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Jaqueline Vargas
Universidade Tecnológica Federal Paraná , Departamento de Engenharia Eletrônica, Toledo, PR; Universidade Federal de Santa Catarina, Departamento de Automação e Sistemas, Florianópolis, SC
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José M. Araújo
Instituto Federal de Educação, Ciência e Tecnologia da Bahia, Engenharia Elétrica, Salvador, BA
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Eugênio B. Castelan
Universidade Federal de Santa Catarina, Departamento de Automação e Sistemas, Florianópolis, SC
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Carlos E. T. Dórea
Universidade Federal do Rio Grande do Norte, Departamento de Eng. de Computação e Automação, Natal, RN
Keywords:
Positive invariance, polyhedral set, second-order systems, eigenstructure assignment, Control under constraints
Abstract
Second-order systems constitute a mathematical model class used to represent a variety of physical processes to be controlled, such as vehicle damping systems, hydraulic pump flow and robot manipulator. Due to the practical limitation inherent to physical systems (or their mathematical representation), as well as constraints on the input variables, the control under constraints became an important research field. In this context, this work aims to develop concepts and tools to control second-order linear systems, using the positive invariance property of polyhedral sets. Positive invariance has the characteristic of keeping the trajectory of the system states inside the set. This characteristic is incorporated into the analysis and design of the control law to ensure internal stability and respect of the constraints. In this work, the control of this specific system is solved by eigenstructure assignment, ensuring that the eigenvalues are in stability regions.
