Control techniques for uncertain second order systems : an LMI approach

• Autor(a) principal: Danielle Silva Gontijo
• Data de Publicação: 2023
• Tipo de documento: Tese
• Idioma: eng
• Título da fonte: Repositório Institucional da UFMG
• Texto Completo: http://hdl.handle.net/1843/60647
• topic: Second-order systems; Robust control; Linear matrix inequalities; Uncertain systems; Engenharia elétrica; Controle robusto; Desigualdades matriciais lineares; Controladores PID

Second-order systems constitute an important class of dynamic systems that are widely em- ployed in engineering to model a variety of physical phenomena. Characterized by their dy- namic behavior, second-order systems require effective control strategies to achieve the de- sired performance. This work presents a design framework for obtaining a robust multivariable Proportional-Integral-Derivative (PID) controller for linear second-order systems. Additionally, a Proportional-Integral-Derivative with Acceleration (PIDA) controller is proposed to address the model regularization problem. Relevant control challenges, such as modeling errors, regu- latory performance optimization, regional pole placement, saturation prevention, input delay, LQR cost function, and observer-based control, are addressed within the framework of control design via Linear Matrix Inequality (LMI). The proposed design strategy is based on rewriting the system model in an appropriate way so that the design of the PID/PIDA controller is equiv- alent to that of a state feedback controller. Firstly, a methodology is proposed for obtaining a PID/PIDA controller, grounded in regional pole placement, H∞ performance, regularization problem, and saturation prevention, all simultaneously addressed. Additionally, a methodology to obtain a robust multivariable Proportional-Integral-Derivative (PID) controller for second- order systems with time-varying input delay is also proposed. Furthermore, a methodologyintroduced to obtain a PD/PID controller using the Linear Quadratic Regulator (LQR) control strategy. Finally, a formulation for observer-based controller design is proposed. This is followed by a methodology based on LMI formulations to obtain an observer-based controller for uncer- tain second-order systems. To demonstrate the efficacy of the proposed control methodologies, simulations with numerical examples and a practical experiment using an inverted pendulum mobile system were conducted. These experiments effectively showcase the advantages of each method.