Pilot in-the-loop oscillation (PIO) is a phenomenon which occurs due to the dynamic interaction between pilot and aircraft. This detrimental aircraft handling quality appears through a variety of flight conditions and is very difficult to predict. Due to this complex behavior, PIO is not easily eliminated. This report describes a method of PIO analysis that is capable of examining multiple asymmetric nonlinearities acting simultaneously. PIO analyses are performed on a model based on the USAF NT-33A variable stability aircraft with nonlinearities including stick position limiting, elevator deflection limiting, and elevator rate limiting. These analyses involve the use of dual input describing functions which enable the prediction of frequency, amplitude, and mean point of oscillation. / Master of Science

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In this thesis, low-order nonlinear models for the prediction of the nonlinear behaviour of thermoacoustic systems are developed. These models are based on thermoacoustic networks, in which linear acoustics is combined with a nonlinear heat release model. The acoustic networks considered in this thesis can take into account mean flow and non-trivial acoustic reflection coefficients, and are cast in state-space form to enable analysis both in the frequency and time domains. Starting from linear analysis, the stability of thermoacoustic networks is investigated, and the use of adjoint methods for understanding the role of the system's parameters on its stability is demonstrated. Then, a nonlinear analysis using various state-of-the-art methods is performed, to highlight the strengths and weaknesses of each method. Two novel frameworks that fill some gaps in the available methods are developed: the first, called Flame Double Input Describing Function (FDIDF), is an extension of the Flame Describing Function (FDF). The FDIDF approximates the flame nonlinear response when it is forced simultaneously with two frequencies, whereas the FDF is limited to one frequency. Although more expensive to obtain, the FDIDF contains more nonlinear information than the FDF, and can predict periodic and quasiperiodic oscillations. It is shown how, in some cases, it corrects the prediction of the FDF about the stability of thermoacoustic oscillations. The second framework developed is a weakly nonlinear formulation of the thermoacoustic equations in the Rijke tube, in which the acoustic response is not limited to a single-Galerkin mode, and is embedded in a state-space model. The weakly nonlinear analysis is strictly valid only close to the expansion point, but is much cheaper than any other available method. The above methods are applied to relatively simple thermoacoustic configurations, in which the nonlinear heat release model is that of a laminar conical flame or an electrical heater. However, in real gas turbines more complex flame shapes are found, for which no reliable low-order models exist. Two models are developed in this thesis for turbulent bluff-body stabilised flames: one for a perfectly premixed flame, in which the modelling is focused on the flame-flow interaction, accounting for the presence of recirculation zones and temperature gradients; the second for imperfectly premixed flames, in which equivalence ratio fluctuations, modelled as a passive scalar field, dominate the heat release response. The second model was shown to agree reasonably well with experimental data, and was applied in an industrial modelling project.

Lean-premixed combustion has the advantage of low emissions for modern gas turbines, but it is susceptible to thermoacoustic instabilities, which can result in large amplitude pressure oscillations in the combustion chamber. The thermoacoustic limit cycle is generated by the unsteady heat release dynamics coupled to the combustor acoustics. In this dissertation, we focused on reduced-order modeling of the dynamics of a laminar premixed flame. From first principles of combustion dynamics, a physically-based, reduced-order, nonlinear model was developed based on the proper orthogonal decomposition technique and generalized Galerkin method. In addition, the describing function for the flame was measured experimentally and used to identify an empirical nonlinear flame model. Furthermore, a linear acoustic model was developed and identified for the Rijke tube experiment. Closed-loop thermoacoustic modeling using the first principles flame model coupled to the linear acoustics successfully reproduced the linear instability and predicted the thermoacoustic limit cycle amplitude. With the measured experimental flame data and the modeled linear acoustics, the describing function technique was applied for limit cycle analysis. The thermoacoustic limit cycle amplitude was predicted with reasonable accuracy, and the closed-loop model also predicted the performance for a phase shift controller. Some problems found in the predictions for high heat release cases were documented. / Ph. D.

