Nonlinear control systems - Vukić, Zoran; Kuljača, Ljubomir; Đonlagić, Dali; Tešnjak, Sejid (New York : McGraw-Hill, Inc, 2003)
Properties of nonlinear systems. Problems in the theory of nonlinear systems. Basic mathematical and structural models of nonlinear systems. Basic specific properties of nonlinear systems. Stability and equilibrium states. Basic properties of nonlinear functions. Typical nonlinear elements. Atypical (non-standard) nonlinear elements. Basic nonlinearity classes. Conclusion. Stability. Equilibrium states and concepts of stability. Lyapunov stability. Absolute stability. Absolute stability of equilibrium states of an unforced system (Popov criterion). Examples of determining absolute stability by using Popov plot. Absolute stability of an unforced system with time-varyng nonlinear characteristic. Absolute stability of forced nonlinear systems. Conclusion. Linearization methods. Graphical linearization methods. Algebraic linearization. Analytical linearization method (linearization in the vicinity of the operating point). Evaluation of linearization coefficients by least-squares method. Harmonic linearization. Describing function. Statistical linearization. Combined (dual-input) describing functions. Conclusion. Operating modes and dynamic analysis methods. Operating modes of nonlinear control systems.Methods of dynamic analysis of nonlinear systems. Phase trajectories in dynamic analysis of nonlinear systems. Phase plane. Methods of defining phase trajectories. Examples of application of various methods to obtain phase trajectories. Harmonic linearization in dynamic analysis of nonlinear control systems operating in stabilization mode. Describing function in dynamic analysis of unforced nonlinear control systems. Forced oscillations of nonlinear systems. Harmonic linearization in dynamic analysis of nonlinear control systems in tracking mode of operational. Vibrational linearization with self-oscillations. Dynamic analysis of nonlinear control systems in tracking mode of operation with forced oscillations. Performance estimation of nonlinear control system transient responses. determining symmetrical transient responses near periodic solutions. Performance diagrams of nonlinear system transient responses. Describing function method in fuzzy control systems. Basics of fuzzy logic. Describing function of SISO fuzzy element. Stability analysis of a fuzzy control system. Influence of fuzzy regulator on resonance jump. Harmonic linearization. Popov diagrams.