Abstract
In this paper the possible application of a novel adaptive solution, the Robust Fixed Point Transformations (RFPT) based adaptive controller was investigated in a complicated practical case: the control a caster-supported Wheeled Mobile Robot (WMR) with two actively driven wheels when the dynamic model of this equipment is only approximately known.
This control task is an interesting problem that is especially burdened from both its kinematic and dynamic aspects. The kinematic problems root in the practical need that we have to control both the orientation and the location of the WMR on a plain surface, i.e. we wish to keep under control three independent quantities (θ, x,y) while we have only two control agents (the torques of the drives of the active wheels), and also have to satisfy the non-holonomic constraints excluding free sliding, slipping or skidding over the plane. The dynamic problems are the formal consequences of the approximate model. While in the possession of a precise model it is possible to design a controller to track the mass center point therefore the equations of motion describing the acceleration of the mass center point and the spinning of the body around it become decoupled, in our case the appearance of the nonlinearly coupled equations is inevitable. Further problem arises from the interaction of the electromagnetic subsystem (the DC motors) and the mechanical one (the cart): for controlling the cart instantaneous torque values i.e. motor currents are needed, however, only the time-derivative of this current can be instantaneously set by the control voltages. Therefore in the practice we need some order reduction technique in the control of nonlinear systems.
It is shown via simulations that the RFPT-based adaptive controller simultaneously can solve these problems.
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Rudas, I.J., Tar, J.K. (2015). New Application of an Adaptive Controller Based on Robust Fixed Point Transformations. In: El-Osery, A., Prevost, J. (eds) Control and Systems Engineering. Studies in Systems, Decision and Control, vol 27. Springer, Cham. https://doi.org/10.1007/978-3-319-14636-2_3
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DOI: https://doi.org/10.1007/978-3-319-14636-2_3
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