Multiobjective Control Via LMI Optimization

The paper is subject to introduce the multi-objective synthesis of states-feedback controllers. Along with the appearance of interior point algorithm in the past ten years, Linear Matrix Inequalities (LMI) has make out a good solution. Here we will use the LMI tools to solve the multi-objective problem.First it introduces the Schur complement lemma and positive-real lemma, and introduces the characteristic that the congruent transformation cannot change the positive character of a positive definite matrix, and introduces how to change eigenvalue problem and riccati inequalities to LMIs. The H∞standard problem can be solved with LMIs. The robust problem of uncertain system can be transformed to H∞standard problem. Then it could be solved with LMI tools as as one objective.The design objectives can be a mix of H∞performance, H 2performance, asymptotic disturbance rejection, time-domain constraints, and constraints on the closed-loop pole location. In addition, these objectives can be specified on different channels of the closed-loop system. When all objectives are formulated in terms of a common Lyapunov function, controller design amounts to solving a system of linear matrix inequalities. Then it could be solved by the convex optimal approach.The paper discussed the significance of the structure of the weighted matrix.The plant is the double inverted pendulum. The model is constructed with the Newton-Euler method. In the condition of quality uncertainty on the top of the upper pendulum, the inverted pendulum system can be considered as three input three output systems. According the practical problem, many objectives have been bought forward. Controllers have been designed to solve the problem. Such as H 2controller, pole location constraints and H 2 controller, and H 2/H∞controller, all above are state feedback controllers.In the purpose of noise suppression, an observer had been designed in the method of H 2/H∞optimization. In practice all the controller can be able to stabilize the inverted pendulum.In the end the multi-objective synthesis of output-feedback controllers had been discussed in the condition that there is an observer in the system.