Numerical methods of designing control systems are currently an active area of research. Convex optimization with linear matrix inequalities (LMIs) is one such method. Control objectives like minimizing the H_2, H_infinity norms, limiting the actuating effort to avoid saturation, pole-placement constraints etc., are cast as LMIs and an optimal feedback controller is found by making use of efficient interior-point algorithms. A full-state feedback controller is designed and implemented in this thesis using this method which then forms the basis for designing a static output feedback (SOF) controller. A profile was generated that relates the change in the SOF control gain matrix required to keep the same value of the generalized H_2 norm of the transfer function from the road disturbance to the actuating effort with the change in the sprung mass of the quarter-car system. The quarter-car system makes use of a linear brushless permanent magnet motor (LBPMM) as an actuator, a linear variable differential transformer (LVDT) and two accelerometers as sensors for feedback control and forms a platform to test these control methodologies. For the full-state feedback controller a performance measure (H_2 norm of the transfer function from road disturbance to sprung mass acceleration) of 2.166*10^3 m/s^2 was achieved ensuring that actuator saturation did not occur and that all poles had a minimum damping ratio of 0.2. The SOF controller achieved a performance measure of 1.707*10^3 m/s^2 ensuring that actuator saturation does not occur. Experimental and simulation results are provided which demonstrate the effectiveness of the SOF controller for various values of the sprung mass. A reduction in the peak-to-peak velocity by 73 percent, 72 percent, and 71 percent was achieved for a sprung mass of 2.4 kg, 2.8 kg, and 3.4 kg, respectively. For the same values of the sprung mass, a modified lead-lag compensator achieved a reduction of 79 percent, 77 percent and, 69 percent, respectively. A reduction of 76 percent and 54 percent in the peak-to-peak velocity was achieved for a sprung mass of 6.0 kg in simulation by the SOF controller and the modified lead-lag compensator, respectively. The gain of the modified lead-lag compensator needs to be recomputed in order to achieve a similar attenuation as that of the SOF controller when the value of the sprung mass is changed. For a sprung mass of 3.4 kg and a suspension spring stiffness of 1640 N/m the peak-to-peak velocity of the sprung mass was attenuated by 42 percent.

Orientador: Edvaldo Assunção / Resumo: Este trabalho aborda o controle via realimentação estática de saída aplicado à sistemas lineares com parâmetro variante (LPV) e lineares incertos invariantes no tempo (LIT). O projeto de ganhos de realimentação estática de saída apresentado neste trabalho é baseado no método dos dois estágios, o qual consiste em primeiramente obter um ganho de realimentação de estados, e então, utilizar esta informação no segundo estágio para obter-se o ganho de realimentação estática de saída desejado. As soluções para os problemas investigados são apresentadas na forma de desigualdades matriciais lineares (no inglês, linear matrix inequalities, LMIs), obtidas por meio da aplicação do Lema de Finsler. Baseado em resultados anteriores encontrados na literatura, este trabalho propõe uma estratégia de relaxação de forma a obter um método menos conservador para obtenção de ganhos robustos de realimentação estática de saída para sistemas incertos LTI. Na estratégia proposta, as variáveis adicionais do Lema de Finsler são consideradas como dependentes de parâmetro, juntamente com o uso de funções de Lyapunov dependentes de parâmetro (no inglês, parameter-dependent Lyapunov functions, PDLFs). É apresentado um estudo avaliando a eficácia da estratégia proposta em fornecer uma maior região de factibilidade para um dado problema. Os resultados foram utilizados em uma comparação com um método de relaxação baseado apenas no uso de PDLFs. Uma segunda contribuição deste trabalho consiste na proposta de um... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: The static output feedback (SOF) control applied to linear parameter-varying (LPV) and uncertain linear time-invariant (LTI) systems are addressed in this work. The approach chosen for the design of SOF gains is based on the two-stage method, which consists in obtaining a state feedback gain at first, and then using that information for deriving the desired SOF gain at the second stage. The solutions for the investigated problems are presented in terms of linear matrix inequalities (LMIs), obtained by means of the application of the Finsler's Lemma. Based on previous papers found in literature, this work proposes a relaxation strategy in order to achieve a less conservative method for obtaining robust SOF gains for uncertain LTI systems. In the proposed strategy, the Finsler's Lemma additional variables are considered to be parameter-dependent along with the use of parameter-dependent Lyapunov functions (PDLFs). A study evaluating the effectiveness of the proposed strategy in providing a larger feasibility region for a given problem is presented. The results were used in a comparison with a relaxation method based only on PDLFs. Another contribution of this work lies in the proposal of a solution for the control of LPV systems via the design of a gain-scheduled SOF controller. The methods proposed for both control problems were applied on the design of controllers for an active suspension system. In the experiments, it was assumed that only one of its four system's states wer... (Complete abstract click electronic access below) / Mestre