Abstract
The dynamical systems theory developed in [4, 7, 8, 9] is applied to the stability analysis of control systems in which the feedback control law requires in real time the solution of a set of nonlinear algebraic equations. Since small sampling period is assumed, the stability and performance of the controlled process can be studied with a continuous-time formulation. A singularly perturbed system is used to model the combined dynamics of the system being controlled and a numerical iterative algorithm required to compute the control law. An updating control procedure has been proposed based on the iterative nature of the control algorithm. The results obtained in [9] regarding the behavior of a dynamical system that models the numerical algorithms lead to a considerable simplification in the analysis. For the case of control problem involving inverse kinematics, the numerical algorithm which solves for inverse kinematics can be considered as an observer (or an estimator) of the state space variables. The study provides an estimate of the required speed of computations to preserve the stability of the controller.
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© 1991 Springer-Verlag
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Zufiria, P.J., Guttalu, R.S. (1991). Stability of controllers with on-line computations. In: Skowronski, J.M., Flashner, H., Guttalu, R.S. (eds) Mechanics and Control. Lecture Notes in Control and Information Sciences, vol 151. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0006741
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DOI: https://doi.org/10.1007/BFb0006741
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