Then, based on the proposed dynamics model, by constructing the modal filter, a robust H∞ independent modal space controller is designed and utilized to decouple the piezo-stage and deal with the unmodeled dynamics, disturbance, and hysteresis compensation error.
The usual state space controller design techniques for such a model often require canonical representations which impose certain challenges in practical implementation of a rather easy and feasible control task.
This model will be used for the design of a state space controller based on a pole placement algorithm, to make the system behave as a fourth order Bessel filter.
Then two control algorithms are designed, one for erecting the pendulum by coordinated robot motions, and one for balancing the pendulum in the upper position based on a state space controller with additional feature of zero point offset adaptation.
This paper proposes a straightforward approach to direct design of state-space controllers for descriptor systems.
Furthermore, we present parameterization of all such state-space controllers by variables satisfying the LMI condition and an arbitrary nonsingular matrix.
Unlike preceding studies, where descriptor-type controllers are first computed and then numerically transformed to state-space controllers, the proposed method carries out the transformation analytically in the parameter domain.
The fact that the feedback interconnection of strictly positive real (spr) systems leads to an asymptotically stable closed loop can be used for the synthesis of robust observer-based state-space controllers.
In the following step a state-space controller is designed in order to control the car along that trajectory.
We derive a necessary and sufficient LMI condition for the existence of a state-space controller with the same dynamic order of the descriptor system to be controlled, which makes the closed-loop system regular, impulse-free, stable, and guarantees the H∞ norm bound imposed on the closed-loop transfer function.
