Abstract
In numerous electric drive applications, the mechanical phenomena in the velocity or position control loop determine real difficulties and challenges for the control system. So-called two-mass drive systems with a flexible shaft are the most important example of this situation. The problem becomes even more difficult if the characteristics of torque transmission along the shaft are nonlinear, nonlinear friction is present, and the plant parameters are unknown, as it happens in numerous robotic systems. A novel adaptive controller is derived for such a system. The recurrent design procedure is based on proper modifications of the adaptive backstepping scheme, including non-strict-feedback plant application, tuning functions to exclude controller overparameterization, robust adaptive laws, proper means to avoid controller complexity explosion, and a nonlinear PI controller in the initial loop to minimize quasi-steady-state tracking error. The closed-loop system uniform ultimate boundedness is proven using Lyapunov techniques and the design and tuning procedures are described. The attractive features of the obtained drive, including the robustness against the violation of assumptions, are presented using several examples.
Highlights
To avoid calculation of the time derivative α φ, which surely is a complicated function, we introduce a linear filter with a new state variable α φ f :
It is supposed to cancel the troublesome components in (43) and introduce an element stabilizing the error e3 f. This must be performed despite unknown parameters, Θ1 is substituted by Θ1 defined before, Θ3 is substituted by Θ3 and κ by κ—to be defined
The distinctive features of the proposed approach are demonstrated by a simulation h i h i of an exemplary drive with load and motor inertia Jb = 374 kg m2, Jr = 2122 kg m2
Summary
The speed and/or position control of a two-mass flexible-shaft drive stays an important problem of motion control. Such a model is always a simplification and it is incorrect if the shaft contains some peculiar couplings In this case, the torque components should be represented by nonlinear functions (curves) of the angle of torsion and its derivative. Even if an ordinary differential equations model is used, we are faced with a highly nonlinear control problem with unknown plant parameters. We propose an improved version of an adaptive nonlinear controller for a two-mass drive with nonlinear stiffness, damping, and friction in the presence of unknown parameters. Using Lyapunov techniques we derive an original, effective controller solving the desired speed tracking for a two-mass drive with nonlinear stiffness, damping, and friction, in the presence of unknown parameters.
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