Evasion of Instabilities Caused by Neglected Subsystems and Saturations in the Control of a Cart of Asynchronous Electric Drives

The task of solving the adaptive control of a partially and imprecisely modeled electrical vehicle driven by three omnidirectional wheels together with the torque and/or power limits of their electric driving motors is considered. The vehicle is very roughly modeled as a rigid body while the a part of the burden carried by it through elastic connection is completely neglected in the controller's model. Instead parameter estimation techniques a simple, kinematically designed, PID-type trajectory tracking is formulated that is implemented via robust fixed point transformations. It is shown that if the nominal trajectory does not significantly excite the vehicle burden connection precise and stable control can be achieved by the adaptivity, while the pure PID-type control may considerably excite this degree of freedom and can be corrupted by achieving either the torque or the power limits of the motors. The motors are supposed to be voltage controlled asynchronous drives with constant frequency excitation. Our statement is substantiated by numerical simulations. The main advantage of the proposed control is that it operates with local basin of attraction developed for convergent iterative Cauchy sequences that is easy to design by setting only a few parameters. Its disadvantage is that it cannot guarantee global stability therefore its application must be preceded by numerical tests. Its use may be especially useful in applications in industrial workshops when modeling the dynamics of the coupled subsystem technically is very difficult, e.g. when it is a tank partially containing heavy liquid.