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Recent Advances in Robust Control Theory and Applications in Robotics and Electromechanics Part 12

Tham khảo tài liệu 'recent advances in robust control theory and applications in robotics and electromechanics part 12', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | LMI Robust Control of PWM Converters An Output-Feedback Approach 319 a Buck converter with stray resistances. b t rL iL t ị rc vc c L b Buck-boost converter with stray resistances. Fig. 3. Schematic of the buck and the buck-boost converter. following strategies. First the classic dynamic output-feedback control problem is treated. This approach can be carried out with a change of variables as in Scherer et al. 1997 . However with such an approach the uncertainty must be modeled with elaborated models as for example weighting functions Wallis Tymerski 2000 . Therefore the chapter also proposes the synthesis of output-feedback controllers based on the static case. Both the static output-feedback and a parametrization Peaucelle Arzelier 2001b to deal with dynamic output-feedback are considered. The advantages and drawbacks of the three approaches shown in the chapter will be discussed and the results will be compared. Notation For symmetric matrices A and B A B means that A B is positive definite. A denotes that the matrix A is an unknown variable. A denotes the transpose of A. Co IVj j 1 . NI denotes the convex hull defined by N vertices Vj 6 R . The identity matrix of order n is noted as 1 and the null n X m matrix is noted as 0 n m. The symbol denotes symmetric blocks in partitioned matrices. 2. Modeling of uncertain dc-dc converters This subsection shows the state-space averaged models of the buck and the buck-boost converters of Figures 3 a and 3 b . The models are assumed to operate in Continuous Conduction Mode CCM i.e. the inductor current is always larger than zero. Besides of the averaged models this section also introduces a model of the sampling effect caused by the PWM. Finally at the end of the section the uncertainty modeling of dc-dc converters is discussed and a simple example is shown. 2.1 Model of the buck converter The first model that is introduced considers a buck converter which is characterized by linear averaged control-to-output dynamics. As