Browsing by Subject "Linearization"
Now showing 1 - 3 of 3
Results Per Page
Sort Options
Item Direct linearization of continuous and hybrid dynamical systems(2009-05-15) Parish, Julie Marie JonesLinearized equations of motion are important in engineering applications, especially with respect to stability analysis and control design. Traditionally, the full, nonlinear equations are formed and then linearized about the desired equilibrium configuration using methods such as Taylor series expansions. However, it has been shown that the quadratic form of the Lagrangian function can be used to directly linearize the equations of motion for discrete dynamical systems. Here, this development is extended to directly generate linearized equations of motion for both continuous and hybrid dynamical systems, where a hybrid system is described with both discrete and continuous generalized coordinates. The results presented require only velocity level kinematics to form the Lagrangian and find equilibrium configuration(s) for the system. A set of partial derivatives of the Lagrangian are then computed and used to directly construct the linearized equations of motion about the equilibrium configuration of interest. This study shows that the entire nonlinear equations of motion do not have to be generated in order to construct the linearized equations of motion. Several examples are presented to illustrate application of these results to both continuous and hybrid system problems.Item Estimation Strategies for Constrained and Hybrid Dynamical Systems(2012-10-19) Parish, Julie Marie JonesThe estimation approaches examined in this dissertation focus on manipulating system dynamical models to allow the well-known form of the continuous-discrete extended Kalman filter (CDEKF) to accommodate constrained and hybrid systems. This estimation algorithm filters sequential discrete measurements for nonlinear continuous systems modeled with ordinary differential equations. The aim of the research is to broaden the class of systems for which this common tool can be easily applied. Equality constraints, holonomic or nonholonomic, or both, are commonly found in the system dynamics for vehicles, spacecraft, and robotics. These systems are frequently modeled with differential algebraic equations. In this dissertation, three tools for adapting the dynamics of constrained systems for implementation in the CDEKF are presented. These strategies address (1) constrained systems with quasivelocities, (2) kinematically constrained redundant coordinate systems, and (3) systems for which an equality constraint can be broken. The direct linearization work for constrained systems modeled with quasi-velocities is demonstrated to be particularly useful for systems subject to nonholonomic constraints. Concerning redundant coordinate systems, the "constraint force" perspective is shown to be an effective approximation for facilitating implementation of the CDEKF while providing similar performance to that of the fully developed estimation scheme. For systems subject to constraint violation, constraint monitoring methods are presented that allow the CDEKF to autonomously switch between constrained and unconstrained models. The efficacy of each of these approaches is shown through illustrative examples. Hybrid dynamical systems are those modeled with both finite- and infinite-dimensional coordinates. The associated governing equations are integro-partial differential equations. As with constrained systems, these governing equations must be transformed in order to employ the CDEKF. Here, this transformation is accomplished through two finite-dimensional representations of the infinite-dimensional coordinate. The application of these two assumed modes methods to hybrid dynamical systems is outlined, and the performance of the approaches within the CDEKF are compared. Initial simulation results indicate that a quadratic assumed modes approach is more advantageous than a linear assumed modes approach for implementation in the CDEKF. The dissertation concludes with a direct estimation methodology that constructs the Kalman filter directly from the system kinematics, potential energy, and measurement model. This derivation provides a straightforward method for building the CDEKF for discrete systems and relates these direct estimation ideas to the other work presented throughout the dissertation. Together, this collection of estimation strategies provides methods for expanding the class of systems for which a proven, well-known estimation algorithm, the extended Kalman filter, can be applied. The accompanying illustrative examples and simulation results demonstrate the utility of the methods proposed herein.Item Linearization and Efficiency Enhancement Techniques for RF and Baseband Analog Circuits(2012-02-14) Mobarak, Mohamed Salah MohamedHigh linearity transmitters and receivers should be used to efficiently utilize the available channel bandwidth. Power consumption is also a critical factor that determines the battery life of portable devices and wireless sensors. Three base-band and RF building blocks are designed with the focus of high linearity and low power consumption. An architectural attenuation-predistortion linearization scheme for a wide range of operational transconductance amplifiers (OTAs) is proposed and demonstrated with a transconductance-capacitor (Gm-C) filter. The linearization technique utilizes two matched OTAs to cancel output harmonics, creating a robust architecture. Compensation for process variations and frequency-dependent distortion based on Volterra series analysis is achieved by employing a delay equalization scheme with on-chip programmable resistors. The distortion-cancellation technique enables an IM3 improvement of up to 22dB compared to a commensurate OTA without linearization. A proof-of-concept lowpass filter with the linearized OTAs has a measured IM3 < -70dB and 54.5dB dynamic range over its 195MHz bandwidth. Design methodology for high efficiency class D power amplifier is presented. The high efficiency is achieved by using higher current harmonic to achieve zero voltage switching (ZVS) in class D power amplifier. The matching network is used as a part of the output filter to remove the high order harmonics. Optimum values for passive circuit elements and transistor sizes have been derived in order to achieve the highest possible efficiency. The proposed power amplifier achieves efficiency close to 60 percent at 400 MHz for -2dBm of output power. High efficiency class A power amplifier using dynamic biasing technique is presented. The power consumption of the power amplifier changes dynamically according to the output signal level. Effect of dynamic bias on class A power amplifier linearity is analyzed and the results were verified using simulations. The linearity of the dynamically biased amplifier is improved by adjusting the preamplifier gain to guarantee constant overall gain for different input signal levels.