Hybrid systems control has been of great scientific interest over the past two decades. This is mostly because of its applicability to a broad range of physical systems, especially those resulting from technological advances. The aim of this study is developing a pragmatic avoidance of nonlinear phenomena in the control of hybrid systems (HSs), focusing on the subgroup of switched affine systems (SASs). The developed control laws will propagate the heuristic approach and present the author’s general idea for the control of nonlinear dynamical systems. The main emphasis will be given to Fuzzy Identification as the universal approximation in the modelling and evolving of multi-‐structural and global models in two directions. First, we identify the steady and stable states of a HS and model it into the global knowledge of a nonlinear dynamical system. Second, we identify the dynamical model of the HS with arbitrary accuracy, which presents the system’s qualitative and quantitative characteristics in an analytical way.
The control methods derived accordingly should emphasize the Fuzzy Model Predictive Control (FMPC) of the HS by reducing the main drawback in the complexity of online computing. Furthermore, the combination with suboptimal control gives a wider applicable control algorithm, even in systems consisting of less-‐powerful microprocessors. Traditionally, the simplification of a HS, i.e. the averaging method in the modelling of electronic circuits, in which the system is presented with an avoidance of the mixed discrete and continuous states by a simple continuous model, as well as the modern theory of hybrid system modelling, will be harmoniously integrated in this study. The conciliation of those two modelling extremes affirms nonlinear identification-‐based modelling as the leading strategy towards a wider applicable solution. The main idea is still to model a complex discrete/continuous system with a continuous counterpart, but by being aware of its complexity caused by the mode transitions influencing their final and unique model. The systems explored are full state measurable. This condition supports the main idea and opens the possibility to gather the system’s information by the measurement of the complex states’ transitions (continuous trajectories and discrete states of the system simultaneously). Later, the information remains preserved by the final state-‐space transformation into the pseudo-‐normed space. These ideas form a firm basis for the novel control methods and the achievement of the defined objectives.
Selected as an example of such a system for performing the expressed methodology, a DC-‐DC Boost converter is not only a good SAS representative, but a contemporary one of the widely used power supplies, applicable in most alternative-‐ energy sources. Its importance has occupied various types of researchers since the first developed semiconductors. The exclusion of the nonlinear phenomena [1,7-‐ 10,56,57] is one of the main motivations and the objective in seeking a control algorithm that is more intelligent, robust and economical in the use of processing space.
The accuracy of the mathematical modelling, in contrast to the first known modelling of the aforementioned system in the works of Ćuk, Ericskon, Middlebrook [23,24], places the emphasis on the transition moment of the states and the function’s discontinuity at that time. Although these problems were well recognized in the middle of the 20th century, but no less importantly they are emerging again in definitions of the chattering effects, the Zeno behaviour and the nonlinear phenomena, even in the established HS methodologies.
A small signal control derived from linear theory gives satisfactory results in the neighbourhood of the operating point, and a linearized model (Averaged-‐Switch Model) opens up the possibility of a complete analytical examination. However, as mentioned previously, to achieve robustness of the control algorithm, the theory of nonlinear dynamical systems must have the main role in improvements to the operating range of the DC-‐DC converters and SAS in general.
The hybrid structure [2,3], robust solution [3,4], natural constraints [3], complexity reduction [5,6] and emerging problem of nonlinearities exclusion [7-‐10], can all be recognized as appealing tasks for the control of a DC-‐DC boost converter. State-‐of-‐the-‐art control solutions [3] are mostly based on Linear Matrix Inequalities (LMIs) optimizations in hybrid systems [3,5,6], relaxation algorithms in the sense of complexity reduction [11], complementarity formalism in reducing the modelling ambiguity [12,13], sliding mode control [14,15] and heuristic approaches, neural networks and fuzzy controls [10,16,138]. The latest [16, 138] work is synthesized, in detail presented in this thesis and forms a unique and advanced control methodology in field of SAS control as a result of excessive research done on the DC-‐ DC boost converter.
|
