Feedback-linearization Control Applied to Power Electronic Converters
Feedback linearization is a powerful instrument that transforms a generic nonlinear plant model into a linear one by using a nonlinear feedback that cancels the original plant nonlinearity. Usually the target plant is a pure integrator; hence it can be co
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Feedback-linearization Control Applied to Power Electronic Converters
Feedback linearization is a powerful instrument that transforms a generic nonlinear plant model into a linear one by using a nonlinear feedback that cancels the original plant nonlinearity. Usually the target plant is a pure integrator; hence it can be controlled (with zero steady-state error) by a simple proportional controller (Isidori 1989). However, this feature comes with a drawback: the linearized system is likely to be sensitive to parameters’ variations and/or to the operating point, as the nonlinear feedback derives from the system model. This control structure outputs a continuous control input that needs supplementary (e.g., PWM) modulation in order to be applied to power switches. For power electronic converters the feedback linearization may be conceived for both singleinput–single-output (SISO) and multi-input–multi-output (MIMO) cases by using their averaged models, but in this chapter the focus is on the first type of method. Corresponding to the primary control target, one may define the direct control in which the linearized dynamics correspond to the controlled variable, or indirect control, in which the linearized dynamics output a different variable (Sira-Ramı´rez and Silva-Ortigoza 2006). In this latter case, the control structure turns out to be more complicated because a supplementary outer control loop is required in order to achieve the primary control target (Jung et al. 1999; Song et al. 2009). Because in this case the outer loop is built on a (generally) nonlinear plant, its design may require either plant-approximated linearization (employing techniques amply presented in Chaps. 8 and 9 of this book) or the employment of a robust nonlinear control law (see, for example, Chaps. 12 and 13). In either case the system’s zero dynamics represent a difficult issue to deal with, except when the system’s relative degree is equal to the system’s order – and zero dynamics do not exist; feedback linearization is called exact in such cases. Using some of the mathematical tools presented in Chap. 10, this chapter introduces feedback linearization of a generic converter and the algorithm to be employed for control law design. Some examples, a case study and a problem with its solution complete the discussion of this subject. The reader is invited to solve several other problems at the end of this chapter.
S. Bacha et al., Power Electronic Converters Modeling and Control: with Case Studies, 307 Advanced Textbooks in Control and Signal Processing, DOI 10.1007/978-1-4471-5478-5_11, © Springer-Verlag London 2014
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Feedback-linearization Control Applied to Power Electronic Converters
Basics of Linearization via Feedback
Theoretical foundations of feedback-linearization control have been proposed by Isidori (1989), in both SISO and MIMO cases; they are based on the differential geometric approach in the theory of nonlinear control systems. This section aims at offering a quick overview of this topic and specific soluti
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