This thesis presents the fundamental issues of the digital controlled DC/DC converter. A lot of challenges exist when you introduce the digital control technique into the control of the DC/DC converter, especially with regards to the voltage regulator module. One issue is the limit cycle oscillation problem caused by the quantization effect from the ADC and DPWM of the digital control chip. Another issue is the delay problem coming from the sample-hold effect. In this thesis, the modeling, analysis and design methodology for the constant frequency voltage-mode control is reviewed. A DPWM (Digital Pulse Width Modulator) model is verified in simulation, which shows what effects the digital control brings to the conventional Pulse Width Modulator. In CPES, the constant on-time control concept is introduced into the digital control of the voltage regulator module. This provides a high resolution of DPWM and allows the digital constant on-time voltage-mode control architecture to be proposed. To limit the oscillation amplitude in the digital control structure, the digital constant on-time current-mode control w/ external ramp is further proposed in CPES. To analyze this structure, a describing function model is proposed for the digital constant on-time current-mode control, which takes both the sample-hold effect and the quantization effect into consideration. This model clearly shows the stability problem caused by the sample-hold effect in the current loop. Using larger ramp's slope values, this stability issue can be alleviated. Based on this model, a design methodology is introduced. By properly designing the current loop's ADC resolution and the voltage loop's ADC resolution, the limit cycle oscillation in this structure can be minimized: the digital constant on-time current-mode control will only have the oscillation coming from the sample-hold effect in the current loop, which can be greatly reduced by adding the large slope's external ramp to this structure. Simulation verification for this design methodology is provided to prove the concepts. Based on the proposed model, the compensator design is performed. The motivation for the compensator design is to push the bandwidth while satisfying the stability condition and the dynamic no-limit-cycle oscillation condition. When analyzing the case of one sample per switching cycle, there is a certain amount of delay, which compromises the phase characteristics. Our design also requires a large external ramp because it will reduce the oscillation amplitude in our system. From our model, it is quite obvious that the external ramp must have a slope larger than one time that of inductor current down slope. A slope that is too larger will weaker the phase and limit the bandwidth. When using the normal current-mode compensator, like the 1-pole 1-zero compensator, the phase is dropped too much and the bandwidth will be limited too low. If we use a 2-pole 2-zero compensator, the phase can be boosted. However, in this case, the gain margin requirement from the dynamic no-limit-cycle oscillation condition will make the further improvements on bandwidth impossible. In our design, the one sixth of the switching frequency is achieved. / Master of Science

Pilot Induced Oscillations (PIO) are described as pilot-aircraft dynamic couplings which can lead to instability in an otherwise stable system. Previous and ongoing research has attempted to explain, predict, and avoid such oscillations. In contrast to other research, this effort backs away from pilot models and PIO avoidance and focuses on the characteristics of the pilot before, during, and after a PIO. Often, PIO''s can be explained by limit cycles occurring in a non-linear system where the non-linearities cause a sustained, constant amplitude oscillation. The primary instigators in such a PIO are usually a non-linear element (i.e. rate limit saturation) and a trigger event (i.e. pilot mode switching or increased pilot gain). By performing analysis in the frequency domain, determining such oscillations becomes easier. Using spectrograms and power spectral density functions, the frequency content of a signal in the pilot-aircraft system can also be investigated. An F-14 flight test was recently performed where the hydraulic system was modified to determine the feasibility of trying to recover the aircraft (land on carrier) during such an extreme hydraulic failure. During testing, a severe PIO occurred because of the tight tracking task used during aerial refueling. While performing spectrograms and power spectral analysis, an increase in power concentration at the PIO frequency was observed. With a linear approximation of the F-14 aircraft dynamics, a closed-loop system containing the aircraft, actuator, and pilot dynamics is developed so that limit cycle analysis can be performed. With stable limit cycle solutions found possible, a pilot-in-the-loop simulation is performed to verify the pilot model used in limit cycle analysis. Using the flight test data, limit cycle analysis, and pilot-in-the-loop simulation, a connection between variation in pilot behavior and PIO predicted by the increase in power concentration is investigated. The resulting connection showed that an increase in pilot gain along with a transition from observing pitch attitude to pitch rate are the possible trigger events causing the PIO. The use of spectrograms as a PIO predictor is shown to be possible, provided the necessary calculations can be completed in real-time. / Master of Science

The thesis focuses on the object-describing lyrics written by Chou Chin-Chen and investigates the selection of ideas, analysis of images, and artistic characteristics. This thesis is divided into six chapters. Chapter 1 is divided into two sections. The first section introduces the research motivation, the research methods, and literature review. The second section studies the origin of object-describing lyrics to describe the relationship of objects and literature and to define the concept of object-describing lyrics. Chapter 2 indicates the formation background of Chou Chin-Chen¡¦s lyrics. The first section discusses the historical origin and litery development of object-describing lyrics in terms of different dynasties: Early Chin dynasty, The Han dynasty, and Wei-Jin Dynasty. In addition, the section further investigates the civil object-describing lyrics in Dunhuang and intellectuals¡¦ object-describing lyrics in early North Song Dynasty. The second section discusses the factors of writing with the respect of the social and cultural background and makes the list of Chou Chin-Chen¡¦s lyrics in order to compare the background influences and literature characteristics. Chapter 3 analyzes the content of Chou Chin-Chen¡¦s lyrics based on the definition made in the previous sections. The chapter discusses 32 lyrics to analyze the selection of ideas with six categories: season, plants, nature, appearance and time. There are two seasonal lyrics (lantern and Chongjiu festivals), ten plant lyrics (plum flowers, willows, pear, lotus, sweet-scented osmanthus, and apricot), seven nature lyrics (snow, moon, and spring rain). The discussion focuses on the image analysis including prototypes and trends and further investigates the historical backgrounds, content structures, writing skills and historical evaluations. Chapter 4 studies and compares Chou Chin-Chen¡¦s object-describing lyrics in terms of the artistic characteristics, rhetoric skills, language styles, and content structures. Chapter 5 describes the comments and influences of Chou Chin-Chen¡¦s object-describing lyrics. Chapter 6 concludes the achievement of Chou Chin-Chen¡¦s object-describing lyrics.