position of the robot with five and eight cables. A graphical user interface has been implemented in order to visualizing the position of the robot. Secondly, we present the desired path and determination the tensions and cables lengths of kinematic model required to follow spiral trajectory. At the end, we study the response of our systems in closed loop with a Proportional-Integrated-Derivative (PID) using MATLAB/Simulink which used to verify the performance of the controller.