Almost sure stability of long cylindrical shells with random imperfections

Liapunov method used to obtain sufficient conditions for buckling stability of long cylindrical shells with random imperfection

Reference list for stability theory in ordinary differential equations

Reference list for stability and control theory in ordinary differential equation

Design and implementation of fuzzy logic controllers

The main objectives of our research are to present a self-contained overview of fuzzy sets and fuzzy logic, develop a methodology for control system design using fuzzy logic controllers, and to design and implement a fuzzy logic controller for a real system. We first present the fundamental concepts of fuzzy sets and fuzzy logic. Fuzzy sets and basic fuzzy operations are defined. In addition, for control systems, it is important to understand the concepts of linguistic values, term sets, fuzzy rule base, inference methods, and defuzzification methods. Second, we introduce a four-step fuzzy logic control system design procedure. The design procedure is illustrated via four examples, showing the capabilities and robustness of fuzzy logic control systems. This is followed by a tuning procedure that we developed from our design experience. Third, we present two Lyapunov based techniques for stability analysis. Finally, we present our design and implementation of a fuzzy logic controller for a linear actuator to be used to control the direction of the Free Flight Rotorcraft Research Vehicle at LaRC

Stability Metrics for Simulation and Flight-Software Assessment and Monitoring of Adaptive Control Assist Compensators

Due to a need for improved reliability and performance in aerospace systems, there is increased interest in the use of adaptive control or other nonlinear, time-varying control designs in aerospace vehicles. While such techniques are built on Lyapunov stability theory, they lack an accompanying set of metrics for the assessment of stability margins such as the classical gain and phase margins used in linear time-invariant systems. Such metrics must both be physically meaningful and permit the user to draw conclusions in a straightforward fashion. We present in this paper a roadmap to the development of metrics appropriate to nonlinear, time-varying systems. We also present two case studies in which frozen-time gain and phase margins incorrectly predict stability or instability. We then present a multi-resolution analysis approach that permits on-line real-time stability assessment of nonlinear systems

Stability Analysis of Nonlinear Dynamic Systems Using the Lyapunov Method Approach

A new approach to the stability analysis of homogeneous nonlinear systems is proposed, based on the concept of candidate Lyapunovfunctions, where the focus is not on the positive definiteness of the candidate Lyapunovfunctions, but on the negative definiteness of their derivatives. After having ensured the negative definiteness of the derivative function, on the basis of the sign assignment of the primitive function, the stability of the equilibrium is analyzed, where the necessary and sufficient conditions are declared at the same time. The selection of the tendency of the Lyapunov candidate function is primarily performed in the form of a linear combination of some simple functions. The unknown coefficients in the structure of the candidate function are computed based on the negative definiteness of the derivative function. Then, using these coefficients in Lyapunov function, sign of primitive function in state space is argued. Thus, the stability/instability of the equilibrium point can be deduced from the triple sign settings of the candidate function. Furthermore, in the process of negative definiteness of the derivative function, the coefficients are obtained using two independent methods. The proposed theoretical results are supported and their effectiveness is demonstrated by numerical simulations.Pendekatan baru terhadap analisis stabilitas sistem nonlinier homogen diusulkan, berdasarkan konsep kandidat fungsi Lyapunov, yang fokusnya bukan pada kepastian positif dari kandidat fungsi Lyapunov, namun pada kepastian negatif turunannya. Setelah memastikan kepastian negatif dari fungsi turunan, berdasarkan penetapan tanda fungsi primitif, stabilitas kesetimbangan dianalisis, di mana kondisi perlu dan kondisi cukup dinyatakan pada saat yang bersamaan. Pemilihan kecenderungan fungsi kandidat Lyapunov terutama dilakukan dalam bentuk kombinasi linier beberapa fungsi sederhana. Koefisien yang tidak diketahui dalam struktur fungsi kandidat dihitung berdasarkan kepastian negatif dari fungsi turunan. Kemudian, dengan menggunakan koefisien-koefisien ini dalam fungsi Lyapunov, tanda fungsi primitif dalam ruang keadaan diperdebatkan. Dengan demikian, kestabilan/ketidakstabilan titik kesetimbangan dapat disimpulkan dari pengaturan tanda tripel fungsi kandidat. Selanjutnya pada proses kepastian negatif fungsi turunan, koefisien diperoleh dengan menggunakan dua metode independen. Hasil teoritis yang diusulkan didukung dan efektivitasnya ditunjukkan oleh simulasi numerik

Nonlinear Robust Control of a Series DC Motor Utilizing the Recursive Design Approach

In this thesis, the investigation of asymptotic stability of the series DC motor with unknown load-torque and unknown armature inductance is considered. The control technique of recursive, or backstepping, design is employed. Three cases are considered. In the first case, the system is assumed to be perfectly known. In the second case, the load torque is assumed to be unknown and a proportional-integral controller is developed to compensate for this unknown quantity. In the final case, it is assumed that two system parameters, load torque and armature inductance, are not known exactly, but vary from expected nominal values within a specified range. A robust control is designed to handle this case. The Lyapunov stability criterion is applied in all three cases to prove the stability of the system under the developed control. The results are then verified through the use of computer simulation