Abstract
Stability of a linear system under fast switching or blending of a set of controllers can be ensured by an appropriate observer-based state-space realization. In this letter, the more specific problem is considered of arbitrary interpolation of a set of state feedback gains based on an initial static state feedback. First, the dynamic augmentation generating this parameterization is derived as well as the associated parameters for local recovery of predefined static controllers. By further simplification, a simple and intuitive structure is obtained with only a single design matrix. We propose to exploit this remaining degree of freedom to maximize robustness in terms of coprime factor uncertainty. The resulting parameterization is comparatively simple to implement in both continuous and discrete time. The robotics problem of active variable impedance control serves to illustrate utility of this parameterization.
Highlights
C ERTAIN control systems demand for switching or interpolation between state feedback
R1) The closed loop must be stable under arbitrary interpolation or switching, and the state feedback controllers must be recovered in the design points
Active variable impedance control, a current robotics research topic [1], requires a robot manipulator to achieve by regulation some desired stiffness/damping characteristics, respectively, a mechanical impedance
Summary
Abstract—Stability of a linear system under fast switching or blending of a set of controllers can be ensured by an appropriate observer-based state-space realization. The more specific problem is considered of arbitrary interpolation of a set of state feedback gains based on an initial static state feedback. Current solutions which consider stability are tailored to the robotics problem domain [7], [8] or do not provide a synthesis method [9]. With these issues in mind, we report an interpolation scheme for state feedback controllers addressing the following requirements. R1) The closed loop must be stable under arbitrary interpolation or switching, and the state feedback controllers must be recovered in the design points.
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