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Stability Analysis of a Neurocontroller with Kalman Estimator for the Inverted Pendulum Case
Departamentos de Electrotecnia y de Electrónica, Laboratorio de Investigación Matemática Aplicada a Control (LIMAC), Facultad de Ciencias Exactas, Físicas y Naturales-Universidad Nacional de Córdoba, Córdoba, Argentina
Departamentos de Electrotecnia y de Electrónica, Laboratorio de Investigación Matemática Aplicada a Control (LIMAC), Facultad de Ciencias Exactas, Físicas y Naturales-Universidad Nacional de Córdoba, Córdoba, Argentina
Departamento de Ingeniería Electrónica, Facultad de Tecnología y Ciencias Aplicadas, Universidad Nacional de Catamarca, Catamarca, Argentina
Departamento de Ingeniería Electrónica, Facultad de Tecnología y Ciencias Aplicadas, Universidad Nacional de Catamarca, Catamarca, Argentina
Departamentos de Electrotecnia y de Electrónica, Laboratorio de Investigación Matemática Aplicada a Control (LIMAC), Facultad de Ciencias Exactas, Físicas y Naturales-Universidad Nacional de Córdoba, Córdoba, Argentina
- 1 Departamentos de Electrotecnia y de Electrónica, Laboratorio de Investigación Matemática Aplicada a Control (LIMAC), Facultad de Ciencias Exactas, Físicas y Naturales-Universidad Nacional de Córdoba, Córdoba, Argentina
- 2 Departamentos de Electrotecnia y de Electrónica, Laboratorio de Investigación Matemática Aplicada a Control (LIMAC), Facultad de Ciencias Exactas, Físicas y Naturales-Universidad Nacional de Córdoba, Córdoba, Argentina
- 3 Departamento de Ingeniería Electrónica, Facultad de Tecnología y Ciencias Aplicadas, Universidad Nacional de Catamarca, Catamarca, Argentina
- 4 Departamento de Ingeniería Electrónica, Facultad de Tecnología y Ciencias Aplicadas, Universidad Nacional de Catamarca, Catamarca, Argentina
- 5 Departamentos de Electrotecnia y de Electrónica, Laboratorio de Investigación Matemática Aplicada a Control (LIMAC), Facultad de Ciencias Exactas, Físicas y Naturales-Universidad Nacional de Córdoba, Córdoba, Argentina
Applied Mathematics·Volume 08 (2017)·Pages 1602–1618·Published 1 November 2017·DOI10.4236/am.2017.811117
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Abstract
In this paper, a practical analysis of stability by simulation for the effect of incorporating a Kalman estimator in the control loop of the inverted pendulum with a neurocontroller is presented. The neurocontroller is calculated by approximate optimal control, without considering the Kalman estimator in the loop following the Theorem of the separation. The results are compared with a time-varying linear controller, which in noiseless conditions in the state or in the measurement has an acceptable performance, but when it is under noise conditions its operation closes into a state space range more limited than the one proposed here.
KeywordsOptimal ControlNeurocontrollerInverted PendulumState EstimationStability
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